Transcript The GSI oscillation mystery

Lepton flavour and neutrino
mass aspects of the Ma-model
Alexander Merle
Max-Planck-Institute for Nuclear Physics
Heidelberg, Germany
Based on:
Adulpravitchai, Lindner, AM: Confronting Flavour Symmetries
and extended Scalar Sectors with Lepton Flavour Violation
Bounds, Phys. Rev. D80 (2009) 055031
Adulpravitchai, Lindner, AM, Mohapatra: Radiative Transmission of Lepton Flavor Hierarchies, Phys. Lett. B680
(2009) 476 - 479
Southampton, Friday Seminar, October 30, 2009
Contents:
1. Introduction
2. The Ma-model
3. Flavour and the Ma-model
4. The LR-extension of the Ma-model
5. Conclusions
1. Introduction: Particle masses
• the masses of the Standard Model
particles seem to increase with the
generation number
• HOWEVER: neutrinos have masses that
are (at least) a factor of 106 smaller than
the one of the electron
→ neutrino masses do not seem to have
the same origin as the other masses
• there are different possibilities to generate
small neutrino masses
• the masses of the Standard Model
particles seem to increase with the
generation number
• HOWEVER: neutrinos have masses that
are (at least) a factor of 106 smaller than
the one of the electron
→ neutrino masses do not seem to have
the same origin as the other masses
• there are different possibilities to generate
small neutrino masses
• the masses of the Standard Model
particles seem to increase with the
generation number
• HOWEVER: neutrinos have masses that
are (at least) a factor of 106 smaller than
the one of the electron
→ neutrino masses do not seem to have
the same origin as the other masses
• there are different possibilities to generate
small neutrino masses
Tree-level diagrams: e.g. seesaw type I
Tree-level diagrams: e.g. seesaw type I
Tree-level diagrams: e.g. seesaw type I
good: “natural” value for the Yukawa coupling
“natural” explanation for large MR
bad: scale for MR is arbitrary
Radiative masses: e.g. Zee/Wolfenstein model
Radiative masses: e.g. Zee/Wolfenstein model
Radiative masses: e.g. Zee/Wolfenstein model
good: neutrino mass loop suppressed
bad: this model is ruled out…
2. Ma’s scotogenic model (Ma-model)
2. Ma’s scotogenic model (Ma-model)
Ingredients apart from the SM:
• 3 heavy right-handed Majorana neutrinos Nk
(SM singlets)
• second Higgs doublet η without VEV (with
SM-like quantum numbers)
• additional Z2-parity, under which all particles
are even except for Nk and η
2. Ma’s scotogenic model (Ma-model)
Ingredients apart from the SM:
• 3 heavy right-handed Majorana neutrinos Nk
(SM singlets)
• second Higgs doublet η without VEV (with
SM-like quantum numbers)
• additional Z2-parity, under which all particles
are even except for Nk and η
2. Ma’s scotogenic model (Ma-model)
Ingredients apart from the SM:
• 3 heavy right-handed Majorana neutrinos Nk
(SM singlets)
• second Higgs doublet η without VEV (with
SM-like quantum numbers)
• additional Z2-parity, under which all particles
are even except for Nk and η
2. Ma’s scotogenic model (Ma-model)
Ingredients apart from the SM:
• 3 heavy right-handed Majorana neutrinos Nk
(SM singlets)
• second Higgs doublet η without VEV (with
SM-like quantum numbers)
• additional Z2-parity, under which all particles
are even except for Nk and η
Features of the Ma-model:
• relatively minimal extension of the SM
(essentially a 2HDM)
• Z2-parity plays a similar role as R-parity in
SUSY
→ stable Dark matter candidates: neutral scalar
η0 or lightest heavy Neutrino N1
• tree-level neutrino mass vanishes
generated at 1 loop
→
Features of the Ma-model:
• relatively minimal extension of the SM
(essentially a 2HDM)
• Z2-parity plays a similar role as R-parity in
SUSY
→ stable Dark matter candidates: neutral scalar
η0 or lightest heavy Neutrino N1
• tree-level neutrino mass vanishes
generated at 1 loop
→
Features of the Ma-model:
• relatively minimal extension of the SM
(essentially a 2HDM)
• Z2-parity plays a similar role as R-parity in
SUSY
→ stable Dark matter candidates: neutral scalar
η0 or lightest heavy Neutrino N1
• tree-level neutrino mass vanishes
generated at 1 loop
→
Features of the Ma-model:
• relatively minimal extension of the SM
(essentially a 2HDM)
• Z2-parity plays a similar role as R-parity in
SUSY
→ stable Dark matter candidates: neutral scalar
η0 or lightest heavy Neutrino N1
• tree-level neutrino mass vanishes
generated at 1 loop
→
The Ma-model neutrino mass:
The Ma-model neutrino mass:
Yukawa coupling:
The Ma-model neutrino mass:
Yukawa coupling:
This part would lead to a neutrino mass.
BUT: ‹η0›=0
→ tree-level contribution vanishes
The Ma-model neutrino mass:
Yukawa coupling:
This part would lead to a neutrino mass.
BUT: ‹η0›=0
→ tree-level contribution vanishes
Leading order: 1-loop diagram
Leading order: 1-loop diagram
Leading order: 1-loop diagram
Leading order: 1-loop diagram
Leading order: 1-loop diagram
Light neutrino mass matrix:
Light neutrino mass matrix:
Light neutrino mass matrix:
Light neutrino mass matrix:
Higgs masses:
Light neutrino mass matrix:
Features:
• “natural” Yukawa couplings
• loop suppression 1/(16π2)
• radiative seesaw → TeV-scale heavy neutrinos
Light neutrino mass matrix:
Features:
• “natural” Yukawa couplings
• loop suppression 1/(16π2)
• radiative seesaw → TeV-scale heavy neutrinos
Light neutrino mass matrix:
Features:
• “natural” Yukawa couplings
• loop suppression 1/(16π2)
• radiative seesaw → TeV-scale heavy neutrinos
Light neutrino mass matrix:
Features:
• “natural” Yukawa couplings
• loop suppression 1/(16π2)
• radiative seesaw → TeV-scale heavy neutrinos
3. Flavour and the Ma-model:
3. Flavour and the Ma-model:
The Yukawa coupling that enters into the neutrino
mass also generates LFV processes:
3. Flavour and the Ma-model:
The Yukawa coupling that enters into the neutrino
mass also generates LFV processes:
3. Flavour and the Ma-model:
The Yukawa coupling that enters into the neutrino
mass also generates LFV processes:
LFV-processes are strongly constrained (MEGA
experiment):
LFV-processes are strongly constrained (MEGA
experiment):
BUT: these bounds only constrain combinations
of Yukawa coupling elements → cancellations
possible → no problem for the Ma-model
LFV-processes are strongly constrained (MEGA
experiment):
BUT: these bounds only constrain combinations
of Yukawa coupling elements → cancellations
possible → no problem for the Ma-model
What will happen if a (discrete) flavour symmetry
is imposed?
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
What will happen if a (discrete) flavour symmetry
is imposed?
• without symmetry, the combination of Yukawa
coupling matrix elements can be zero
• a flavour symmetry imposes structure on the
Yukawa matrix
→
easy example:
h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0
→ then, the above amounts to: 3|a|2
→ trivial or non-zero
→ may get in conflict with the constraints
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Key points (for multi-scalar models):
• the Yukawa coupling elements are not
arbitrary:
- flavour symmetry imposes structure
- correct neutrino masses required
- Dark Matter abundance has to be correct (BUT:
this depends on the DM-candidate)
• these ingredients are easily sufficient to
destroy the models consistency with LFVconstraints!
Two explicit examples:
Two explicit examples:
Model 1: A4 x Z4,aux → very predictive
Two explicit examples:
Model 1: A4 x Z4,aux → very predictive
Two explicit examples:
Model 1: A4 x Z4,aux → very predictive
Two explicit examples:
Model 1: A4 x Z4,aux → very predictive
Two explicit examples:
Model 1: A4 x Z4,aux → very predictive
3 free parameters: a, b, M
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
MR diagonal
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
MR diagonal
7 free parameters: a, b, c, d, M1, M2, M3
Constraints on the Higgs sector with η0 as DM:
Constraints on the Higgs sector with η0 as DM:
• DM: only a few parameter ranges lead to the
correct abundance
• ρ-parameter
• decay widths of W± and Z0 & collider limits
• stability & consistency
Constraints on the Higgs sector with η0 as DM:
• DM: only a few parameter ranges lead to the
correct abundance
• ρ-parameter
• decay widths of W± and Z0 & collider limits
• stability & consistency
Constraints on the Higgs sector with η0 as DM:
• DM: only a few parameter ranges lead to the
correct abundance
• ρ-parameter
• decay widths of W± and Z0 & collider limits
• stability & consistency
Constraints on the Higgs sector with η0 as DM:
• DM: only a few parameter ranges lead to the
correct abundance
• ρ-parameter
• decay widths of W± and Z0 & collider limits
• stability & consistency
Constraints on the Higgs sector with η0 as DM:
• DM: only a few parameter ranges lead to the
correct abundance
• ρ-parameter
• decay widths of W± and Z0 & collider limits
• stability & consistency
→ 4 scenarios:
Then, one can fit the neutrino data:
Then, one can fit the neutrino data:
Model 1:
Then, one can fit the neutrino data:
Model 1:
Model 2:
Then, one can fit the neutrino data:
Model 1:
Model 2:
Example: Model 1 & Scenario α
Example: Model 1 & Scenario α
• Method: χ2-fit
Example: Model 1 & Scenario α
• Method: χ2-fit
• Best-fit parameters: model fits neutrino data
Example: Model 1 & Scenario α
• Method: χ2-fit
• Best-fit parameters: model fits neutrino data
• 1σ- and 3σ-ranges: quite narrow
LFV: ei→ejγ and μ-e conversion
LFV: ei→ejγ and μ-e conversion
LFV: ei→ejγ and μ-e conversion
LFV: ei→ejγ and μ-e conversion
Results for Model 1 (A4-model, 3 D.O.F.):
Results for Model 1 (A4-model, 3 D.O.F.):
Results for Model 1 (A4-model, 3 D.O.F.):
• the model is very predictive (3 params)
• when fitted to neutrino data, this model
is already ruled out by μ→eγ
Results for Model 2 (D4-model, 7 D.O.F.):
Results for Model 2 (D4-model, 7 D.O.F.):
Results for Model 2 (D4-model, 7 D.O.F.):
• the model is less predictive (7 params)
• BUT: even this model is (can be) excluded
by current (future) data for 2 scenarios
The general principle behind:
The general principle behind:
• any model with an extended scalar sector will
lead to flavour changing neutral currents
(under “normal” circumstances)
• as LFV only constrains combinations of
Yukawa matrix elements, cancellations can
always rescue the model
• flavour symmetries impose more structure
and can destroy the possibility of cancellations
→ will be true in a much more general context
The general principle behind:
• any model with an extended scalar sector will
lead to flavour changing neutral currents
(under “normal” circumstances)
• as LFV only constrains combinations of
Yukawa matrix elements, cancellations can
always rescue the model
• flavour symmetries impose more structure
and can destroy the possibility of cancellations
→ will be true in a much more general context
The general principle behind:
• any model with an extended scalar sector will
lead to flavour changing neutral currents
(under “normal” circumstances)
• as LFV only constrains combinations of
Yukawa matrix elements, cancellations can
always rescue the model
• flavour symmetries impose more structure
and can destroy the possibility of cancellations
→ will be true in a much more general context
The general principle behind:
• any model with an extended scalar sector will
lead to flavour changing neutral currents
(under “normal” circumstances)
• as LFV only constrains combinations of
Yukawa matrix elements, cancellations can
always rescue the model
• flavour symmetries impose more structure
and can destroy the possibility of cancellations
→ will be true in a much more general context
4. The LR-version of the Ma-model:
4. The LR-version of the Ma-model:
There are still questions left:
4. The LR-version of the Ma-model:
There are still questions left:
• Can the Ma-model be extended to the quark
sector?
• Is there an “origin” of the Ma-model
structure?
• Can the model be embedded into a GUT?
4. The LR-version of the Ma-model:
There are still questions left:
• Can the Ma-model be extended to the quark
sector?
• Is there an “origin” of the Ma-model
structure?
• Can the model be embedded into a GUT?
4. The LR-version of the Ma-model:
There are still questions left:
• Can the Ma-model be extended to the quark
sector?
• Is there an “origin” of the Ma-model
structure?
• Can the model be embedded into a GUT?
4. The LR-version of the Ma-model:
There are still questions left:
• Can the Ma-model be extended to the quark
sector?
• Is there an “origin” of the Ma-model
structure?
• Can the model be embedded into a GUT?
→ consider a left-right symmetric extension
Particle content:
Particle content:
Particle content:
• scalar bi-doublet: contains the SM-Higgs as
well as the inert Higgs η
• Higgs triplets: allow for a symmetry breaking
pattern that leads to an effective Ma-model in
the lepton sector (LR → Ma → effective SM)
• additional Z4-symmetry → will play the role of
an effective Z2-parity in the lepton sector
Particle content:
• scalar bi-doublet: contains the SM-Higgs as
well as the inert Higgs η
• Higgs triplets: allow for a symmetry breaking
pattern that leads to an effective Ma-model in
the lepton sector (LR → Ma → effective SM)
• additional Z4-symmetry → will play the role of
an effective Z2-parity in the lepton sector
Particle content:
• scalar bi-doublet: contains the SM-Higgs as
well as the inert Higgs η
• Higgs triplets: allow for a symmetry breaking
pattern that leads to an effective Ma-model in
the lepton sector (LR → Ma → effective SM)
• additional Z4-symmetry → will play the role of
an effective Z2-parity in the lepton sector
VEV structure:
VEV structure:
→ like in the Ma-model
VEV structure:
→ like in the Ma-model
→ LR-breaking
VEV structure:
→ like in the Ma-model
→ LR-breaking
→ no tree-level light
neutrino mass
VEV structure:
→ like in the Ma-model
→ LR-breaking
→ no tree-level light
neutrino mass
→ below SU(2)R x U(1)B-L breaking scale, the
model is an effective Ma-like model
The neutrino mass formula:
The neutrino mass formula:
• most general Yukawa coupling:
The neutrino mass formula:
• most general Yukawa coupling:
• key point: the neutrino Yukawa couplings are
the same as the ones of the charged leptons
The neutrino mass formula:
• most general Yukawa coupling:
• key point: the neutrino Yukawa couplings are
the same as the ones of the charged leptons
→ then, the neutrino mass formula looks like:
The neutrino mass formula:
• most general Yukawa coupling:
• key point: the neutrino Yukawa couplings are
the same as the ones of the charged leptons
→ then, the neutrino mass formula looks like:
IMPORTANT: charged lepton masses involved
Plausible assumption for scalar Dark Matter:
Plausible assumption for scalar Dark Matter:
→ this leads to:
Plausible assumption for scalar Dark Matter:
→ this leads to:
The log-term can be absorbed into MN…
Then, the light neutrino mass matrix is given by:
Then, the light neutrino mass matrix is given by:
ml=diag(me,mμ,mτ)
Then, the light neutrino mass matrix is given by:
ml=diag(me,mμ,mτ)
→ everything known except for λ5 and MN
Then, the light neutrino mass matrix is given by:
ml=diag(me,mμ,mτ)
→ everything known except for λ5 and MN
→ with a certain form for the light neutrino mass
matrix, it is possible to reconstruct MN!
Then, the light neutrino mass matrix is given by:
ml=diag(me,mμ,mτ)
→ everything known except for λ5 and MN
→ with a certain form for the light neutrino mass
matrix, it is possible to reconstruct MN!
→ radiative transmission of hierarchies!
Radiative transmission of hierarchies:
Radiative transmission of hierarchies:
tri-bimaximal form for UPMNS (semi-realistic) →
it is possible to reconstruct the heavy neutrino
mass matrix:
Radiative transmission of hierarchies:
tri-bimaximal form for UPMNS (semi-realistic) →
it is possible to reconstruct the heavy neutrino
mass matrix:
a
Radiative transmission of hierarchies:
tri-bimaximal form for UPMNS (semi-realistic) →
it is possible to reconstruct the heavy neutrino
mass matrix:
→ roughly:
Radiative transmission of hierarchies:
tri-bimaximal form for UPMNS (semi-realistic) →
it is possible to reconstruct the heavy neutrino
mass matrix:
→ roughly:
→ MN has a form that can easily be obtained
by the Froggat-Nielsen mechanism!
Key points:
Key points:
• the hierarchical structure of the charged
lepton masses translates a (quasi) FroggatNielsen pattern of MN into an anarchical form
of the light neutrino mass matrix
• this makes large mixing angles in the lepton
sector perfectly possible!
• no flavour symmetry argument is required
Key points:
• the hierarchical structure of the charged
lepton masses translates a (quasi) FroggatNielsen pattern of MN into an anarchical form
of the light neutrino mass matrix
• this makes large mixing angles in the lepton
sector perfectly possible!
• no flavour symmetry argument is required
Key points:
• the hierarchical structure of the charged
lepton masses translates a (quasi) FroggatNielsen pattern of MN into an anarchical form
of the light neutrino mass matrix
• this makes large mixing angles in the lepton
sector perfectly possible!
• no flavour symmetry argument is required
Key points:
• the hierarchical structure of the charged
lepton masses translates a (quasi) FroggatNielsen pattern of MN into an anarchical form
of the light neutrino mass matrix
• this makes large mixing angles in the lepton
sector perfectly possible!
• no flavour symmetry argument is required
→ the radiative transmission is a mechanism
that can explain large mixings for leptons
Currently under investigation:
Currently under investigation:
• “problem”: ‹η0›=0 → down quarks massless →
two ways out: soft Z2-breaking with colour triplet
scalars ωL,R (→ 1-loop d-mass) OR introduction
of new vector-like down-quarks
Currently under investigation:
• “problem”: ‹η0›=0 → down quarks massless →
two ways out: soft Z2-breaking with colour triplet
scalars ωL,R (→ 1-loop d-mass) OR introduction
of new vector-like down-quarks
• FCNCs in the quark sector
Currently under investigation:
• “problem”: ‹η0›=0 → down quarks massless →
two ways out: soft Z2-breaking with colour triplet
scalars ωL,R (→ 1-loop d-mass) OR introduction
of new vector-like down-quarks
• FCNCs in the quark sector
• further investigations of radiative transmission
5. Conclusions:
5. Conclusions:
• the Ma-model is an interesting toy with
surprisingly many interesting features
• it is the prime example for the fact that
extended scalar sectors in combination with
flavour symmetries have trouble with LFV
• the LR-extension of the Ma-model even yields
a new possibility to simultaneously generate
small neutrino masses and large lepton mixings
• hopefully, the surprises will go on…
5. Conclusions:
• the Ma-model is an interesting toy with
surprisingly many interesting features
• it is the prime example for the fact that
extended scalar sectors in combination with
flavour symmetries have trouble with LFV
• the LR-extension of the Ma-model even yields
a new possibility to simultaneously generate
small neutrino masses and large lepton mixings
• hopefully, the surprises will go on…
5. Conclusions:
• the Ma-model is an interesting toy with
surprisingly many interesting features
• it is the prime example for the fact that
extended scalar sectors in combination with
flavour symmetries have trouble with LFV
• the LR-extension of the Ma-model even yields
a new possibility to simultaneously generate
small neutrino masses and large lepton mixings
• hopefully, the surprises will go on…
5. Conclusions:
• the Ma-model is an interesting toy with
surprisingly many interesting features
• it is the prime example for the fact that
extended scalar sectors in combination with
flavour symmetries have trouble with LFV
• the LR-extension of the Ma-model even yields
a new possibility to simultaneously generate
small neutrino masses and large lepton mixings
• hopefully, the surprises will go on…
THANK YOU!!!