Abstract
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved $Z_2$ in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the $R$-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy $S_4$ flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Highlights
The large lepton mixing angles motivate the use of discrete flavour symmetries,and this approach has been widely explored
Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle
We apply the formalism to a high energy S4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis
Summary
We will consider the classic example of leptogenesis from the lightest RH neutrino N1 (the so-called N1 leptogenesis) in the type-I seesaw model [9,10,11,12]. We will choose to work in the basis where both the heavy neutrinos Ni and the charged leptons mass terms are diagonal. The most general gauge invariant Lagrangian relevant to lepton masses and flavour mixing can be written as. The efficiency factor η(mα) accounts for the washing out of the lepton asymmetry Yα due to the inverse decay and lepton number violating scattering. For M1 > 1012 GeV, the interactions mediated by all the three charged lepton Yukawa are out of equilibrium, and all lepton flavours are indistinguishable. For 109 GeV ≤ M1 ≤ 1012 GeV, only the interactions mediated by the τ Yukawa coupling are in equilibrium and the final baryon asymmetry is well approximated by [68, 72]. The predicted baryon asymmetry would be too small to account for the observed value in this scenario
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