A compact analytical approximation for a light sterile neutrino oscillation in matter * * Jiajie Ling acknowledges the support from National Key R&D program of China (2018YFA0404103) and National Natural Science Foundation of China (11775315). F. Xu is supported partially by NSFC (11605076), as well as the FRFCU (Fundamental Research Funds for the Central Universities in China) (21616309)

Abstract

The existence of light sterile neutrinos is a long-standing question in particle physics. Several experimental “anomalies” might be explained by introducing eV mass scaled light sterile neutrinos. Many experiments are actively searching for such light sterile neutrinos through neutrino oscillation. For long baseline experiments, the matter effect should be treated carefully for precise calculation of the neutrino oscillation probabilities. However, this is usually time-consuming or analytically complex. In this manuscript, we adopt a Jacobi-like method to diagonalize the Hermitian Hamiltonian matrix and derive analytically simplified neutrino oscillation probabilities for 3 (active) + 1 (sterile)-neutrino mixing for a constant matter density. These approximations can reach a considerably high numerical accuracy while retaining their analytical simplicity and fast computing speed. This would be useful for current and future long baseline neutrino oscillation experiments.