Leptonic CP violation theory

Transcription

1 p. 1/30 Leptonic CP violation theory C. Hagedorn CP 3 -Origins, SDU, Odense, Denmark XXVII International Conference on Neutrino Physics and Astrophysics, , London, UK

2 p. 2/30 Low energy CP phases in the lepton sector Parametrization U PMNS = Ũ diag(1,e iα/2,e i(β/2+δ) ) with Ũ = c 12 c 13 s 12 c 13 s 13 e iδ s 12 c 23 c 12 s 23 s 13 e iδ c 12 c 23 s 12 s 23 s 13 e iδ s 23 c 13 s 12 s 23 c 12 c 23 s 13 e iδ c 12 s 23 s 12 c 23 s 13 e iδ c 23 c 13 and s ij = sinθ ij, c ij = cosθ ij Experimental status first indications for δ 3 2 π (Bergström et al. ( 16), Capozzi et al. ( 16)) no constraints on Majorana phases α and β

3 p. 3/30 Prediction of CP phases with a flavor symmetry framework: 3 copies of charged leptons & Majorana neutrinos impose flavor symmetry G f on space of 3 lepton generations G f is non-abelian, finite and discrete G f must be broken at low energies and we assume residual symmetries G e (G ν ) in the charged lepton (neutrino) sector (Blum/H/Lindner ( 07), Lam ( 07, 08)) form of charged lepton mass matrix m e & Majorana mass matrix m ν restricted by G e and G ν contributions U e & U ν to lepton mixing U PMNS are fixed

4 p. 4/30 Prediction of CP phases with a flavor symmetry ւ G f ց charged leptons G e neutrinos G ν = Z 2 Z 2 U e ց ւ U ν U PMNS = U eu ν [Masses do not play a role in this approach.]

5 p. 5/30 Prediction of CP phases with a flavor symmetry U PMNS = U eu ν 3 unphysical phases are removed by U e U e K e neutrino masses are made real and positive through U ν U ν K ν permutations of columns of U e, U ν are possible U e,ν U e,ν P e,ν Predictions Mixing angles up to exchange of rows/columns Dirac phase δ up to π Majorana phases undetermined

6 p. 6/30 Prediction of CP phases with a flavor symmetry surveys of groups G f, G e and G ν (H/Meroni/Vitale ( 13), King/Neder/Stuart ( 13), Joshipura/Patel ( 13), Holthausen et al. ( 12), Lam ( 12), Fonseca/Grimus ( 14), Talbert ( 14)) have shown that all patterns have trimaximal column (sin 2 θ 12 1/3) and Dirac phase δ = 0,π, if mixing angles are accommodated well studies with one massless neutrino, (partially) degenerate neutrino masses or Dirac neutrinos also exist (Joshipura/Patel ( 13, 14), King/Ludl ( 16), Hernandez/Smirnov ( 13), Esmaili/Smirnov ( 15))

7 p. 7/30 Prediction of CP phases with a flavor symmetry For less symmetry, e.g. G ν = Z 2, Dirac phase is less constrained (Hernandez/Smirnov ( 12)) example with G f = PSL(2,7), G e = Z 7 and G ν = Z 2 thick line: δ = 0 dashed line: δ = π/4 dotted line: δ = π/2

8 p. 8/30 Prediction of CP phases with a flavor symmetry With corrections Dirac phase is less constrained (Marzocca et al. ( 11), Petcov ( 14), Shimizu et al. ( 14), Ballett et al. ( 14), Girardi et al. ( 14, 15, 16)) assume U PMNS = U e ΨU ν with U e = R 23 (θ23) e R 12 (θ12) e and Ψ phases and U ν is tribimaximal (TBM), bimaximal (BM), golden ratio (GR) mixings as well as hexagonal mixing (HEX/HG) (all have in common θ ν 13 = 0 and θ ν 23 = π/4) relation of δ, lepton mixing angles θ ij and θ ν 12 follows cosδ = tanθ 23 sin 2 θ 12 + sin2 θ 13 cos 2 θ 12 tanθ 23 sin 2 θ ν 12 sin2θ 12 sinθ 13 ( ) tanθ 23 + sin2 θ 13 tanθ 23

9 p. 9/30 Prediction of CP phases with a flavor symmetry With corrections Dirac phase is less constrained (Ballett et al. ( 14))

10 p. 10/30 Prediction of CP phases with a flavor symmetry With corrections Dirac phase is less constrained (Girardi et al. ( 14)) Other possible corrections originate from RG running (Zhang/Zhou ( 16)).

11 p. 11/30 Prediction of CP phases with a flavor and a CP symmetry impose also CP symmetry in fundamental theory CP symmetry acts non-trivially on the flavor space (Grimus/Rebelo ( 95)) its action is φ i X ij φ j and XX = XX = 1 in a theory with G f and CP certain conditions have to be fulfilled (Feruglio/H/Ziegler ( 12, 13), Holthausen et al. ( 12), Chen et al. ( 14)) prediction of Majorana phases becomes possible for m ν invariant under CP (Feruglio/H/Ziegler ( 12, 13)) U ν is further constrained Xm ν X = m ν

12 p. 12/30 Prediction of CP phases with a flavor and a CP symmetry well-known example: µτ reflection symmetry muon (tau) neutrino tau (muon) antineutrino (Harrison/Scott ( 02, 04), Grimus/Lavoura ( 03)) which leads in the charged lepton mass basis to sinθ 23 = cosθ 23 and sin2θ 12 sinθ 13 cosδ = 0 and trivial Majorana phases

13 p. 13/30 Prediction of CP phases with a flavor and a CP symmetry (Feruglio/H/Ziegler ( 12, 13)) G f and CP ւ charged leptons G e ց neutrinos G ν = Z 2 CP U e ց U ν = Ω ν R(θ)K ν ւ U PMNS = U eω ν R(θ)K ν [Masses do not play a role in this approach.]

14 p. 14/30 Prediction of CP phases with a flavor and a CP symmetry U PMNS = U eω ν R(θ)K ν 3 unphysical phases are removed by U e U e K e U PMNS contains one free parameter θ permutations of rows and columns of U PMNS possible Predictions Mixing angles and all CP phases are predicted in terms of one free parameter θ only, up to permutations of rows/columns

15 p. 15/30 Example of predictions of low energy CP phases: (3n 2 ), (6n 2 ) and CP (H/Meroni/Molinaro ( 14); see also Ding et al. ( 14)) (3n 2 ), (6n 2 ) and CP ւ charged leptons G e = Z 3 ց neutrinos G ν = Z 2 CP U e ց U ν = Ω ν R(θ)K ν ւ U PMNS = U eω ν R(θ)K ν four different types of mixing patterns with different characteristics

16 p. 16/30 Example of predictions of low energy CP phases: (3n 2 ), (6n 2 ) and CP Case 3 b.1) (H/Meroni/Molinaro ( 14)) first column is fixed via choice of residual Z 2 symmetry Z 2 (m) in neutrino sector in particular, solar mixing angle constrains m to be m n 2 free parameter θ is fixed by reactor mixing angle for m = n 2 we find lower limit on CP violation via Dirac phase sinδ 0.71 and both Majorana phases α, β depend on X = X(s) only sinα = sinβ = sin6φ s with φ s = πs n and s = 0,...,n 1

17 p. 17/30 Example of predictions of low energy CP phases: (3n 2 ), (6n 2 ) and CP Case 3 b.1) and n = 8, m = 4: (H/Meroni/Molinaro ( 14)) some viable choices of s s sin 2 θ 13 sin 2 θ 12 sin 2 θ 23 sinδ sinα = sinβ s = / / 2 s = s =

18 p. 18/30 Low energy CP phases in 0νββ decay Case 3 b.1) and n = 8, m = 4 (H/Molinaro ( 16)) Other type of constraints on α, β and 0νββ decay comes from neutrino mass sum rules (Altarelli/Feruglio ( 05), King et al. ( 13), Gehrlein et al. ( 15, 16)).

19 p. 19/30 Further approaches with CP symmetries many more flavor symmetries have been combined with CP (Di Iura/H/Meloni ( 15), Li/Ding ( 15), Ballett et al. ( 15), Rong ( 16), Yao/Ding ( 16),...) study of more general CP symmetries (Everett et al. ( 15)) two CP symmetries in neutrino sector (Chen et al. ( 14)) textures of CP transformations (Chen et al. ( 16)) considerable efforts in building models in recent past (Altarelli, Antusch, Branco, Centelles Chulia, Chen, Chu, Dasgupta, de Medeiros Varzielas, Ding, Everett, Feruglio, Gehrlein, Girardi, Gonzalez Felipe, Grimus, H, He, Joaquim, King, Lavoura, Luhn, Mahanthappa, Machado, Meloni, Meroni, Mohapatra, Neder, Nishi, Päs, Pascoli, Petcov, Rodejohann, Schumacher, Serodio, Shimizu, Smirnov, Spinrath, Srivastava, Stuart, Tanimoto, Valle, Vien, Xu, Yamamoto, Ziegler,...)

20 p. 20/30 High energy CP phases in the lepton sector context: type-i seesaw mechanism 3 right-handed (RH) Majorana neutrinos N i their masses M i are taken to be GeV M i GeV integrating N i out, light neutrino masses are m ν m D M 1 R mt D with m D = Y D H What can we say about CP phases?

21 p. 21/30 High energy CP phases in the lepton sector What can we say about CP phases? mass matrix M R contains six complex parameters CP phases in M R not related to low energy ones but they are relevant for leptogenesis (Fukugita/Yanagida ( 86))

22 p. 22/30 High energy CP phases in the lepton sector What can we say about CP phases? mass matrix M R contains six complex parameters CP phases in M R not related to low energy ones but they are relevant for leptogenesis (Fukugita/Yanagida ( 86)) simplest scenario (unflavored) Y B 10 3 ǫη with ǫ CP asymmetry, η efficiency factor compare to observations: Y B = (8.65±0.09) (Planck ( 15)) if 10 3 η 1, we need 10 4 ǫ 10 7

23 p. 23/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP How to apply G f and CP here? (H/Molinaro ( 16)) M R is invariant under G ν, while Y D is invariant under G f and CP m e is invariant under G e

24 p. 24/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP How to apply G f and CP here? (H/Molinaro ( 16)) M R is invariant under G ν, while Y D is invariant under G f and CP m e is invariant under G e What can we say about neutrino masses and lepton mixing? for Y D 1 in flavor space we find m i 1 M i and U ν = U R = Ω ν R(θ)K ν and together with m e diagonal we get U PMNS = U ν = U R = Ω ν R(θ)K ν

25 p. 25/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP How to apply G f and CP here? (H/Molinaro ( 16)) M R is invariant under G ν, while Y D is invariant under G f and CP m e is invariant under G e Result: no CP asymmetry ǫ is produced (Jenkins/Manohar ( 08), Bertuzzo et al. ( 09), H/Molinaro/Petcov ( 09), Aristizabal Sierra et al. ( 09))

26 p. 26/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP How to apply G f and CP here? (H/Molinaro ( 16)) M R is invariant under G ν, while Y D is invariant under G f and CP m e is invariant under G e Needed: corrections δy D κ to Y D that are invariant under G e

27 p. 27/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP How to apply G f and CP here? (H/Molinaro ( 16)) M R is invariant under G ν, while Y D is invariant under G f and CP m e is invariant under G e Needed: corrections δy D κ to Y D that are invariant under G e Results: ǫ κ 2 explains small value of ǫ sign of ǫ can be fixed because of determined phases

28 p. 28/30 Example of predictions of high energy CP phases: (3n 2 ), (6n 2 ) and CP Case 3 b.1) and n = 8, m = 4 (H/Molinaro ( 16)) For flavored leptogenesis in theories with flavor & CP symmetry see (Mohapatra/Nishi ( 15), Chen et al. ( 16), Yao/Ding ( 16)).

29 p. 29/30 Comments on CP violation in the quark sector flavor symmetries can successfully explain Cabibbo angle (Blum/H/Lindner ( 07), Lam ( 07)) ( π V us = sin from dihedral groups D 7 and D 14 14) however, describing all quark mixing angles well is difficult (Holthausen/Lim ( 13), Araki et al. ( 13), Ishimori et al. ( 14), Yao/Ding ( 15), de Medeiros Varzielas et al. ( 16)) smaller quark mixing angles likely from corrections CP violation in the quark sector is still a mystery

30 p. 30/30 Conclusions leptonic CP violation flavor symmetries alone can predict Dirac phase if in addition a CP symmetry is present, also both Majorana phases can be predicted in a scenario with RH neutrinos we constrain high energy CP phases as well and thus the sign of the baryon asymmetry of the Universe Thank you for your attention.