Neutrino Mixing and Mass Sum Rulesvietnam.in2p3.fr/2017/neutrinos/transparencies/3...Julia Gehrlein,...

NeutrinoMixingandMassSumRules

Mar4nSpinrathNa4onalCenterforTheore4calSciences,Hsinchu,Taiwan

RencontresduVietnam:Neutrinos-19/07/2017

Basedoncollabora-onswith:JuliaGehrlein,AlexanderMerle,JensP.Oppermann,DanielaSchäfer,SergueyT.Petcov,ArseniiV.Titov

19/07/17-RencontresduVietnam:NeutrinosMar4nSpinrath(NCTS) NeutrinoMixingandMassSumRules

Outline

• Introduc4on

• NeutrinoMixingSumRules

• NeutrinoMassSumRules

• SummaryandConclusions

2


Outline

• Introduc-on




3


TheFlavourPuzzle

• Whydowehavethreegenera4ons?

• WhyaretheSMfermionmassessovastlydifferent?

• WhatistheoriginofCPviola4on?

• Whyarethequarkmixinganglesrathersmallandtheleptonicmixinganglesratherlarge?

4

Mar4nSpinrath(NCTS) 19/07/17-RencontresduVietnam:Neutrinos NeutrinoMixingandMassSumRules

Non-Abelian(discrete)familysymmetries

5

GF

Gn

Ge

A4,S4,T',SO(3),SU(3),...

e.g.:Zn≥3

e.g.:Z2xZ2

UPMNS

symmetryofme

symmetryofmn

(tri-)bimaximal,goldenra4o,trimaximal,...

[forarecentreviewseeKing,Luhn2013]


SumRulesintheLeptonSector

• Mixingsumrules,e.g.,

• Masssumrules,e.g.,

6

m1e�i�1 +m2e

�i�2 �m3 = 0

sin

2 ✓12 ⇡ 1

3

+

2

p2

3

sin ✓13 cos �

[Antusch,Aranda,BalleR,Boudjemaa,Damanik,deMedeiros-Varzielas,Ding,Gehrlein,Girardi,Hagedorn,He,Hochmuth,King,Luhn,Malinsky,Marzocca,Masina,Merle,Pascoli,Petcov,Rodejohann,Romanino,Schmidt,Stuart,

Tanimoto,Titov,Valle,Volkas,….?]

[Antusch,Aranda,BalleR,Boudjemaa,Damanik,deMedeiros-Varzielas,Ding,Gehrlein,Girardi,Hagedorn,He,Hochmuth,King,Luhn,Malinsky,Marzocca,Masina,Merle,Pascoli,Petcov,Rodejohann,Romanino,Schmidt,Stuart,

Tanimoto,Titov,Valle,Volkas,….?]


Outline

• Introduc4on




7


MixingSumRules

• Knownforalong4meandmanypeopleworkedonthem

• Rela4onsbetweenanglesandDiracCPphase

8

sa(✓ij , �) = 0


MixingSumRulesOrigin

• ThePMNSmatrixisacombina4on

• Without1-3neutrinomixingandonlysmall1-2chargedleptonmixing

• Correc4onstosymmetryvaluesbychargedleptonmixing

9

UPMNS = UeU†�

sin �13 � �e12 sin ��

23


MixingSumRulesExamples

• Ingeneraltolowestorder

• ForBimaximalmixing:

• ForTri-Bimaximalmixing:

10

sin

2 ✓12 ⇡ 1

2

+ sin ✓13 cos �

sin

2 ✓12 ⇡ 1

3

+

2

p2

3

sin ✓13 cos �

[notthefirstones,bute.g.:Marzocca,Romanino,Petcov,MS2011]

sin2 �12 � sin2 ��12 + O(�e

12)


NoteonRGEeffects

• Typicalsizeofthecorrec4ons

• SmallinStandardModel

• PossiblylargeintheMSSM11

�✓ij ⇠ 10�6(1 + tan2 �)m2

�m2

��i ⇠ 10�6(1 + tan2 �)m2

�m2

�mi ⇠ (O(1) + 10�6(1 + tan2 �))mi

[e.g.,Antusch,Kersten,Lindner,Ratz’03]


RGEcorrectedLikelihoods• Systema4cstudyofRGE

effects

• Examplefortri-bimaximalmixing

12

[Geh

rlein,Petcov,M

S,Tito

v’16;

seealsoZha

ng,Zho

u'16]

Global analysis

SM

MSSM tan = 30

MSSM tan = 50

0.2

0.4

0.6

0.8

1.0

L

NO

m1 = 0.01 eV

IO

m3 = 0.01 eV

0.2

0.4

0.6

0.8

L

m1 = 0.05 eV m3 = 0.05 eV

0 90 180 2700.0

0.2

0.4

0.6

0.8

[°]

L

m1 = 0.1 eV

90 180 270 360

[°]

m3 = 0.1 eV

23e = 0, TBM

sin ��12 =

1�3

,

sin ��23 =

1�2

,

sin ��13 = 0 ,

�e13 = �e

23 = 0 �= �e12


Outline

• Introduc4on




13


Generalremarks

• Notspecifictoaspecialfamilysymmetry

• Notrelatedtoanyresidualsymmetry

• Notspecifictoanymassmechanism

• Onlyincommon:3complexneutrinomassesdependon2complexparameters ➜2Rela4ons

14

[Gehrlein,MS'17]


Oneexample

• SU(5)xA5GUTFlavourModel

• TypeIseesawwith

• givesmasssumrule

15

[Gehrlein,Oppermann,Schäfer,MS’14]

Y ⇠

0

@1 0 00 0 10 1 0

1

A and MRR ⇠

0

BBB@

2q

23 (v2 + v3) �

p3v2 �

p3v2

�p3v2

p6v3 �

q23 (v2 + v3)

�p3v2 �

q23 (v2 + v3)

p6v3

1

CCCA

�1

m1+

�2

m2=

1

m3


TheParametrisa4on

• c1,c2,d,Dc13andDc23fixedbythemodel

• Forinstance,inthepreviousexample,

16

s ⌘ c1�m1e

�i�1�d

ei��13 + c2�m2e

�i�2�d

ei��23 +md3

!= 0

[King,Stuart,Merle’13;Gehrlein,Merle,MS’15]

c1 = c2 = 1 d = �1 ��13 = ��23 = ⇡

)�1

m1+

�2

m2=

1

m3


KnownRules

17

Sum rule c1 c2 d ��13 ��23

1 1 1 1 ⇡ ⇡2 1 2 1 ⇡ ⇡3 1 2 1 ⇡ 04 1/2 1/2 1 ⇡ ⇡

5 2p3+1

p3�1p3+1

1 0 ⇡

6 1 1 �1 ⇡ ⇡7 1 2 �1 ⇡ 08 1 2 �1 0 ⇡9 1 2 �1 ⇡ ⇡/2, 3⇡/210 1 2 1/2 ⇡, 0,⇡/2 0,⇡,⇡/211 1/3 1 1/2 ⇡ 012 1/2 1/2 �1/2 ⇡ ⇡



GeometricalInterpreta4on

18

β=-�·ϕ�+Δχ��

α=-�·ϕ�+Δχ��

β-π

π+α-β

π-α

��

��(��-� ϕ�)�� Δχ��(��-� ϕ�)�� Δχ��



Ques4ons

• Canwerecons4tuteforbiddenorderingswithsmallcorrec4ons?

• Howbigistheimpactofsmallcorrec4onsonpredic4onsforneutrinolessdoublebetadecay?

19


ForbiddenOrderings• SumRule2

• Fromgeometryandinvertedordering

• Noinvertedorderingontreelevel20

m1e�i�1 + 2m2e

�i�2 �m3 = 0

cos↵tree=

m21 � 4m2

2 �m23

4m2m3

< �1

4

✓3

m22

m23

+ 1

◆< �1

[Gehrlein,Merle,MS’15]


ForbiddenOrderings

• RGEcorrec4onsinMSSM

• Forbiddenorderingspossiblyallowedonlyinveryextremeregionsofparameterspace

21

�(cos↵)RGE ⇡ � Cy2⌧192⇡2| {z }

>0

2.8m21 � 0.4m2

2 + 0.1m23

m2m3| {z }>0

log

MS

MZ| {z }>0



MapofOrderings

22

Rule 1 2 3 4 5 6 7 8 9 10 11 12

NO ✓ ✓ ✓ X X ✓ ✓ ✓ ✓ ✓ ✓ ✓

IO ✓ X X ✓ ✓ ✓ ✓ ✓ ✓ X ✓ X


NumericalResults(RGcorrec4onsonly)

23

10-4 0.001 0.01 0.1 110-4

0.001

0.01

0.1

1

m @eVD

»m ee»@eVD

DisfavouredbyCosmology

Disfavoured by 0nbb

Dm312 < 0

Dm312 > 0

Best& 3s

nu-fit.orgv2.0

Rule 06

SM

10-4 0.001 0.01 0.1 110-4

0.001

0.01

0.1

1

m @eVD

»m ee»@eVD


Disfavoured by 0nbb

Dm312 < 0

Dm312 > 0

Best& 3s

nu-fit.orgv2.0

Rule 06

tanb=30

10-4 0.001 0.01 0.1 110-4

0.001

0.01

0.1

1

m @eVD

»m ee»@eVD


Disfavoured by 0nbb

Dm312 < 0

Dm312 > 0

Best& 3s

nu-fit.orgv2.0

Rule 06

tanb=50


IO SumRule&IOSumRule&NOBFw/oSumRule3sw/oSumRule

�1

m1+

�2

m2=

1

m3


Outline

• Introduc4on




24


SummaryandConclusions

• NeutrinoFlavourModelss4llinteres4ng

• ConstraintsonCPviola4on,neutrinomassscaleandordering

• Masssumrulepredic4onsareratherrobust

• Mixingandmasssumrulescombinedareverypowerful!

25


Thanksalotforyouramen4on!

26


Backup

27


RGEcorrectedLikelihoods• Systema4cstudyofRGE

effects

• Examplefortri-bimaximalmixing

28

[Geh

rlein,Petcov,M

S,Tito

v’16;

seealsoZha

ng,Zho

u'16]

sin ��12 =

1�3

,

sin ��23 =

1�2

,

sin ��13 = 0 ,

�e13 = 0 �= �e

23 and 0 �= �e12

Global analysis

SM

MSSM tan = 30

MSSM tan = 50

0.2

0.4

0.6

0.8

1.0

L

NO

m1 = 0.01 eV

IO

m3 = 0.01 eV

0.2

0.4

0.6

0.8

L

m1 = 0.05 eV m3 = 0.05 eV

0 90 180 2700.0

0.2

0.4

0.6

0.8

[°]

L

m1 = 0.1 eV

90 180 270 360

[°]

m3 = 0.1 eV

23e 0, TBM


TheModel

• SU(5)xA5GUTFlavourModel

• GoldenRa4oNeutrinoMixing

• Cabibbo-like1-2chargedleptonmixing

29

tan ✓⌫12 =2

1 +p5, ✓⌫23 = ⇡/4 , ✓⌫13 = 0

✓e12 ⇡ ✓C ) ✓13 ⇡ ✓Cp2⇡ 9�

[Gehrlein,Oppermann,Schäfer,MS2014]


ModelConstraints

• Mixingsumrule

• Masssumrule

• Fromfermionmassra4os

30

✓PMNS12 ⇡ ✓⌫12 + ✓C cos �

ei ↵1

m1+

ei ↵2

m2=

1

m3

tan� & 30



Implica4ons

• Fromthemixingsumrule

• Fromthemasssumrule

• FromRGEs

31

0.011 eV . m1 for NO

0.028 eV . m3 . 0.454 eV for IO

24� . ✓PMNS12 (MS) . 39�


☠�12 (MS) � 33.5�

�12 (MS) � 5.7� �

Neutrino Mixing and Mass Sum Rulesvietnam.in2p3.fr/2017/neutrinos/transparencies/3...Julia Gehrlein,...

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Transcript of Neutrino Mixing and Mass Sum Rulesvietnam.in2p3.fr/2017/neutrinos/transparencies/3...Julia Gehrlein,...