A biased review of Leptogenesis. Lotfi Boubekeur ICTP

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1 A biased review of Leptogenesis Lotfi Boubekeur ICTP

2 Baryogenesis: Basics Observation Our Universe is baryon asymmetric. n B s n b n b s BAU is measured in CMB and BBN. Perfect agreement with each other. Theory Sakharov Conditions for successful baryogenesis B violation C & CP violation τ p yrs Departure from thermal equilibrium

3 EW Sphalerons ( One of the great successes of SM is to explain why Baryon and Lepton numbers are conserved perturbatively. ( ( But at the non perturbative level, B and L are no more conserved due to EW anomaly. J B µ = 1 3 J L µ = l colors generations (ūγµ u + dγ µ d ( lγµ l + ν l γ µ ν l E µ J µ B = µj µ L = N B = N L n f N CS, n ( f 32π Tr µν F 2 µν F, M sph N CS = 1 N CS = 0 [ A N CS = 1 sph, ϕ sph ] [ A, ϕ ]

4 Rate of B+L violation is given by ( 4π exp α W , T = 0 Γ (α W T 4 ( m sph 7 ( m T exp sph T, T < TC α 5 W T 4 T > T C => Sphalerons are in equilibrium for 10 2 GeV < T < GeV ( 8ng + 4n H B = L 22n g + 13n H

5 GUT Baryogenesis B violation mediated by X and Y bosons present in GUTs The scenario works however it is disfavoured because of the required high reheat temperature to produce X and Y => gravitinos, monopoles,... g X L R µ q u g q e X L µ R q Y L L h ij i j l d u Y R R h ij i j q q Y L L y ij i _ j _ g l d X L R µ u e Y R R y ij i j

6 Affleck-Dine Baryogenesis -In SUSY, there exists plenty of flat directions (F=D=0. -Their flatness is only lifted by SUSY or non-renormalizable operators. -Furthermore during inflation, SUSY is broken since V=0. / Example W = λ (LH u 2 M L i = 1 2 ( ϕ 0, H u = 1 2 ( 0 ϕ n L = i 2 (ϕ ϕ ϕϕ, This flat direction carries lepton number 4M V (ϕ = (m 2 3/2 c H H 2 ϕ 2 + a H H ϕ4 ϕ 4 λ 2 +a m m 3/2 [ [ + h.c. + 4M 4M M 2 ϕ 6. ( ch M During inflation H m 2 H 2 1/4 3/2 => ϕ 0. λ 2 n L + 3Hn L = Im [ ϕ V (ϕ ϕ ] n L m 3/2 2M Im(a mϕ 4 t erse, the expansion rate sc

7 Spontaneous Baryo/Leptogenesis Important Caveat: CPT is assumed to be conserved. If CPT, then Baryogenesis can proceed in equilibrium. Baryon or lepton number can couple through L J µ B µφ n B φ If φ 0 Poincare is broken => CPT (Greenberg Theorem. The evolution of baryon number will follow: µ J µ B 2 φ ṅ B + 3Hn B φ E.g. coupling with Ricci,... µ R µ φ => model dependent predictions

8 Type I See-saw & leptogenesis The existence of a heavy right handed (RH explains the smallness of neutrino masses H ν R H m ν Y T Y ν L ν L The decay of RH neutrinos leads to a L asymmetry which is converted to a baryon asymmetry through SM sphalerons. M νr H 2 m q,l = Y q,l H H H H ν Ri ν Ri ν Ri l Lj l Lj l Lj n B s CP violation = ɛ ν R1 η( m 1 n ν R1 s (T M ν R1 washout factor

9 Baryogenesis through leptogenesis Lepton number produced through L decay of Right handed neutrino Exploits EW sphalerons to transform L to B. Y B n B s = ( 8ng + 4n H 22n g + 13n H nl s, CP violation: interference of tree + 1-loop (vertex and self energy ε i with j Γ(N i l j h u j Γ(N i l j hu j Γ(N i l j h u + j Γ(N i l j hu 1 (Y Y ii = 1 8π k i F V (x = x ln [ ] [ ( ( Im [ {(Y Y ik } 2] [ F V ( M 2 k M 2 i ( x + F S ( M 2 k M 2 i, F S (x = 2 x x 1 ]

10 Departure from thermal equilibrium vs. thermal production Consider hierarchical RH neutrino masses => B is created through decay of Departure from thermal equilibrium => Γ Decay < H N 1 Γ(T = 0 H(T = M = (Y Y 11 M 8π / ( g 1/2 M 2 2π 3/2 M P 45 m ev < 1, On the other hand, thermal production of RH neutrinos => Γ Prod > H Γ Prod = nσv g (Y Y 11 T > g 1/2 T 2 T /M P m 1 > 10 5 ev =M 10 5 ev m ev In general, one invokes the presence of B-L gauge bosons, which are in equilibrium for M Z < ( TRH GeV 3/ GeV.

11 The gravitino problem in leptogenesis Thermal production of => N 1 T RH > M 10 9 GeV N1 ( ( ( On the other hand, in the SUSY version of leptogenesis Ω 3/2 h 2 = 0.21 ( TRH GeV ( 100 GeV m 3/2 ( m g 1 TeV 2, T RH < 10 9 GeV No overproduction of gravitinos =>. Possible solutions Either the gravitino is very heavy or very light. Gravitino is dark matter. Non-thermal production (preheating, inflaton decay,... Low reheat temperature.

12 Low Scale Leptogenesis LB, hep-ph/ Thermal production T RH > 10 9 GeV LB, T. Hambye & G. Senjanović, PRL 04. Gravitinos T RH < 10 9 GeV Proposed solution: RH neutrinos could have masses ~ TeV. Then New sources de CP and L violation. T RH ~TeV. LÑ = (m 2 Ñ ijñ i Ñj + B ij Ñ i Ñ j + A U ij L i H U Ñ j + A U ij L i H U Ñ j + AD ij L i H DÑj + A D ij L i H DÑ j + h.c. Lm φ α L m φ α N I N I N K NK φ β L j φ β L j

13 Going to the diagonal basis LÑ = M 2N I 2 N I + µ α N Ij I Lj φ α + µ α N Ij I L [ j φ α, ] The CP asymmetry reads ε V I = 1 1 8πM 2N µ α Ij 2 I ε S I = K I 1 1 4πM 2N µ α Ij 2 I K I [ ] Im [ µ β Im µβ Im [ µ β Im µβ Kj µα Km µα Kmµ α Ij] FV (x K, Kjµ α Ij] FS (x K, With x K = M 2N I /M 2N K. and F V (x = ln(1 + x, F S (x = x/(1 x. Numerical example: M 2 TeV, M 6TeV bn1 bn2 (µ α 1j max M N 1, (µ α 2j max 10 3 M N 2 m = 700 GeV, one can check that a large enough ε , gives n /n 6 1 and s ε 1 10, and n B /n γ

14 New contributions to light neutrino masses φ α ν j N I ν j χ 0 φ β ν k ν k (m rad ν jk α 4π [ µ α Ij µβ Ik M 2N I m 2 ν j m 2 ν j m 2 χ m χ m 2 ν j m 2 ν k φ α φ β ln m ν j 2 m 2 χ j k ]. m νi 500 GeV For our numerical example with and gives in the numert m rad 1 ev! ν Degenerate spectrum for light neutrinos m χ 100 GeV

15 Non thermal production of RH neutrinos LB & Davidson, Peloso, Sorbo, PRD 02 Mechanism N Yukawa h N mass φ-n coupling Thermal 10 5 ev < m 1 < 10 3 ev 10 9 GeV < M 1 < T RH irrelevant { M eff Affleck Dine 10 9 ev < m ν1 < 10 4 ev M i < H i < H infl infl ( M eff 2 i < 0 Pert.φ decay } Γ LV < H(τ i { Mi < m φ /2 M i > m φ /2 } BR(φ N i N i 1 BR(φ N i N i 1 N preheating eq. (14 Γ LV < H(τ i M i > GeV g i > 0.03 Ñ preh./resc. eq. (19 Γ LV < H(τ i M i < g i GeV g i > λ

16 RH neutrinos are produced through the coupling L N, φ = N (M + g φ N Rescattering is important Rescattering term dn 3/2 dt + 3 H N 3/2 σ v N X N N Eventough RHN are produced at lower temperture, also gravitinos could be produced Log 10 ~ h Log 10 g ~

17 Non-Gaussianity due to. Inhomogeneous Leptogenesis LB & P. Creminelli, PRD 06 See-saw with couplings depending ( on a light field ( χ χ L = L SM + Y ij L i HN j + M i N i N i + ( χ 2 M P M P RH neutrinos will decay differently in different places => curvature fluctuations. χ ds2 = dt 2 + e 2ζ( x a(t 2 d x χ f NL Constraints on Log m 1 m f NL χ M(χ/M P Y (χ/m P => Light neutrinos have hierarchical or inverse hierarchical spectrum. Constraints on the dynamics of =>,

18 Conclusions In general baryogenesis probes physics beyond the standard model. Leptogenesis is a typical working example. Links neutrinos to BAU. Gravitino overproduction => low scale models. Gravitino overproduction => preheating and rescattering. Inhomogeneous leptogenesis could be responsible for CMB temperature anisotropies. Good opportunity to test ideas.