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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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, mhand 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