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Flavour mixing predictions from generalized CP symmetries

Salvador Centelles Chuliá – AHEP groupIFIC (CSIC-Univ. Valencia)

Original works by: Peng Chen, Cai-Chang Li, Chang-Yuan Yao, Gui-Jun Ding, Felix González-Canales, José WF Valle

Works done in collaboration with: Peng Chen, Gui-Jun Ding, Rahul Srivastava, José WF Valle

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Outline

● Introduction: Generalized CP Symmetries.

● Generalized μτ reflection in the neutrino sector.reflection reflection in the neutrino sector.in reflection in the neutrino sector.the reflection in the neutrino sector.neutrino reflection in the neutrino sector.sector.

● Generalized reflection in the neutrino sector.eμ, reflection in the neutrino sector.eτ reflection in the neutrino sector.and reflection in the neutrino sector.μτ reflection in the neutrino sector.reflections reflection in the neutrino sector.in reflection in the neutrino sector.the reflection in the neutrino sector.charged reflection in the neutrino sector.lepton reflection in the neutrino sector.sector.

● Revamped reflection in the neutrino sector.TBM reflection in the neutrino sector.from reflection in the neutrino sector.generalized reflection in the neutrino sector.CP reflection in the neutrino sector.symmetries.

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Generalized CP Symmetries

● Definition:

● If this (remnant) symmetry is conserved in the Lagrangian (after SSB), it implies:

1412.8352 Peng Chen, Cai-Chang Li, Gui-Jun Ding 1507.03419 Peng Chen, Chang-Yuan Yao, Gui-Jun Ding

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Generalized CP symmetries

● After some algebra, we can find a constraint for the mixing matrix given the gCP symmetry:

● We can Takagi decompose X:● Which leads to the 'master formula':

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Generalized μτ reflectionμτ μτ reflectionreflection

● Assumptions:

– Neutrinos are Majorana fields.– The charged lepton mass matrix is

diagonal.– We impose a generalized μτ reflection in

the neutrino sector:

1512.01551 Peng Chen, Gui-Jun Ding, Felix Gonzalez-Canales, J.W.F. Valle

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Generalized μτ reflectionμτ μτ reflectionreflection

● Imposing generalized μτ reflection in the neutrino sector.reflection leads to:

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Generalized μτ reflectionμτ μτ reflectionreflection

● Imposing generalized μτ reflection in the neutrino sector.reflection leads to:

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Generalized μτ reflectionμτ μτ reflectionreflection

● Imposing generalized μτ reflection in the neutrino sector.reflection leads to:

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Charged μτ reflectionlepton μτ reflectionsector: μτ reflectiongeneralized μτ reflectioneμ μτ reflectionreflection

● Same spirit, now in the charged lepton sector.● The analogous situation to μτ reflection in the neutrino sector.in reflection in the neutrino sector.the reflection in the neutrino sector.neutrino reflection in the neutrino sector.sector is eμ reflection in the neutrino sector.in reflection in the neutrino sector.the reflection in the neutrino sector.charged reflection in the neutrino sector.lepton reflection in the neutrino sector.sector.

1802.04275 Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. Valle

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Charged μτ reflectionlepton μτ reflectionsector: μτ reflectiongeneralized μτ reflectioneμ μτ reflectionreflection

● Analogue predictions for mixing angles changing 23←→12:

● Different predictions for the Majorana phases:

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Charged μτ reflectionlepton μτ reflectionsector: μτ reflectiongeneralized μτ reflectioneμ μτ reflectionreflection

● Analogue predictions for mixing angles changing 23←→12:

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Charged μτ reflectionlepton μτ reflectionsector: μτ reflectiongeneralized μτ reflectioneμ μτ reflectionreflection

● Very different predictions for the phases:

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Charged μτ reflectionlepton μτ reflectionsector: μτ reflectiongeneralized μτ reflectioneμ μτ reflectionreflection

● Neutrinoless double beta decay predictions:

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Reflections μτ reflectionin μτ reflectionthe μτ reflectioncharged μτ reflectionlepton μτ reflectionsector

● We can also impose generalized eτ reflection in the neutrino sector.and reflection in the neutrino sector.μτ reflection in the neutrino sector.generalized reflection in the neutrino sector.reflections.

● Results reflection in the neutrino sector.are reflection in the neutrino sector.‘messier’ reflection in the neutrino sector.but reflection in the neutrino sector.some reflection in the neutrino sector.nice reflection in the neutrino sector.predictions reflection in the neutrino sector.can reflection in the neutrino sector.be reflection in the neutrino sector.obtained. reflection in the neutrino sector.See reflection in the neutrino sector.paper reflection in the neutrino sector.for reflection in the neutrino sector.details reflection in the neutrino sector.1802.04275.

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GCP μτ reflectionas μτ reflectionguiding μτ reflectionposts: μτ reflectiongeneralized μτ reflectionTBM μτ reflectionmixing

● Given the gCP symmetry you obtain a restricted mixing. But given the mixing you can extract the compatible CP symmetries.

● We reflection in the neutrino sector.can reflection in the neutrino sector.do reflection in the neutrino sector.this reflection in the neutrino sector.exercise reflection in the neutrino sector.with reflection in the neutrino sector.the reflection in the neutrino sector.famous reflection in the neutrino sector.TBM reflection in the neutrino sector.mixing reflection in the neutrino sector.matrix.

● Starting reflection in the neutrino sector.with reflection in the neutrino sector.TBM reflection in the neutrino sector.you reflection in the neutrino sector.can reflection in the neutrino sector.do reflection in the neutrino sector.perturbations reflection in the neutrino sector.to reflection in the neutrino sector.the reflection in the neutrino sector.mass reflection in the neutrino sector.matrix reflection in the neutrino sector.that reflection in the neutrino sector.satisfy reflection in the neutrino sector.just reflection in the neutrino sector.partial reflection in the neutrino sector.symmetry reflection in the neutrino sector.of reflection in the neutrino sector.the reflection in the neutrino sector.full reflection in the neutrino sector.TBM reflection in the neutrino sector.matrix.

● Many possibilities, see future paper for details 1812.xxxxx.

1812.xxxxx Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. ValleComing soon, stay tuned

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Realistic μτ reflectionTBM μτ reflectionneutrino μτ reflectionmixing

● Of those possibilities the golden boy is the reflection in the neutrino sector.“realistic reflection in the neutrino sector.tribimaximal reflection in the neutrino sector.neutrino reflection in the neutrino sector.mixing”.

● Derived reflection in the neutrino sector.from reflection in the neutrino sector.generalized reflection in the neutrino sector.CP reflection in the neutrino sector.symmetries reflection in the neutrino sector.principles reflection in the neutrino sector.this reflection in the neutrino sector.matrix reflection in the neutrino sector.takes reflection in the neutrino sector.the reflection in the neutrino sector.form:

1806.03367 Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. Valle

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Realistic μτ reflectionTBM μτ reflectionneutrino μτ reflectionmixing

● This matrix has reflection in the neutrino sector.nice reflection in the neutrino sector.correlations reflection in the neutrino sector.between reflection in the neutrino sector.physical reflection in the neutrino sector.observables.

● Several reflection in the neutrino sector.interesting reflection in the neutrino sector.limits reflection in the neutrino sector.(real reflection in the neutrino sector.TBM, reflection in the neutrino sector.μτ reflection in the neutrino sector.reflection, reflection in the neutrino sector.maximal reflection in the neutrino sector. reflection in the neutrino sector.atmospheric reflection in the neutrino sector.mixing...) reflection in the neutrino sector.

● The reflection in the neutrino sector.most reflection in the neutrino sector.general reflection in the neutrino sector.case reflection in the neutrino sector.leads reflection in the neutrino sector.to:

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Realistic μτ reflectionTBM μτ reflectionneutrino μτ reflectionmixing

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Conclusions

● Generalized CP symmetries are a powerful method to obtain testable correlations between observables.

● Given a CP symmetry you can restrict the lepton mixing matrix.

● Given a mixing pattern (for example TBM) you can extract the compatible cp symmetries and then do a perturbation that satisfies only partial symmetry.

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Thank μτ reflectionyou μτ reflectionfor μτ reflectionyour μτ reflectionattention● References:

– 1412.8352 Lepton Flavor Mixing and CP Symmetry Peng Chen, Cai-Chang Li, Gui-Jun Ding, PhysRevD.91.033003

– 1507.03419 Neutrino Mixing from CP Symmetry Peng Chen, Chang-Yuan Yao, Gui-Jun Ding PhysRevD.92.073002

– 1512.01551 Generalized reflection symmetry and 𝜇−𝜏 reflection symmetry and leptonic CP violation Peng Chen, Gui-Jun Ding, Félix González-Canales, J.W.F. Valle, j.physletb.2015.12.069

– 1802.04275 Neutrino Predictions from Generalized CP Symmetries of Charged Leptons, Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. Valle, JHEP07(2018)077

– 1806.03367 Realistic tribimaximal neutrino mixing, Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. Valle, PhysRevD.98.055019

– 1812.xxxxx Peng Chen, SCC, Gui-Jun Ding, Rahul Srivastava, J.W.F. Valle Coming soon, stay tuned