Abstract: We analyze the possible generalized CP symmetries admitted by the Tri-Bi-Maximal (TBM) neutrino mixing. Taking advantage of these symmetries we construct in a systematic way other variants of the standard TBM Ansatz. Depending on the type and number of generalized CP symmetries imposed, we get new mixing matrices, all of which related to the original TBM matrix. One of such revamped TBM variants is the recently discussed mixing matrix of arXiv:1806.03367. We also briefly discuss the phenomenological implications following from these mixing patterns.

Abstract: In this paper, we explore in detail the cosmological implications of an abelian L – L gauge extension of the Standard Model featuring a light and weakly coupled Z. Such a scenario is motivated by the longstanding approximate to 4 sigma discrepancy between the measured and predicted values of the muon's anomalous magnetic moment, (g – 2), as well as the tension between late and early time determinations of the Hubble constant. If sufficiently light, the Z population will decay to neutrinos, increasing the overall energy density of radiation and altering the expansion history of the early universe. We identify two distinct regions of parameter space in this model in which the Hubble tension can be significantly relaxed. The first of these is the previously identified region in which a approximate to 10 – 20 MeV Z reaches equilibrium in the early universe and then decays, heating the neutrino population and delaying the process of neutrino decoupling. For a coupling of g (-) similar or equal to (3 – 8) x 10(-4), such a particle can also explain the observed (g – 2) anomaly. In the second region, the Z is very light (mZ approximate to 1eV to MeV) and very weakly coupled (g (-) approximate to 10(-13) to 10(-9)). In this case, the Z population is produced through freeze-in, and decays to neutrinos after neutrino decoupling. Across large regions of parameter space, we predict a contribution to the energy density of radiation that can appreciably relax the reported Hubble tension, N-eff similar or equal to 0.2.

Abstract: Observables of neutrino oscillations in matter have, in general, contributions from the effective matter potential. It contaminates the CP violation asymmetry adding a fake effect that has been recently disentangled from the genuine one by their different behavior under T and CPT. Is the genuine T-odd CPT-invariant component of the CP asymmetry coincident with the T asymmetry? Contrary to CP, matter effects in uniform matter cannot induce by themselves a non-vanishing T asymmetry; however, the question of the title remained open. We demonstrate that, in the presence of genuine CP violation, there is a new non-vanishing CP-even, and so CPT-odd, component in the T asymmetry in matter, which is of odd-parity in both the phase delta of the flavor mixing and the matter parameter a. The two disentangled components, genuine A(alpha beta)(T;CP) and fake A(alpha beta)(T;CPT), could be experimentally separated by the measurement of the two T asymmetries in matter (nu(alpha) <-> nu(beta)) and ((nu) over bar <-> (nu) over bar (beta)). For the (nu(mu) <-> nu(e)) transitions, the energy dependence of the new A(mu e)(T;CPT) component is like the matter-induced term A(mu e)(CP;CPT) of the CP asymmetry which is odd under a change of the neutrino mass hierarchy. We have thus completed the physics involved in all observable asymmetries in matter by means of their disentanglement into the three independent components, genuine A(alpha beta)(CP;T) and fake A(alpha beta)(CP;CPT) and A(alpha beta)(T;CPT).