Issues in Leptogenesis1 Eung Jin Chun Korea Institute of Advanced Study, Seoul APCTP, Yonsei, Sep. 15, 2007

Issues in Leptogenesis2 Issues in leptogenesis To summarize (not so) new developments in leptogenesis = my two works done in Ann Arbor. Quintessence and leptogenesis with S. Scopel, arXiv: Flavor-symmetry for resonant leptogenesis. with K. Turzynski, hep-ph/

Issues in Leptogenesis3 Introduction Non-zero neutrino masses and mixing angles provide a convincing evidence of physics beyond the Standard Model. See-saw mechanism: a paradigm to understand neutrino masses. The see-saw scenario involves a high- energy scale where lepton number L is not conserved: baryogenesis through leptogenesis.

Issues in Leptogenesis4 Seesaw Mechanism Dimension-5 effective operator: added in Standard Model 3 singlet heavy fermions N (RHN) W=

Issues in Leptogenesis5 Leptogenesis Seesaw mechanism can meet the Sakharov conditions to generate lepton asymmetry from RHN deacy: Fukugita and Yanagida, PLB174, 45 L C and CP Out-of-equilibrium decay → neutrino mass op. → phases in Y → Γ/H < 1 decay rate Hubble constant K=  /H(T=M) k>1 wash-out regime k<1 out-of-equilibrium decay SU(2) L sphaleron interactions convert the lepton asymmetry into a baryon asymmetry

Issues in Leptogenesis6 Non-standard cosmology & leptogenesis Standard scenario: 1) population of RHN due to thermalization -- independent of prehistory. 2) RHN freeze-out during radiation-dominated era. 3) Hierarchical RHN mass. Non-standard scenario: 1) different origins for populating RHN: non-thermal like from inflaton decay. 2) the Universe before big-bang nucleosynthesis may be dominated by non-radiation energy density. 3) Resonance enhancement of CP/L asymmetry: degenerate RHN mass

Issues in Leptogenesis7 Quintessential Kination and Leptogenesis

Issues in Leptogenesis8 Dark energy & quintessence Ω Dark Energy ~ 0.7 may indicate the existence of a slowly-rolling scalar field,  : Quintessence Caldwell et al., PRL80,1582 A possibility:   dominance in an earlier stage. Driven by inflation? Chung et al., arXiv: [hep-ph] A thermal Cold Dark Matter particle decouples earlier and its relic density can be enhanced. Salati., PLB571,121

Issues in Leptogenesis9 equation of state: Nb) Kination Dark Energy Cosmological evolution of Quintessence ρ α a -3(1+w) :

Issues in Leptogenesis10 Tracking solution explaining  m »  DE Steinhardt et al., PRD59,123504

Issues in Leptogenesis11 Impact on Dark Matter physics Salati, PLB571,121 Chung et.al., arXiv: During kination the Universe expands faster than during radiation domination a thermal Cold Dark Matter particle decouples earlier and its relic density can be enhanced

Issues in Leptogenesis12 Kination Cosmology T r is a free parameter with the only bound: Define T r at which

Issues in Leptogenesis13 Kination Cosmology ln(ρ) ln(a) arar a -4 a -6 isoentropic expansion (a 3 s=constant):

Issues in Leptogenesis14 Kination Cosmology ln(H) ln(T) TrTr T2T2 T3T3 ln(ρ) ln(T) TrTr T4T4 T6T6 time

Issues in Leptogenesis15 Leptogenesis with Kination A useful parametrization: (kination) (radiation) M≡RHN mass

Issues in Leptogenesis16 Leptogenesis with Kination When z r » M/T r >>1 with T r » 1 MeV: g *r =10.75 g * (T)= (SUSY) Require thermalization of SM particles & RHN: Γ gauge ~ α 2 T > H Γ sphaleron ~ α 4 T > H Require sphaleron interactons in thermal equilibrium: Thermal leptogenesis can occur at low temperature.

Issues in Leptogenesis17 Wash-out parameter in Kination Leptogenesis RHN decay rate Wash-out parameter: Effective neutrino mass wide range of possibilities depending on z r, from strong (K À 1) to super-weak (K ¿ 1) wash-out at fixed effective neutrino mass

Issues in Leptogenesis18 Super-weak wash-out regime When kination dominates, z r À 1: 1) Vanishing initial number density of RHN: decay & inverse decay too weak to popularize RHN efficiency of leptogenesis suppressed by 1/K 2) Thermal initial distribution of RHN: maximal efficiency

Issues in Leptogenesis19 Boltzmann equations CP asymmetry in decay:

Issues in Leptogenesis20 Decay & scattering rates decay s-channel scattering t-channel scattering N.B.) scattering is important at high temperature, z<<1

Issues in Leptogenesis21 Final lepton asymmetry Definition of efficiency: If RHNs thermalize early and decay out-of-equilibrium when they are still relativistic (K<1), we get η=1 With vanishing initial RHN distribution, we get  » 1 for K » 1 and  ¿ 1 for K ¿ 1 or K À 1.

Issues in Leptogenesis22 Super-weak wash-out regime (K ¿ 1) vanishing initial RHN density (N(0)=0) ^ Semi-analitic solution defining: (n=1 radiation, n=2 kination) negligible, main contribution from z<<1 Scattering dominates. Neglecting scattering: η ~ K 2

Issues in Leptogenesis23 radiation kination Super-weak wash-out regime (K ¿ 1) vanishing initial RHN density (N(0)=0) ^ lepton asymmetry produced early RHN decay freeze-out RHN production

Issues in Leptogenesis24 Strong wash-out regime (K À 1) vanishing initial RHN density (N(0)=0) ^ Semi-analitic solution Strong inverse-decay ) late decoupling (z f À 1) (n=1 radiation, n=2 kination) useful fit: For the decoupling to happen when kination still dominates (zf < zr)

Issues in Leptogenesis25 Strong wash-out regime (K À 1) integrating BEs using saddle-point technique: n=1 radiation, n=2 kination RHNs decouple late, when scatterings are negligible decouple later for kination

Issues in Leptogenesis26 Strong wash-out regime (K À 1) radiation kination RHNs thermalize before z f → thermal equilibrium erases any dependence on initial conditions

Issues in Leptogenesis27 Evolution of  for various K

Issues in Leptogenesis28 Efficiency vs. K N(0)=0 ^ N(0)=1 ^ kination radiation

Issues in Leptogenesis29 Efficiency vs. z r radiation kination T r =1 MeV→z r ~10 8 smooth transition from radiation dominance (z r <1) to kination dominance (z r >1). strong supression of the efficiency if z r >>1 increased efficiency for 1<z r <100 if m>0.01 eV

Issues in Leptogenesis30 Quasi-degenerate Neutrinos and Leptogenesis with L  – L 

Issues in Leptogenesis31 Neutrino mass pattern and non-resonant leptogensis Efficient leptogenesis: With Quasi-degenerate neutrinos: Gravitino problem constrains RHN mass: Requires resonant mechanism

Issues in Leptogenesis32 L  -L  flavor symmetry Automatic maximal atmospheric mixing correction forbidden by Z n : high resonance Fine-tunning: a 2 /X=bd/Y for m 1 =m 2,3 Flavon fields and charge assignment:

Issues in Leptogenesis33 Solar mixing and mass differences Perturbative calculation from corrections with 3,4 : Fine-tunings for smaller solar mass difference: Consistent with large solar mixing  for  correction for  23

Issues in Leptogenesis34 Fit to Neutrino data Success rate AFM: HKV: Ours: 10 -4

Issues in Leptogenesis35 Leptogenesis with L  -L  Baryon asymmetry with degenerate RHNs: CP asymmetry:

Issues in Leptogenesis36 Leptogenesis with L  -L  Degenerate RHNs ) Radiative generations of  N & Re[yy y ] 23

Issues in Leptogenesis37 Successful Leptogenesis Final expression for CP asymmetry: ) y  2 dependence 2 suppression

Issues in Leptogenesis38 Fit to Leptogenesis

Issues in Leptogenesis39 Life in Ann Arobr Convenient rural life; can be boring Beautiful colors in Autumn Too long winter (6 months…) Fantastic spring/summer