Overall feature of CP dependence for neutrino oscillation probability in arbitrary matter profile

Abstract

We study the CP dependence of neutrino oscillation probability for all channels in arbitrary matter profile within three generations. We show that an oscillation probability for ν e → ν µ can be written in the form P (ν e → ν µ ) = A eµ cos δ+B eµ sin δ+C eµ without any approximation using the CP phase δ. This result holds not only in constant matter but also in arbitrary matter. Another probability for ν µ → ν τ can be written in the form P (ν µ → ν τ ) = A µτ cos δ + B µτ sin δ + C µτ + D µτ cos 2δ + E µτ sin 2δ. The term which is proportional to sin 2δ disappear, namely E µτ = 0, in symmetric matter. It means that the probability reduces to the same form as in constant matter. As for other channels, probabilities in arbitrary matter are at most the quadratic polynomials of sin δ and cos δ as in the above two channels. In symmetric matter, the oscillation probability for each channel reduces to the same form with respect to δ as that in constant matter. *

A novel approach to study atmospheric neutrino oscillation

“…We first develop a general framework in the propagation basis [106,107] for phenomenological study of neutrino oscillation. It can analytically decompose the contributions of the neutrino mass hierarchy, the atmospheric mixing angle, and the CP phase.…”

“…In the propagation basis, the atmospheric mixing angle θ 23 [106] and the CP phase δ [107] can be disentangled from the other mixing parameters as well as the Earth matter potential [108]. This can be seen from the effective Hamiltonian,…”

“…The 2-3 mixing matrix O 23 and the rephasing matrix P δ can be extracted out as overall matrices [107,108], In this way, O 23 and P δ are separated from the neutrino mass hierarchy, which is encoded in the first term inside the square bracket, as well as the matter effect, represented by the second term. In other words, the atmospheric mixing angle θ a and the CP phase δ are disentangled from the remaining mixing parameters, analytically.…”

“…Correspondingly, we can define a propagation basis (ν ′ i ) [106,107] that is related to the flavor basis (ν α ) and the mass eigenstates (ν i ) as follows:…”

“…According to the definition of the mixing matrix in (2.5), O 23 P δ can be explicitly written as, The mixing from the propagation to the flavor basis occurs between the second and the third indices. We can expect the first element of S ′ to be unaffected when (2.13) is combined with (2.12) [107], Note that only the elements among e and µ flavors are shown since they are sufficient to derive all the flavor basis oscillation probabilities, 15) from ν e and ν µ (as well as fromν e andν µ , as shown below). Explicitly we find, …”