mu-tau Symmetry and Leptogenesis

mu-tau Symmetry and Leptogenesis Jeju Island, Oct. 13, 2006 Jake Lee (이재익) (CQUeST, Sogang Univ.) [hep-ph/0602160, 0610007] in collaboration with Y.H. Ahn, S.K. Kang, C.S. Kim "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Outlines • mu-tau symmetry • Phased breaking of mu-tau symmetry in seesaw model • Observables in our scenario: mass spectrum, mixing angles, CP phase, neutrioless double beta decay • Baryon Asymmetry via Leptogenesis • Some remarks and conclusions • mu-tau symmetry and radiatively generated leptogenesis "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Experimental results of neutrino mixings M.Maltoni et al., New J. Phys. 6, 122 (2004) "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

mu-tau symmetry For symmetric case : Symmetric over interchange between the indices 2 and 3. Diagonalized by with Non-zero 13 angle would mean breaking of the symmetry "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

mu-tau symmetry and its breaking in light neutrino mass matrix (Mohapatra ’04, ’05) mu-tau sym. case sym broken cases "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

mu-tau symmetry in seesaw scenario Consider mu-tau symmetric Dirac Yukawa coupling and heavy Majorana mass matrix as follows: Note that M2=M3 from the presumed mu-tau symmetry "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Phased breaking of mu-tau symmetry: minimal case with only one phase (2,1) and (3,1) entries of Ynu are free from the experimental constraint: Any phases in 23-sub matrix of m_eff must be small to satisfy The non-trivial value of the phase alpha breaks the mu-tau symmetry. "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Light neutrino mass spectrum The heavy Majorana mass matrix is diagonal form  Our model predicts normal hierarchical (NH) mass spectrum. is expected to be very small  we take NH: depending on "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Diagonalization "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Diagonalization (cont’d) Masses: Angles: Dirac phase: where "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis With experimental 3-sigma bounds: We can scan all the parameter space: In order to get more physical insight : All the parameter space of Case 1 gives very small angle "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis (cont’d) Case 2 "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis (cont’d) Case 3 Consistent as long as "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis (cont’d) Overall mass scale of the light neutrinos "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis (cont’d) In the limit of maximal and small "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Numerical Analysis (cont’d) Neutrionless double beta decays "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Leptogenesis For the decay of a heavy Majorana neutrino Ni, the CP asymmetry generated through the interference between tree and one-loop diagrams: In our scenario due to  With small non-zero value, its effect is negligible. Therefore, the lepton asymmetry can be generated only in case that the degeneracy between N2 and N3 is broken.  so-called resonant leptogenesis "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Resonant leptogenesis Introducing a parameter representing the degree of degeneracy: Using In terms of our parameters, From the definition, "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Resonant leptogenesis (cont’d) "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Resonant leptogenesis (cont’d) In the resonantly enhanced leptogenesis scheme, it appears that one could arbitrarily enhance the asymmetry by lowering However, in order for the perturbative approach to be valid, the tree-level decay width must be much smaller than the mass difference: Maximum degeneracy in our scenario: "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Baryon asymmetry The resulting baryon-to-photon ratio can be estimated as where the efficiency factor describe the washout of the produced lepton asymmetry. The efficiency is usually controlled by the parameter defined as Our scenario resides in so-called strong washout regime with "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Baryon asymmetry (cont’d) (Nielsen, Takanishi ’02) Using an approximate expression of the efficiency factor applicable for large Ki "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Remarks and Conclusions • The breaking of degeneracy M2=M3 in heavy Majorana mass spectrum may affect our analysis for the neutrino masses and mixing. However, we found its effect is very small to be safely neglected: • We proposed a new simple and economical scenario to break mu-tau symmetry by introducing a single CP phase in seesaw context. • All the breaking effects in obervables are parameterized in terms of the phase: deviation of from the maximal mixing and non-vanishing Ue3, neutrinoless double beta decay, etc. • We considered baryon asymmetry through resonant leptogenesis through a tiny breaking of the degeneracy between M2 and M3. • Current observation of baryon asymmetry severely constrains our predictions. Future measurement of Ue3 would play an important role. "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Radiatively generated leptogenesis "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

"mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

Thank You! "mu-tau Symmetry and Leptogenesis" by Jake Lee (CQUeST, Sogang Univ.)

mu-tau Symmetry and Leptogenesis