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

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 T;CP αβ and fake A T;CPT αβ , could be experimentally separated by the measurement of the two T asymmetries in matter (ν α ↔ ν β ) and (ν α ↔ν β ). For the (ν µ ↔ ν e ) transitions, the energy dependence of the new A T;CPT µe component is like the matter-induced term A CP;CPT µe 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 CP;T αβ and fake A CP;CPT αβ and A T;CPT αβ .

Symmetries and Their Breaking in the Fundamental Laws of Physics

“…Although they are well separated in the effective Hamiltonian, in general they are not in the experimental observables and, in particular, in the CP asymmetry. The ideal way to solve this problem would be the independent measurement of T-odd [105] and CPT-odd asymmetries, but this route requires sources of electron neutrinos and antineutrinos above the muon mass energies, which is at present unavailable for accelerator facilities. As an alternative, the solution consists in disentangling these two components, genuine and matter-induced CP violation, in the observable CP asymmetry.…”

Tests of discrete symmetries

“…Disentangling such 'matter effects' from genuine CP violation requires adequate modelling of the interactions (see e.g. [67]) and the use of additional information, such as the energy dependence of the oscillation probabilities [68].…”

The impact of different parameterizations on the interpretation of CP violation in neutrino oscillations

“…For example, mediumbaseline reactor neutrino experiments at L ≃ 1 km actually de-termine 4|U e3 | 2 (|U e1 | 2 + |U e2 | 2 ) but by unitarity this is equal to 4|U e3 | 2 (1 − |U e3 | 2 )which can be expressed as sin 2 2θ 13 under the assumption the matrix is unitary 3. The presence of matter modifies neutrino oscillations[27] and induces additional apparent CP (or CPT) violation which has been discussed extensively in the literature[28][29][30][31][32][33][34][35][36][37][38], but this is easily accounted for and is not the focus of this paper.…”