Do T asymmetries for neutrino oscillations in uniform matter have a CP-even component?

Abstract

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 δ of the flavor mixing and the matter parameter a. The two disentangled components, genuine A αβ T;CP and fake A αβ T;CPT , could be experimentally separated by the measurement of the two T asymmetries in matter (ν α ↔ ν β ) and ( $$ {\overline{\nu}}_{\alpha}\leftrightarrow {\overline{\nu}}_{\beta } $$ ν ¯ α ↔ ν ¯ β ). For the (ν μ ↔ ν β ) transitions, the energy dependence of the new A μe T;CPT component is like the matter-induced term A μe 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 αβ CP;T and fake A αβ CP;CPT and A αβ T;CPT .