Leptogenesis with type II see-saw in SO(10)

Transcription

1 Leptogenesis wit type II see-saw in SO(10) Andrea Romanino SISSA/ISAS Frigerio Hosteins Lavignac R, arxiv:

2 Te baryon asymmetry η B n B n B n γ = n B n γ Generated dynamically if = (6.15 ± 0.5) (1 number) B is violated C and CP are violated out of equilibrium evolution Models of Baryogenesis Planck GUT Troug leptogenesis Electroweak Affleck-Dine...

3 See-saw induced neutrino masses L eff E Λ = L ren SM + a ij Λ (l i)(l j ) +... N (1,1,0) l i M X l j N N k See-saw type I See-saw type II Δ Δ (1,3,1) l i l j T (1,3,0) l i M X l j T T k See-saw type III (Any number of N, T, Δ ) (SU(3) c,su() L,Y)

4 Model dependence in see-saw type-i Relevant interactions: Overall size of neutrino Yukawa couplings Unknown flavour structure λ E ije c il j d + λ N ij N i l j u + M ij N in j λ N k λ N M k M m ν m ν BR(e i e j γ) k 4 log k BR(e i e j γ) [ m ν = v u λ T N ] 1 M λ N v d λ E, v u λ N, M m e m µ m τ, m ν1 m ν m ν3, U e.g. v u λ N = v u λ diag N V N or M diag, R = 1/ M diag v u λ N U / M diag 1 pysical parameters 1 known or measurable parameters 9 unknowns = 3 masses + 3 angles + 3 pases Type-II: LFV more predictive [Rossi 0], leptogenesis as well in SO(10)

5 Type-II see-saw in SO(10) Δ (1,3,1) _ 15 SU(5) Δ + Δ 54 SO(10) = 15 SU(5) + 15 SU(5) +4 SU(5) (or or > 500) Note: 10 x 10 = 1 s + 45 a + 54 s 54 < 5 (perturbativity) 54 does not couple to 16 x 16 But it does couple to 10 x 10, and 10 (1,,-½) l Reminder: SM embedding 16 SO(10) = 5 SU(5) + 10 SU(5) + 1 SU(5) 10 SO(10) = 5 SU(5) + 5 SU(5) 5 SU(5) = l + d c = d + H 3 10 SU(10) = q + u c + e c

6 A predictive Type II SO(10) model - SO(10): 10 isu(5) 16 iso(10), 5 isu(5) 10 iso(10) W y ij 16 i16 j 10 + ij 16 i 10 j 16 + f ij 10 i10 j 54 + σ W vev+nr m U ij = v u y ij m E ij = v d ij m ν ij = σ v u M f ij <16> pairs up te spare components in 16 i 10 i (pure type II) 16 ij16 i 10 j 16 V 16 ij 5 i 5 10 j =V 16 ij ( L i L j + D c i D c j) W is R P invariant, generic up to mass terms; no type-i - _ Below M GUT : SM + (5 i +5 i ) + ( ) (+ N i ) LNV from Δ (and N i ) M Δ = M 15 < M 4 M N

7 CP asymmetry l j Type II L l f lj l j Type I l j λ N kj f ij l i L k ( ) fij 10 i10 j 54 f kl S, T f ki 4 SU(5) l i N 1 λ N 1i l i N 1 λ N 1j λ N ki N k l i f ij, M L ij from m ν, m E (up to overall factors, W NR ) L 1 ligter tan M Δ /? M L1 < M Δ < M L, M 4 : M L1 (in te diagonal m E basis) ɛ 1 10π 1 V GeV cos β M M 4 λ 4 l λ l + λ λ l ij ( V GeV Im[m 11(mm m) 11 ] ( i m i ) f ij, λ σ ɛ Γ( l l ) Γ( ll) Γ + Γ )

8 Maximal CP asymmetry Need: ηɛ 10 8 ε max /λ L Normal Hierarcy 10 4 Inverted Hierarcy sin Θ sin Θ m ligtest ev m ligtest ev

9 Γ( l ) H Maximal efficiency - Δ kept in equilibrium by gauge interactions (ΔΔ SM) and especially decays (Δ l * l *, u u, ~ L * 1L ~ * 1) ( no dependence on initial conditions!) Still, a quasi-maximal efficiency can arise if one (decoupled) decay cannel is out of equilibrium [Hambye Raidal Strumia 05] In our case: Δ ~ L * 1L ~ * 1 Γ( u) H. 10 sin 4 β i m i m 3 O(1) efficiency if f 11 is sufficiently small: >. 10 Γ( L, 1) Γ( l ) m ee i m i ( ) 1/ M f GeV

10 O(1) efficiency region m 1 «m «m 3, M Δ /M 4 = 0.1, sinσ = 1, sin θ 13 = 0.05, tanβ = K L Ε Ε 10 8 Ε Λ H 0.15 M GeV M 10 1 GeV K L1 c 1 K H (K = Γ/H) Λ L

11 Analytical estimate of η Toy model: no SUSY, no GUT (SM + Δ + L i L i ) Define L1 = η 0 ɛσ eq (T M ), η 0 = O (1) η 0 1 in te limit: γ A «γ D ( ) + B L «1 (see eqs) Y X n X /s Δ X Y X - Y X - Σ X Y X + Y X - Hypercarge conservation: L1 = l + Lepton number asymmetry at T «M Δ : lep = l + L1 = If bot Δ l*l*, are in equilibrium: Ten: B L = Y eq Y eq (n B /s) exp η 0 ε Y eq l L1 l Y eq l + Σ eq 0, Y eq = 4 7 η 0ɛΣ eq (T M ) η = 4 7 η 0 Σ eq 0

12 FCNCs - New effects from new eavy fields below M GUT : (5 i +5 i ) + 54 m l = (m l ) MSSM 1 [ ( m (4π) 10 + m ) 54 f 3 ln M GUT M ln MGUT m d = c (m d c) MSSM 1 ( m (4π) 10 + m ) 54 f M + M L M L [ 3 ln M GUT M + [ m e = c (m e c) MSSM c ( m (4π) 16 + m ) d y ln M GUT M L M L [ m q = (m q) MSSM c ( m (4π) 16 + m ) d y ln M GUT ln M GUT M + M L M L + 3 ln MGUT ] M + M D M f c D c ln MGUT ] M + M D M f. c D c M D cm D c ] y ] y,

13 SO(10) breaking and -3 splitting W vev = W (1) vev + W () vev W (1) vev = σ (λ S S + σ 1 54) λ (M16 + g 45 1 )16 W () vev = M η new implementation of te DW mecanism room to suppress D=5 proton decay

14 Gravitinos Weak wasout M Δ GeV Large T RH and SUSY T RH up to few GeV: m 3/ > 100 TeV (e.g. anomaly mediation) gravitino LSP (specific NLSP or RPV) T RH > GeV m 3/ < 16 ev + CDM m 3/» 100 TeV No sugra/susy Small T RH Δ from reeating, preeating, oter mecanisms Lower M Δ (strong wasout)

15 Model dependence m D = m E T only (approximately) compatible wit 3 rd family No surprise it does not work for ligter families: small Yukawas are sensitive to iger dimensional operators, possibly involving SO(10) breaking fields Suc operators also affect te relation between ligt and eavy leptons in a model-dependent way Te quantitative effect is negligible in leptogenesis unless M Δ M i, mild in FCNC because it is O(1) and enters logaritmically; negligible if te triplet is eavier tan te second eavy family

16 Conclusions By implementing type-ii see-saw in SO(10) we improve on dependence on unknown parameters dependence on initial conditions perturbativity D=5 proton decay Baryogenesis closer to be testable