Leptogenesis Parameterized by Lepton Mass Matrices Pei-Hong Gu and Xiao-Gang He arXiv:1511.03835

Baryon Asymmetry of Our Universe Possible, but certain conditions need to be satisfied.

The Sakharov Conditions for Baryogenesis (1967) Baryon Number B Violation C and CP Violation Interactions Out Of Thermal Equilibrium In the Standard Model, all the above three conditions are satisfied: Baryon number violation: Sphelaron effects-tunneling effects from different vacuum states with non-zero baryon number differences. Violated B+L, but conserves B-L. C and CP violation: Electroweak interaction violates C, and phase in Kobayashi-Maskawa mixing matrix violates CP. Out of thermal equilibrium: Electroweak symmetry breaking. But, CP violation rate too small, out of thermal equilibrium too weak. Not enough to generate a large enough Baryon Asymmetry. Needs to go beyond SM! Electroweak baryogenesis, Gut baryogenesis….

Leptogenesis Fukugita and Yanagida, 1986 Translate lepton number asymmetry generated in the early universe to baryon number asymmetry! Requires lepton asymmetry generated before Sphelaron effects to be in effective ( T ~ 1012 – a few TeV). Initial aL(i)=a, aB(i)=0. Sphelaron effect: Conserve B-L, but violates B+L After: aL(i)+ aB(i) = aL(f)+aB(f) = 0, aL(i) – aB(i) = aL(f) – aB(f) aL(f) = a/2, aB(f) = -a/2 half of initial lepton asymmetry will be translated into baryon asymmetry if complete. SM Sphelaron effect: aB (f) = - (28/79)aL (i)

Seesaw model and leptogenesis In the minimal SM, neutrinos do not have mass. To have Dirac mass, need to introduce right handed neutrinos νR: (1,1)(0)

Some theoretical models for neutrino masses Loop generated neutrino masses: The Zee Model(1980); Zee-Babu Model (zee 1980; Babu, 1988) Other loop models: Babu&He; E. Ma; Mohapatra et al; Geng et al Seesaw Models: Type I Introduce singlet neutrinos

Seesaw leptogenesis

Leptogenesis Parameterized by Lepton Mass Matrices Pei-Hong Gu and Xiao-Gang He Dirac leptogenesis: Neutrinos are Dirac particles. No net lepton asymmetry can be generated. But can have generational lepton number asymmetry. In the early universe it can be possible that certain generation of lepton asymmetry be transformed into baryon asymmetry to solve the BAU problem! Construct a specific model doing the job. Also try to solve the strong CP problem.

The Model SU(3)CxSU(2)LxSU(2)RxU(1)LxU(1)RxZ4&parity symmetry -> SU(3)CxSU(2)LxSU(2)RxU(1)B-LxZ4 -> SU(3)CxSU(2)LxU(1)YxZ4 -> SU(3)CxU(1)emxZ4 Parity symmetry crucial for solving strong CP problem, and also ensure neutrino mass matrix is Hermitian. Allow soft broken, separate SU(2)L and SU(2)R breaking scales. Z4 symmetry not broken, neutrinos do not have Majorana mass.

Particle Quantum numbers SU(3)CxSU(2)LxSU(2)RxU(1)LxU(1)RxZ4&parity symmetry Potential, some terms playing special roles

Symmetry breaking

Lepton mass matrices fS is Hermitian due to left-right symmetry

Lepton and Baryon Asymmetry Generational lepton asymmetry generated by EL and ER decays.

Before entering Sphelaron era, eet produced tau-number asymmetry is erased to zero. Only m and e number enter Sphelaron ransfer process.