Transcript PANIC2008 Beyond MSSM baryogenesis
Slide 1
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 2
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 3
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 4
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 5
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 6
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 7
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 8
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 9
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 10
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 11
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 12
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 13
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 14
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 15
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 16
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 17
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh and for its vulnerability to quantum corrections
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 2
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 3
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 4
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 5
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 6
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 7
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 8
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 9
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 10
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 11
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 12
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 13
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 14
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 15
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 16
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well
Slide 17
Beyond MSSM Baryogenesis
Kfir Blum and Yosef Nir,
Phys.Rev.D78:035005,2008
2
(B)MSSM
Higgs and stop masses
(Un-)Observable: Higgs boson mass
3
Higgs and stop masses
• In MSSM, LEP bound on higgs boson mass violates tree level prediction
• This implies sizable quantum corrections
• The most important corrections come from top and stop loops
• To satisfy LEP bound, stop masses are pushed high
Little hierarchy problem
4
BMSSM higgs sector I
• MSSM quartic higgs couplings dictated by D-terms, controlled by gauge couplings
• Same feature responsible for the tree level relation, mh
• Little hierarchy problem avoided if MSSM quartic higgs potential is modified
- Many microscopic extensions do this
- May or may not add light dof to the MSSM particle content
- Here, deal with the second possibility, via effective low-energy action
• BMSSM: Effective lagrangian summarized by adding non-renormalizable
superpotential terms
(DST =
)
5
BMSSM higgs sector II
• In the scalar potential, leading BMSSM contribution is
• Light higgs mass shifted
Stops can go light!
~ ~
Both t1 , t 2 at 100-300 GeV
6
(B)MSSM
Electroweak Baryogenesis
Observable: Baryon Asymmetry of the Universe (BAU)
7
ElectroWeak BaryoGenesis
(EWBG)
•
BAU measured via
- Deuterium abundance (D/H), dictated by BBN
when the universe was ~102 sec old
- Relative magnitude of Doppler peaks in CMBR
temperature anisotropies, measured by WMAP from
photons released when the universe was ~105 sec old
- Both methods agree on η ≈ 6x10-10 with <10% errors
•
EWBG: BAU generated during EW Phase Transition (EWPT)
- Sakharov conditions: Thermal non-equilibrium, CP violation, B violation
•
EWPT Imposes constraints on weak-scale dof: predictive
Object to calculate:
Effective scalar potential at finite temperature
8
Effective potential
9
EWPT I
10
EWPT
• First order: barrier forms
between EW breaking and
conserving minima
• Barrier height depends on
light scalar dof coupling to
the higgs field, and on
thermal screening
• In SM, only gauge bosons
contribute to barrier
• In MSSM, negative soft
squared-mass can reduce
thermal screening for stops,
making them the dominant
player by far
II
11
EWPT III
• Condition to avoid sphaleron wash-out:
• Effective cubic term - parameterize by E:
λ = effective quartic coupling:
~
• With a light t R :
…Observe:
12
BMSSM EWPT
• λ ~ mh bound from below by experimental limit on higgs mass
• EWBG window in MSSM *:
~
- Make t R as light as possible to enhance potential barrier
~
- Keep mh fixed by making t L very massive
• MSSM window heavy stop at several TeV
hierarchy problem exponentially worse!
BMSSM solution: Keep mh fixed by ε term
EWBG window hierarchy-free
* Latest: M. Carena, G. Nardini, M. Quiros, C.E.M. Wagner,
arXiv:0809.3760 [hep-ph] and ref. Therein
13
BMSSM higgs & stops
14
Conclusions & Outlook
Conclusions:
• BMSSM: Effective action approach to MSSM extensions
at the few TeV scale. Impact on higgs sector captured by dim.5
operators
• Little hierarchy problem ameliorated DST, Phys.Rev.D76:095004,2007
• EWBG significantly more natural
BN, Phys.Rev.D78:035005,2008
To-do list:
• Constraints on dim>4 operators
- Stability of scalar potential
- EDMs, EW Precision Tests
• DM implications
• CPV analysis – EDMs, Baryogenesis
• Collider signatures
15
Xtras
16
Choice of basis
Leading mass shift
Dimension 6 scalar term,
and condition for neglecting it
2-loop thermal corrections
associated with dim 6 term
17
BMSSM higgsinos
Chargino-chargino-scalar-scalar
terms and modifications to the mass
matrices exist as well