Abstract
In this paper, we consider the imbedding of the popular and well-motivated trimaximal mixing and μ–τ reflection symmetry (which can help us shape the forms of the neutrino mass matrix) in the minimal seesaw model (which contains much fewer parameters than the general seesaw model) with two TeV-scale right-handed neutrinos (for realizing a low-scale seesaw) of nearly degenerate masses (for realizing a resonant leptogenesis). However, either for the trimaximal mixing scenario (which is realized through the Form Dominance approach here) or for the μ–τ reflection symmetry scenario, leptogenesis cannot proceed. To address this issue, we consider the possibility that the special forms of the neutrino mass matrix for the trimaximal mixing and μ–τ reflection symmetry are slightly broken by the renormalization group evolution effect, thus allowing leptogenesis to proceed. It is found that in the normal case of the neutrino mass ordering, the baryon asymmetry thus generated can reproduce the observed value. For completeness, we have also extended our analysis to the scenario that two right-handed neutrinos are not nearly degenerate any more. Unfortunately, in this scenario the final baryon asymmetry is smaller than the observed value by several orders of magnitude.
Highlights
Mass matrix for the light neutrinos arises as Mν −MDMR−1MDT
We consider the possibility that the special forms of the neutrino mass matrix for the trimaximal mixing and μ–τ reflection symmetry are slightly broken by the renormalization group evolution effect, allowing leptogenesis to proceed
The most popular and natural way of generating the tiny but non-zero neutrino masses is the type-I seesaw mechanism, which provides an appealing explanation for the baryon asymmetry of the Universe via the leptogenesis mechanism
Summary
It is well known that, according to the temperature where leptogenesis takes place (the right-handed neutrino mass scale), there are three possible regimes for leptogenesis [49, 50]. (1) Unflavored regime: in the temperature range above 1012 GeV where the charged-lepton Yukawa yα interactions have not yet entered thermal equilibrium, three lepton flavors are indistinguishable and should be treated in a universal manner. (2) Two-flavor regime: in the temperature range 109–1012 GeV where the yτ -related interactions are in thermal equilibrium, the τ flavor is distinguishable from the other two flavors which remain indistinguishable and should be treated separately. (3) Three-flavor regime: in the temperature range below 109 GeV where the yμ-related interactions enter thermal equilibrium, all the three flavors are distinguishable and should be treated separately. (1) For the low-scale (leading us to the three-flavor regime) resonant leptogenesis scenario, the final baryon asymmetry is given by [47, 48]. We see that in the present scenario two right-handed neutrinos are on an equal footing in contributing to leptogenesis This is because they are nearly degenerate. (2) But in the scenario that two right-handed neutrinos are not nearly degenerate any more, the contribution to leptogenesis mainly comes from the lighter one because that from the heavier one suffers from its washout effects. In the two-flavor regime, the baryon asymmetry receives two contributions from εIτ and εIγ = εIe + εIμ which are subject to different washout effects controlled by mIτ and mIγ = mIe + mIμ [49, 50].
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