Neutrino Phenomenology from and CP

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Neutrino Phenomenology from and CP

· María Luisa López Ibáñez · Università di Roma Tre ·

hep-ph/1811.09662, hep-ph/1812.xxxx

Work in collaboration with: Davide Meloni, Andrea di Iura.

Aurora Melis, Óscar Vives

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Outline

● Why flavour symmetries?

The SM flavour puzzle A5 and generalised CP

● Neutrino Phenomenology

● SUSY bounds

● Conclusions

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Why f lavour

symmetries?

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Why Flavour Symmetries?

The Flavour Puzzle

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4 types of fermions in the SM (after

EWSB

).

The Flavour Puzzle

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EWSB

).

3 copies of each of them,

same quantum numbers but different masses.

Why Flavour Symmetries?

The Flavour Puzzle

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EWSB

).

3 copies of each of them,

same quantum numbers but different masses.

Neutrinos are strictly massless in the SM:

no RH neutrinos, no triplet representations of the Higgs under SU(2), SM Lagrangian is renormalisable.

Charged fermion masses the Higgs mechanism

The Flavour Puzzle

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Why Flavour Symmetries?

The Flavour Puzzle

1. Why are charged-fermions masses so hierarchical?

Why up-type quarks the most hierarchical? Why small mixing among generations?

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The Flavour Puzzle

1. Why are charged-fermions masses so hierarchical? Why up-type quarks the most hierarchical? Why small mixing among generations?

2. Why are neutrino masses less hierarchical? Why large mixing for leptons? What’s their ordering?

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Why Flavour Symmetries?

The Flavour Puzzle

2. Why are neutrino masses less hierarchical? Why large mixing for leptons?

What’s their ordering?

3. How are neutrino masses generated? Why are them so small? Are neutrinos mostly Dirac or Majorana?

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Why Flavour Symmetries?

The Flavour Puzzle

4. What’s the origin of the three families?

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Why Flavour Symmetries?

The Flavour Puzzle

4. What’s the origin of the three families?

5. What’s the physics behind CP violation?

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Why Flavour Symmetries?

The Flavour Puzzle

Is there any

symmetry behind

this?

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Froggatt-Nielsen Mechanism

Flavour Symmetries

and generalised CP transformations

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Yukawa couplings may be effectively generated after the spontaneous breaking of a flavour symmetry by some scalar fields called flavons.

Flavour Symmetries

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Yukawa couplings may be effectively generated after the spontaneous breaking of a flavour symmetry by some scalar fields called flavons.

Flavour Symmetries

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Neutrino Textures

The leptonic sector, where the mixing

pattern seems to be specially well defined,

the use of discrete symmetries has been

particularly popular.

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The leptonic sector, where the mixing pattern seems to be specially well defined, the use of discrete symmetries has been particularly popular.

Bimaximal Mixing TriBimaximal Mixing

Neutrino Textures

Golden Ratio Mixing

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The leptonic sector, where the mixing pattern seems to be specially well defined, the use of discrete symmetries has been particularly popular.

Bimaximal Mixing TriBimaximal Mixing

Neutrino Textures

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Neutrino Textures

Golden Ratio

The leptonic sector, where the mixing

pattern seems to be specially well defined,

the use of discrete symmetries has been

particularly popular.

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Neutrino Textures

Golden Ratio Mixing Majorana neutrino mass matrix is the most

general matrix symmetric under .

Golden Ratio

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Majorana neutrino mass matrix is the most general matrix symmetric under . Then, one may assume the existence of

residual symmetries

:

Klein group

for neutrinos

Residual Symmetries

Golden Ratio

Neutrinos

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residual symmetries

:

Klein group

for neutrinos and an

Abelian group

(which distinguish among generations) for the charged sector.

Golden Ratio

Neutrinos

Charged Leptons

Residual

Symmetries

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residual symmetries

:

Klein group

Abelian group

Golden Ratio

Neutrinos

If Q is diagonal, the product the mass matrix for charged leptons has to be diagonal too.

Charged Leptons

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

residual symmetries

:

Klein group

Abelian group

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

^NLO corrections to previous

patterns,

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

^NLO corrections to previous

patterns, non diagonal charged leptons,

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

^NLO corrections to previous patterns, non diagonal charged leptons, decreasing the symmetry neutrino sector

Klein group

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

Klein group

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

Klein group

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

Klein group

Residual

Symmetries

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Golden Ratio

Neutrinos

Charged Leptons

Solutions:

Klein group

Residual

Symmetries

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A5 and CP

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Residual symmetries that reproduce UPMNS?

A. Di Iura, C. Hagedorn, D. Meloni

1503.04140

Lepton

Mixing

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Residual Symmetry in the neutrino sector is All possibilities for CP transformations:

All possibilities for charged leptons:

All possible row and column permutations for A. Di Iura, C. Hagedorn, D. Meloni

1503.04140

Lepton

Mixing

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Lepton Mixing

1503.04140

Only 4 patterns

at 3 or better

All possible row and column permutations for

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Lepton Mixing

1503.04140

Only 4 patterns

at 3 or better

All possible row and column permutations for

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Lepton

Mixing Residual symmetries that reproduce UPMNS?

Residual Symmetry in the neutrino sector is:

All possibilities for CP transformations:

All possible row and column permutations for A. Di Iura, C. Hagedorn, D. Meloni

1503.04140

Only 4 patterns

at 3 or better

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Case II Lepton

Masses

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II Lepton

Masses

Diagonal

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Case II

Weinberg Operator

Mechanism II

a-2 c-2

Type II see-saw

Type I see-saw

Type III see-saw

Mechanism I

a-1 a-1

Case II Lepton

Masses

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Results mechanism I

Weinberg operator

and type II see-saw.

hep-ph/1811.09662

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Results mechanism I

Weinberg operator

hep-ph/1811.09662

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Results mechanism I

Weinberg operator

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Results mechanism I

Weinberg operator

hep-ph/1811.09662

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Results mechanism I

Correlations for all cases well confirmed numerically.

The perturbative relations obtained for the mass ratio and reactor angle show an agreement of 10%-20%.

hep-ph/1811.09662

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Results mechanism II a-1 Type I see-saw

and type III see-saw.

Trivial Dirac

mass matrix and .

hep-ph/1811.09662

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Results mechanism II a-1 Type I see-saw

Trivial Dirac

mass matrix and .

hep-ph/1811.09662

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Results mechanism II a-1

Correlations for all cases are confirmed numerically.

Corrections to analytical expressions are 10% for Z=0. NLO corrections important for the case X=0.

hep-ph/1811.09662

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Results

mechanism II a-2 Type I see-saw

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

mechanism II a-2 Type I see-saw

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

mechanism II a-2

Good agreement between analytical expressions for the reactor angle and the numerical estimates. Not so good for the mass splitting and the ratio of masses. NLO reduces considerably the discrepancies to 10%-20%.

hep-ph/1811.09662

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Results

mechanism II c-2 Type I see-saw

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

Trivial Majorana

mass matrix and .

hep-ph/1811.09662

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Results

mechanism II c-2

Perturbative expressions for the reactor angle in good agreement, except for the case fr=0=hr2 Larger discrepancies for the mass splitting at LO, which is strongly reduced to 5%-10% after considering NLO corrections.

hep-ph/1811.09662

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Super

symmetry

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Results

Flavour violating

effects from

soft terms

can set bounds over the SUSY spectrum, even in the most conservative scenario where SUSY breaking is due to one universal spurion field. Condition:

hep-ph/1607.06827 hep-ph/1710.02593 hep-ph/1807.00860

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Results

Flavour violating

effects from soft terms can set bounds over the SUSY spectrum, even in the most conservative scenario where SUSY breaking is due to one universal spurion field. Condition:

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Results

Mechanism II a-2 Mechanism II c-2

Mechanism I

Flavour violating

effects from soft terms can set bounds over the SUSY spectrum, even in the most conservative scenario where SUSY breaking is due to one universal spurion field. Condition:

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Results

Mechanism II a-2 Mechanism II c-2

Mechanism I

Flavour violating

effects from

soft terms

can set bounds over the SUSY spectrum, even in the most conservative scenario where SUSY breaking is due to one universal spurion field. Condition:

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Results

In this framework it is possible to predict testable

relations

among the

LFV observables

in the charged sector and the

neutrino

mass observables

. This allows to disentangle cases that initially were not distinguishable.

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Conclusions

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Conclusions

● The flavour sector remains one of

the most puzzling legacies of the

SM. Family symmetries may help to

disentangle the origin masses and

mixing.

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Conclusions

● The flavour sector remains one of the most puzzling legacies of the SM. Family symmetries may help to disentangle the origin masses and mixing.

● We have performed a global analysis

for A5 and CP broken to Z5 and Z2

x CP residual symmetries

considering all possible ways for the

generation of neutrino masses.

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Conclusions

● We have performed a global analysis for A5 and CP spontaneously broken to Z5 and Z2 x CP residual symmetries considering all possible ways for the generation of neutrino masses.

● In SUSY, the introduction of family

symmetries may help to explore the

susy mass spectrum beyond LHC

sensitivity and give related

predictions for different sectors.

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Conclusions

Thank you!

● We have performed a global analysis for A5 and CP spontaneously broken to Z5 and Z2 x CP residual symmetries considering all possible ways for the generation of neutrino masses.

● In SUSY, the introduction of family symmetries may help to explore the susy mass spectrum beyond LHC sensitivity and give related predictions for different sectors.