Neutrino Oscillation, Leptogenesis and Spontaneous CP Violation

Transcription

1 Neutrino Oscillation, Leptogenesis and Spontaneous CP Violation Mu-Chun Chen Fermilab (Jan 1, 27: UC Irvine) M.-C. C & K.T. Mahanthappa, hep-ph/69288, to appear in Phys. Rev. D; Phys. Rev. D71, 351 (25) Miami 26, Fort Lauderdale, FL, December 13, 26

2 Introduction CP violation in quark sector not sufficient to explain the observed matter -anti-matter asymmetry of the Universe t n b /s = (.87 ±.4) 1 1, Neutrino oscillation opens up the possibility that CP violation in the lepton sector may be responsible for the observed BAU Relating leptogenesis with low energy CP violation is generally not possible due to the additional phases and mixing angles in the RH neutrino sector

3 Introduction CP violation at high energy: L = l Li iγ µ µ l Li + e Ri iγ µ µ e Ri + N Ri iγ µ µ N Ri +f ij e Ri l Lj H + h ij N Ri l Lj H 1 2 M ijn Ri N Rj + h.c. Yukawa matrix hij : general complex matrix 3 families: 9-3 = 6 physical phases; 6 mixing angles CP violation at low energy: L eff = l Li iγ µ µ l Li + e Ri iγ µ µ e Ri + f ii e Ri l Li H + 1 h T ik 2 h H 2 kjl Li l Lj + h.c. M k k Majorana mass matrix: symmetric 3 families: 6-3 = 3 physical phases; 3 mixing angles

4 Introduction In minimal left-right symmetric model, there exist very strong correlations between these high (1 16 GeV) and low energy processes M.-C. C & K.T. Mahanthappa, Phys. Rev. D71, 351 (25) two intrinsic phases if CP broken spontaneously left-right parity relate LH and RH Majorana mass matrices

5 Minimal LR Model Gauge symmetry: SU(3) C SU(2) L SU(2) R U(1) BL P SU(3) C SU(2) L U(1) Y Q=T 3,L +T 3,R (BL) Particle content: Fermions: Q i,l = u d i,l ~(1/2,,1/3) Q i,r = u d i,r ~(,1/2,1/3) L i,l = e i,l ~(1/2,, 1) L i,r = e i,r ~(,1/2, 1) Scalars: = ~(1/2,1/2, ) R = R R R R ~(,1, +2) L = L L L L ~(1,, +2) Under parity P: L R, L R, +

6 In general, = ei 'e i ', L = L e i, L R = R e i R To get SM gauge boson masses, bi-doublet VEV s satisfy The two triplet VEV s related by sol is seesaw suppressed 2 +' 2 2m W 2 /g 2 (174GeV) 2 L = 2 R Small neutrino masses:r~ 1 15 GeV;L~.1 ev precision EW constraints OK

7 The Lagrangian is invariant under unitary transformations The fields transform as: U L = ei L, U e i L R = ei R e i R L U L L, R U R R U R U + L, L U L L U + L, R U + R R U R e i( L R ), ''e i( L R ) L L e 2i L, R R e 2i R Under these unitary transformations, we can rotate away two phases and are left with only two intrinsic phases = 'e i, ' L = L e i, L R = R

8 Yukawa sector: quarks L q =Q i,r (F ij +G ij )Q j,l +h.c. where = 2 2 mass matrices M u =F ij +G ij 'e i ', M d =F ij 'e i ' +G ij all Yukawa couplings real due to spontaneous CP violation responsible for all CP violation in quark sector satisfy FCNC constraints in quark sector requires a large hierarchy in bi-doublet VEV s /'m t /m b >>1

9 Lepton sector: L l =Li,R(P ij +R ij )L j,l + f ij (L T i,l L L j,l +L T i,r R L j,r )+h.c. M e =P ij 'e i ' +R ij M Dirac =P ij +R ij 'e i ', M LL = f ij v L e i L, M RR = f ij v R, M LL M LR T M LR M RR H H L R R L SU(2) L SU(2) R U(1) BL R SU(2) L U(1) Y f R ew U(1) EM f L h ew h ew f R H L L H L

10 Lepton sector: M.-C. C & K.T. Mahanthappa, Phys. Rev. D71, 351 (25) M Dirac =P ij +R ij 'e i ', M LL = f ij v L e i L, M RR = f ij v R, M LL M LR T M LR M RR M eff =M II M I (fe i L 1 PT f 1 P) L M I =(M Dirac ) T (M RR ) 1 (M Dirac )=(P+'e i ' R)T ( R f) 1 (P+'e i ' R) L PT f 1 P M II = L e i L f the connection between CP violation in quark sector and that in lepton sector appears only at sub-leading order ('/) the connections are thus very weak

11 leptonic mixing matrix (MNS matrix) c 12 c 13 s 12 c 13 s 13 1 U MNS = s 12 c 23 c 12 s 23 s 13 e i c 12 c 23 s 12 s 23 s 13 e i s 23 c 13 e i s 12 s 23 c 12 c 23 s 13 e i c 12 s 23 s 12 c 23 s 13 e i c 23 c 13 e i three leptonic phases are function of L affect the following processes: e i 21/2 e i 31 /2 (i) neutrino oscillation P( )= 4 Re(U i U j U j U i )sin 2 2 L (m )+2 J ij 4E CPsin 2 ( i>j i> j J CP = Im(H 12H 23 H 31 ) sin 2 L, HM eff (M eff ) + m 2 21 m 2 32 m 31 (ii) neutrinoless double beta decay 2 L m ) ij 4E m ee 2 =m1 2 U e1 4 +m 2 2 U e2 4 +m 3 2 U e3 4 +2m 1 m 2 U e1 2 U e2 2cos 21 +2m 1 m 3 U e1 2 U e3 2 cos 31 +2m 2 m 3 U e2 2 U e3 2 cos( )

12 (iii) leptogenesis: two ways to get lepton number asymmetry (1) (2) N 1 l+h, = (N 1l+H )(N 1 l+h) (N 1 l+h )+(N 1 l+h) l+l, = ( L l+l)( L l+l) ( L l+l)+( L l+l) L A natural scenario: M L > M1 decay of the lightest RH neutrino dominates: (1) Two types of diagrams contribute to the asymmetry: D =O R M D (a) N k l l H N j H N k l l H N j H 3 = 16 M 1 2 Im( D(M I ) T D ) 11 = ( D + D ) 11 l i l i (b) N k H l l L H = 3 16 M 1 2 Im( D(M II ) T D ) 11 sin ( D + L D ) 11 l i Independent of the choice of the unitary transformation U L,R M.-C. C & K.T. Mahanthappa, Phys. Rev. D71, 351 (25)

13 out-of-equilibrium condition: H T=M1 = M Pl + ( ) 11 M 1 (1.7)(32) g 2 D D + ( ) 11 1 (.1eV) D D <1 M 1 require m= + ( D D ) 11 M 1 <.1 ev M1 cannot be too light hierarchy among heavy neutrino masses cannot be too large (problem in standard leptogenesis in GUT models)

14 Specific Flavor Ansatz M eff =(fe i L 1 PT f 1 P) L m u /m t P m c /m t 1 t 2 t t f ij = t 1 1 t 1 1 may arise from underlying U(1) family symmetry deviation of atmospheric mixing angle from maximal negligible leptonic Jarlskog invariant 1 1 PT f 1 P=s t 1 t m u m c m t 2 m u m c m t 2 1 t m u m t J CP = 2st2 (1t 2 ) L 6 m 2 21 m m 32 M.-C. C & K.T. Mahanthappa, Phys. Rev. D71, 351 (25) m u m t 1 t m u m t m c m t m c m t sin L

15 Current Status of Oscillation Parameters 3 model parameters: t, s, L circa 26, at 1 sigma: m 2 32 = (2.4±.3) 1 3 ev 2 m 2 21 = (7.9±.4) 1 5 ev 2 sin 2 θ 23 >.9.4 < tan 2 θ 12 <.59 sin 2 θ 13 <.16

16 .3 <mee> (ev).2.1!.3!.2! JCP Jcp ranges from -.2 <mee> ranges from 1-4 to 1-2 ev; current limit ~.1 ev in the large Jcp region, strong correlation between Jcp and <mee>

17 .6.4!".2!.2!.4!.6!.3! JCP symmetry between 2nd and 4th quadrants large Jcp region, strong correlation between Jcp and % no wash-out: % D % +D ) ( 1 " 11 # $ <1 M1 H T = M 1 (.1eV ) (% D % +D )11 M1!.2 " R ~ (112#13 )GeV, M1 ~.1" R & m )2 ~ ( c +, L = 1-7 ev!!! ' mt * total lepton number asymmetry For Jcp ~ 1-5 " = 1#2 $ %"'< (1#4 #1#5 ) sufficient leptogenesis can be obtained

18 Lowering Seesaw Scale with an addition U(1)s symmetry: SU(2)R breaking scale can be significantly lower U(1)s broken by <S> ; Q(S) = +1 U(1)s forbids dim-4 operators mass terms arise only through operators with higher dimensionality M.-C. C & K.T. Mahanthappa, hep-ph/69288, to appear in Phys. Rev. D ω = s M S <1 M νd = P ij κω Q(L L) Q(L R ) Q(Φ) + R ij κ e iα κ ω Q(L L) Q(L R )+Q(Φ). M e = P ij κ e iα κ ω Q(L L) Q(L R ) Q(Φ) + R ij κω Q(L L) Q(L R )+Q(Φ) M RR ν = f ij v R ω Q( R)+2Q(L R ), M LL ν = f ij v L e iα L ω Q( L)+2Q(L L )

19 induced triplet VEV v L β κ2 v R, Lowering Seesaw Scale M.-C. C & K.T. Mahanthappa, hep-ph/69288, to appear in Phys. Rev. D β β Max { ω Q( R) Q( L ) 2Q(Φ), rω Q( R) Q( L ), r 2 ω Q( R) Q( L )+2Q(Φ) }, U(1) charge assignment consistent with LR symmetry: Q(Φ) = Q( Φ) = 2, Q( L ) = Q( R ) = 4, Q(L L ) = Q(L R ) = 2, v L v R β κ 2 ω 8, M e R ij κω 2 + O(ω 6 ), M νd R ij κe iα κ ω 4 + O(ω 6 ), M LL ν = f ij v L e iα L, M RR ν = f ij v R M eff ν = M LL ν M νd (Mν RR ) 1 Mν T D = v L [ fij e iα L sr ij f 1 ij RT ij e 2iα κ ] with~.1,l ~ (.1-.1) ev R ~ 1 6 GeV quark phase now affect leptonic CPV at dominant order

20 EDM of the Electron W L W R l a a N a l a mixing between WL and WR d e eα κκ 4πMW 2 vr 2 Im(e iα κ M D ) ee v2 L ( ) GeV 2 ( ) 1 19 (MνD ) ee r sin(2α κ ) e-cm MeV v R R ~ 1 6 GeV de ~ 1-32 e-cm can be obtained (within reach of next generation of experiments) current limit: de < 1.67x1-27 e-cm at 9% CF

21 Leptogenesis! L MR1 sin(αl + 2ακ! ) JCP sin(αl + ακ! ).6.4!" de 1 e-cm de 1 e-cm.1 32!" JCP JCP.5.1

22 Leptogenesis ɛ = ɛ L 1 8 ɛ O(1 9 ) t n b /s = (.87 ±.4) 1 1, n b s n H n H ɛη Y eq N 1 (T M 1 ), n b /s ɛη SM sufficient BAU can be obtained with efficiency factor 1-1 efficiency dominantn 1 thermaln 1 zeron m 1ineV Giudice, Notari, Raidal, Riotto & Strumia, Nucl. Phys. B685, 89 (24)

23 Non-anomalous U(1) at TeV SM expanded by non-anomalous U(1) with N RH neutrinos six anomaly cancellation conditions [SU(3)c] 2 U(1) [SU(2)L] 2 U(1) [U(1)Y] 2 U(1) U(1)Y[U(1)] 2 U(1) gauge-gravitational anomaly [U(1)] 3 cubic equation M.-C. C,A. de Gouvea & B. Bobrescu, hep-ph/61217 forbid dim-4 (Dirac) and dim-5 (HHLL) operators; neutrino masses generated by operators with higher dimensionality

24 Leptocratic Model with N=3 RH neutrinos, rational solutions for charges UV cutoff is at ~ a TeV quark charges flavor blind; lepton charges flavor dependent neutrinos can either be Dirac (only Dirac masses are allowed) or Majorana (Dirac, LH Majorana and RH Majorana masses are all allowed) bi-large mixing pattern can arise exist light quasi-sterile neutrinos, might be relevant for cosmology coupling to Z : probing neutrino sector at colliders

25 Conclusions In minimal LR model, there are only two intrinsic phases that account for all observed CP violation in nature, provided CP is broken spontaneously Due to parity in the model, LH and RH neutrino Majorana mass terms are proportional pronounced correlation between leptogenesis and low energy leptonic CP violation CP violation in quark sector and in lepton sector related if seesaw scale is low; such low scale seesaw can be achieved with an additional U(1) symmetry

26 Minimization Condition Minimization of this scalar potential leads to the following relations, (2ρ 1 ρ 3 )v R v L = β 1 κκ cos(α L α κ ) + β 2 κ 2 cos α L + β 3 κ 2 cos(α L 2α κ ), (A5) = β 1 κκ sin(α L α κ ) + β 2 κ 2 sin α L + β 3 κ 2 sin(α L 2α κ ), (A6) [ = v R v L 2κκ [ (β 2 + β 3 )sin(α L α κ ) + β 1 κ 2 sin α L + κ 2 sin(α L 2α κ ) ]] +κκ sinα κ [ α3 (v 2 L + v2 R ) + (4λ 3 8λ 2 )(κ 2 κ 2 ) ]. (A7)