Modular A4 invariance and leptogenesis

Takehiko Asaka,Takahiro Yoshida,Takuya H Tatsuishi,Yongtae Heo

doi:10.1007/jhep01(2020)144

Takehiko Asaka, Takahiro Yoshida + Show 2 more

Open Access

https://doi.org/10.1007/jhep01(2020)144

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Abstract

We consider a model with three right-handed neutrinos in which Yukawa coupling constants and Majorana masses are obtained by requiring the modular A4 symmetry. It has been shown that the model can explain mass hierarchies and mixing patterns of charged leptons and neutrinos with the seesaw mechanism. In this article we investigate the leptogenesis by decays of right-handed neutrinos in this model. It is shown that masses of right-handed neutrinos are about 1013 GeV in order to account for the observed baryon asymmetry of the universe. Furthermore, the positive sign of the baryon asymmetry is obtained only for the limited ranges of mixing angles and CP violation phases of active neutrinos, which can be tested by future neutrino experiments.

Highlights

JHEP01(2020)144 the Weinberg’s dimension five operators or right-handed neutrinos with the seesaw mechanism, and both possibilities have been shown to be successful
It is shown that masses of right-handed neutrinos are about 1013 GeV in order to account for the observed baryon asymmetry of the universe
We have considered the leptogenesis in the model with three right-handed neutrinos introducing the modular A4 invariance

Summary

Modular group and its finite quotient subgroups

We give a brief review on the modular symmetry on a torus. A twodimensional torus T 2 can be constructed by R2/Λ, where Λ denotes a two-dimensional lattice. Ab c d a, b, c, d ∈ Z, ad − bc = 1 ≡ Γ This transformation of basis vectors is written in terms of the modulus τ ≡ α2/α1 by aτ + b τ → τ = γτ =. Modular forms f (τ ) of weight k and level N are holomorphic functions transforming under the Γ(N ) as f (γτ ) = (cτ + d)kf (τ ), γ ∈ Γ(N ),. A coupling constant for the n-th order term between φ(I1), · · · , φ(In) should be a modular form of weight kY (n) and a representation of ΓN transformed as YI1,I2,...,In (γτ ) = (cτ + d)kY (n)ρ(γ)YI1,I2,...,In (τ ),. We note that Yukawa couplings as well as higher order couplings depend on modulus and can have non-vanishing modular weights. The lepton flavor physics and the leptogenesis can be discussed without SUSY. The modular symmetry is broken by the vacuum expectation value of τ at the compactification scale which is the Planck scale or slightly lower scale order

Lepton flavor model with modular A4 symmetry

Leptogenesis

Sign and magnitude of baryon asymmetry

Conclusions