DecryptingSO(10)-inspired leptogenesis

Abstract

Encouraged by the recent results from neutrino oscillation experiments, we perform an analytical study of SO(10)-inspired models and leptogenesis with hierarchical right-handed (RH) neutrino spectrum. Under the approximation of negligible misalignment between the neutrino Yukawa basis and the charged lepton basis, we find an analytical expression for the final asymmetry directly in terms of the low energy neutrino parameters that fully reproduces previous numerical results. This expression also shows that it is possible to identify an effective leptogenesis phase for these models. When we also impose the wash-out of a large pre-existing asymmetry N p,i B−L , the strong thermal (ST) condition, we derive analytically all those constraints on the low energy neutrino parameters that characterise the ST-SO(10)-inspired leptogenesis solution, confirming previous numerical results. In particular we show why, though neutrino masses have to be necessarily normally ordered, the solution implies an analytical lower bound on the effective neutrinoless double beta decay neutrino mass, m ee 8 meV, for N p,i B−L = 10 −3 , testable with next generation experiments. This, in combination with an upper bound on the atmospheric mixing angle, necessarily in the first octant, forces the lightest neutrino mass within a narrow range m 1 (10-30) meV (corresponding to i m i (75-125) meV). We also show why the solution could correctly predict a non-vanishing reactor neutrino mixing angle and requires the Dirac phase to be in the fourth quadrant, implying sin δ (and J CP ) negative as hinted by current global analyses. Many of the analytical results presented (expressions for the orthogonal matrix, RH neutrino mixing matrix, masses and phases) can have applications beyond leptogenesis.

A full analytic solution of SO(10)-inspired leptogenesis

“…9 As pointed out in [31], the validity of these results relies on hierarchical RH neutrino masses, M3 M2 M1 and breaks down in the close vicinity of crossing level solutions found in [36] where either | mν11| or |( m −1 ν )33| or both vanish. However, as we will point out, when | mν11| or |( m −1 ν )33| vanish separately, corresponding to M1 M2 and M2 M3 respectively, successful leptogenesis is not attained, and the case when they both get very small, leading to a compact spectrum M1 ∼ M2 ∼ M3, necessarily implies a huge fine-tuning in the seesaw formula since in this case the orthogonal matrix elements become huge, as we are going to show.…”

“…To this extent, for an inclusion of more subtle effects in the derivation of the low energy neutrino constraints, a full analytical calculation of the final asymmetry allows a fast generation of solutions, something essential also for a precise statistical derivation of the constraints, so far qualitatively derived just from scatter plots. Driven by these motivations, in this paper we extend the analytic procedure of [31], taking into account the mismatch between the Yukawa basis and the weak basis. This will allow to reproduce with great accuracy all results obtained only numerically so far.…”

“…In section 2 we review the seesaw type I mechanism and current neutrino oscillation data. In section 3 we discuss SO(10)-inspired leptogenesis extending the analytical procedure discussed in [31] taking into account the mismatch, described by a unitary matrix V L , between the Yukawa basis, where the neutrino Dirac mass matrix is diagonal, and the weak basis, where the charged lepton mass matrix is diagonal. 6 In this way we obtain some general results that in section 4 we specialise to reproduce a few different effects governed by the matrix V L including the application to strong thermal leptogenesis showing how the upper bound on the atmospheric mixing angle gets relaxed.…”

“…The analytical procedure discussed in [31], within the approximation V L I, gets easily generalised for V L = I replacing m ν → m ν [36] and in this case one finds for the…”

A consistent model for leptogenesis, dark matter and the IceCube signal

“…(3.8) and a fully hierarchical light neutrino spectrum. We also notice that the requirement m 1 0 (in particular m 1 10 −4 eV) implies that this setup cannot be realised within the so-called SO(10)-inspired leptogenesis models [66][67][68][69][70][71][72][73].…”