One-loop radiative correction to the Toshev relation for neutrino oscillations in matter

TL;DR

This paper investigates how one-loop electroweak radiative corrections slightly violate the Toshev relation in neutrino oscillations in matter, providing a quantum-level understanding of neutrino matter effects.

Contribution

The paper derives differential equations for effective neutrino oscillation parameters incorporating one-loop radiative corrections, revealing quantum effects on the Toshev relation.

Findings

Radiative corrections cause small deviations from the Toshev relation.

Differential equations describe how neutrino parameters evolve with matter density.

Quantum effects slightly modify neutrino oscillation parameters in matter.

Abstract

The one-loop electroweak radiative corrections to coherent forward neutrino scattering in a medium slightly violates the tree-level universality of neutral-current contributions of three neutrino flavors to the matter potential that is relevant to neutrino oscillations in matter. We examine this small but nontrivial quantum effect by deriving the differential equations of those effective neutrino oscillation quantities with respect to the electron number density of matter. The tree-level Toshev relation $\sin 2\tilde{\theta}_{23} \sin\tilde{\delta} = \sin 2\theta_{23} \sin\delta$, which links the fundamental flavor-mixing and CP-violating parameters