Realization of thermal inflation in SUSY discrete flavour symmetry model

Transcription

1 Realization of thermal inflation in SUSY discrete flavour symmetry model Hiroaki Nagao (Niigata univ.) 01/03/9 The 5 th Workshop Cosmic Neutrino (To be appeared arxiv:hep- ph/104.xxxx) in collaboration with Y.Shimizu, T.Shimomura and Y.Nakagawa

2 Introduction Discrete flavour symmetry suggested from neutrino experimental data, [ex: Ishimori et.al ( 10)] based on the non- Abelian discrete groups, (ex: A_4, S_4,Δ(54) ) elegantly derive the flavour structures of elementally particles, naturally explain the mass spectrum Flavon Gauge singlet scalar fields. [ex:altarelli et.al ( 05)] VEVs of flavons derive the flavour structures via vacuum alignment generate the masses of leptons (ex: Heavy RH ν s) Controlled by flavour symm. & Z_n symm. & U(1)_R symm.

3 Problems of disc. flavour symm. However, SUSY discrete flavour symmetry model has problems Domain wall problem Origin of vacuum structure of flavon Deviation from Tri- bimaximal mixing... Existence of pseudo moduli of flavon Our focus!

4 Pseudo moduli flavon F- flat direction among the flavon fields Expected to spontaneously breaks the flavour symmetry V ( u ) =V 0 m u u + V νr + V νr ( W y R uν c Rν c R ) 1- loop effective potential [ex:bando et.al ( 93)] ( Soft SUSY breaking mass V νr V νr = yri u ln 3 y Ri 4 u 4 = 3 π i=1 3 m νr i + y Ri u i=1 3 π m u ln 3 m νr i + y Ri u 3 m u

5 Pseudo moduli flavon F- flat direction among the flavon fields Expected to spontaneously breaks the flavour symmetry V ( u ) =V 0 m u u + V νr + V νr ( W y R uν c Rν c R ) u ( V νr V νr = yri u ln 3 y Ri 4 u 4 = 3 π i=1 3 m νr i + y Ri u i=1 m u yr exp 3 π 8π m u 3 y R m ν R m u ln 3 m νr i + y Ri u 3 m u Strongly depend on Soft SUSY breaking mass [ H.N & Y.Shimizu ( 1)] V 0 = 3 y R 16 π m ν R u V 0 u u

6 Thermal history of pseudo moduli flavon Once, we consider the thermal history of flavon V ( u ) =V 0 m u u + V νr + V νr + ct u Thermal evolution of flavon T u T T m u : u trapped at origin by thermal potential V 0 u V (T = 0) u T< m u : u rolls down to the minimum à u obtain non- vanishing VEV

7 Thermal history of pseudo moduli flavon Once, we consider the thermal history of flavon V ( u ) =V 0 m u u + V νr + V νr + ct u Thermal evolution of flavon T u T T m u T<V 1/4 0 : u trapped at origin by thermal potential : Start to dominate the energy of universe V 0 u V (T = 0) u T< m u : u rolls down to the minimum à u obtain non- vanishing VEV T = T (sec) R : Energy transfer from u into SM Must above few MeV Realize in the flavour symm. models??

8 Γ(u a) 1 64π Decay rate of flavon Interaction lagrangian L int y R δu νc Rν c R + h.c. + δu u ( µ a) Decay rate of pseudo moduli flavon Γ(u ν) 3 16 π m 3 u u mν m u u Reheating temperature after u domination T (sec) R 0.45 Γ(a SM)M p T (sec) R 1MeV ( W y R uν c Rν c R ) u u + δu a exp i v Dominate decays of u Br(u a) 1 [ H.N & Y.Shimizu ( 1)] ( m u 3 y R m ν R 4π m a 0 Energy transfer from flavon does NOT complete before BBN!! (

9 Problem Energy transfer from u complete before BBN? (Realize Br(uà a)<<1??) Possible solutions [ H.N & Y.Shimizu ( 1)] ) Introduce the coupling with vector- like quarks W = y Q uqq 3) Explicit breaking term of disc. flav. symm. L = κ (u + u ) Coupling with vector- like quarks 1) Light RH neutrino m νr m u / via higher- dim. operator

10 Light RH neutrino Generate mass of RHν by suppressed interaction [ H.N et. al ( 1)] u W y R Λ νc RνR c cf. usual charge assignment Λ:O(M p ) m νr y R u W y R uνrν c R c Λ m νr y R u O(10 13 GeV) Allow u ν R ν R on- shell Br a Branching ratio of decays of u Γ(u a) Br(u a) < 0.3 (BBN) Γ(u a) + Γ(u ν R ) [Cyburt et.al ( 04)] 1 = m ν R m βf 3 < u ~ 45 % β f 1 4m ν R /m u m νr /m u Not suppressed enough! ( But can reproduce the DayaBay result)

11 Problem Energy transfer from u complete before BBN? (Realize Br(uà a)<<1??) Possible solutions [ H.N & Y.Shimizu ( 1)] ) Introduce the coupling with vector- like quarks W = y Q uqq 3) Explicit breaking term of disc. flav. symm. L = κ (u + u ) Coupling with vector- like quarks 1) Light RH neutrino m νr m u / via higher- dim. operator Not enough moderate the problem Br(u a) < 45 % ~ mνr m u β 3 f 1 1 Br a m νr /m u

12 Coupling with vector- like quarks Interaction btwn u and quarks W = y Q uqq ( Q: 5 rep. of SU(5), Q :5* rep. ) u [ex:kim et.al ( 08)] Q g Decay channel of u [ex:chun et.al( 00)] g Γ(u gg) N q α s 144π 3 m 3 u u Γ(u gg) Γ(u a) = 4N q αs 9π To overcome uà a, we should introduce N q > 100 Huge number of quarks!! [ex:morrissey et.al ( 05)] Gauge coupling will blow up below the GUT scale!

13 Problem Energy transfer from u complete before BBN? Possible solutions [ H.N & Y.Shimizu ( 1)] ) Introduce the coupling with vector- like quarks W = y Q uqq (Realize Br(uà a)<<1??) 3) Explicit breaking term of disc. flav. symm. L = κ (u + u ) Coupling with vector- like quarks 100 flavors of quarks Breaks pgcu below GUT scale [ex:morrissey et.al ( 05)] 1) Light RH neutrino m νr m u / via higher- dim. operator Not enough moderate the problem Br(u a) < 45 % ~ mνr m u β 3 f 1 1 Br a m νr /m u

14 Explicit breaking term To kinematically forbid uà a, we assume L = κ (u + u ) V 0 Mass of circumferential comp. of u m a = κ v If κ> m uu 4 In addition, we introduce uqq coupling u, uà a forbidden kinematically! Re(u) Γ tot Γ(u gg) N q α s 144π 3 m 3 u u [ex:chun et.al ( 00)] T (sec) R 0.45 Γ tot M p 6MeV mu 10 3 GeV 3/ u GeV 1 Energy transfer from u into SMs can complete before BBN begins

15 Energy transfer from u complete before BBN? 3) Explicit breaking term of disc. flav. symm. Coupling with vector- like quarks u a can be forbidden Problem (Realize Br(uà a)<<1??) L = κ (u + u ) T (sec) R few MeV Possible solutions m a = κ u >m u ( u gg ) ) Introduce the coupling with vector- like quarks W = y Q uqq 100 flavors of quarks Breaks pgcu below GUT scale 1) Light RH neutrino m νr m u / via higher- dim. operator Not enough moderate the problem Br(u a) < 45 % ~ mνr m u [ H.N & Y.Shimizu ( 1)] β 3 f 1 1 Br a [ex:morrissey et.al ( 05)] m νr /m u

16 Energy transfer from u complete before BBN? 3) Explicit breaking term of disc. flav. symm. Problem (Realize Br(uà a)<<1??) L = κ (u + u ) Coupling with vector- like quarks u a can be forbidden T (sec) R few MeV Possible solutions m a = κ u >m u ( u gg ) ) Introduce the coupling with vector- like quarks W = y Q uqq 100 flavors of quarks Breaks pgcu below GUT scale [ex:morrissey et.al ( 05)] 1) Light RH neutrino m νr m u / via higher- dim. operator Not enough moderate the problem Br(u a) < 45 % ~ mνr m u [ H.N & Y.Shimizu ( 1)] β 3 f 1 1 Br a Applicable to thermal inflation by domination of flavon m νr /m u

17 Realization of thermal inflation Contours satisfying T (sec) R few MeV = 10 0 [ H.N & Y.Shimizu ( 1)] (ß Primary moduli diluted enough) y ave y ave <u> m ave [GeV] m ave m Q + m νr y ave y Q + y R m ave [GeV] Thermal inflation scenario can realize by u domination in SUSY discrete flavour model

18 Summary Study the thermal evolution of pseudo moduli flavon in SUSY discrete flavour symmetry Obtain analytic expression of VEV of flavon Flavon can dominate the universe at m u <T <V 1/4 0 Energy transfer from flavon does not complete before BBN ( at least minimal framework ) Br of dominate the decay process Should introduce linear potential into lagrangian Domination by can be applied into thermal inflation scenario Apply to the continuous flavour symmetry??