lepton flavour and neutrino mass aspects of the ma-model alexander merle max-planck-institute for...
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Lepton flavour and neutrino mass aspects of the Ma-model
Alexander MerleMax-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 Trans-mission 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
• 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
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
good: neutrino mass loop suppressed
bad: this model is ruled out…
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:
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
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:
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):
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?
• 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 LFV-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 LFV-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 LFV-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 LFV-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 LFV-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 LFV-constraints!
Two explicit examples:
Model 2: D4 x Z2,aux → less predictive
7 free parameters: a, b, c, d, M1, M2, M3
MR diagonal
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:
Example: Model 1 & Scenario α
• Method: χ2-fit
• Best-fit parameters: model fits neutrino data
• 1σ- and 3σ-ranges: quite narrow
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.):
• 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:
• 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:
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:
• 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:
→ like in the Ma-model
→ LR-breaking
→ below SU(2)R x U(1)B-L breaking scale, the model is an effective Ma-like model
→ no tree-level light neutrino mass
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
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:
tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:
Radiative transmission of hierarchies:
a
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:
→ roughly:
Radiative transmission of hierarchies:
tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:
→ MN has a form that can easily be obtained by the Froggat-Nielsen mechanism!
→ roughly:
Key points:
• the hierarchical structure of the charged lepton masses translates a (quasi) Froggat-Nielsen 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) Froggat-Nielsen 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) Froggat-Nielsen 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) Froggat-Nielsen 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:
• “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:
• FCNCs in the quark sector
• “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:
• FCNCs in the quark sector
• further investigations of radiative transmission
• “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
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…