Gravitational Effects on Quantum Coherence in Neutrino Oscillation

Abstract

In this paper, we investigate the quantum coherence for two flavor neutrinos propagating in a Schwarzschild metric. In fact, this issue is explored both qualitatively via calculating the parameter $K_3$ in Leggett-Garg inequality (LGI) and also quantitatively by evaluating the $l_1$-norm, $\mathcal{C}(\rho )$. Using the weak field approximations, we show that the gravitational effects decrease the maximum value of $K_3$ for some intervals of energy such a way that there is no violation, while it leaves the maximum amount of the quantum coherence, $\mathcal{C}(\rho )$ unchanged.

Comments: 21 pages, 2 figures, to appear in Phys. Rev. D