Neutrino Helicity and Chirality Transitions in Schwarzschild Space-Time

TL;DR

This paper investigates how neutrino helicity and chirality change in Schwarzschild space-time, revealing that curvature affects their conservation and proposing methods to estimate neutrino mass and chiral states.

Contribution

It derives an ultrarelativistic approximation of the Dirac Hamiltonian in curved space-time, analyzing helicity and chirality transitions and their dependence on curvature and frame effects.

Findings

Neutrino helicity is not conserved in curved space-time even in the massless limit.

Chirality transition rates depend on the neutrino's helicity transition rate and curvature effects.

A method is proposed to estimate neutrino mass and chiral states from transition rates.

Abstract

We study the helicity and chirality transitions of a high-energy neutrino propagating in a Schwarzschild space-time background. Using both traditional Schwarzschild and isotropic spherical co-ordinates, we derive an ultrarelativistic approximation of the Dirac Hamiltonian to first-order in the neutrino's rest mass, via a generalization of the Cini-Touschek transformation that incorporates non-inertial frame effects due to the noncommutative nature of the momentum states in curvilinear co-ordinates. Under general conditions, we show that neutrino's helicity is not a constant of the motion in the massless limit due to space-time curvature, while the chirality transition rate still retains an overall dependence on mass. We show that the chirality transition rate generally depends on the zeroth-order component of the neutrino's helicity transition rate under the Cini-Touschek transformation. It is also shown that the chiral current for high-energy neutrinos is altered by corrections due to curvature and frame-dependent effects, but should have no significant bearing on the chiral anomaly in curved space-time. We determine the upper bound for helicity and chirality transitions near the event horizon of a black hole. The special case of a weak-field approximation is also considered, which includes the gravitational analogue of Berry's phase first proposed by Cai and Papini. Finally, we propose a method for estimating the absolute neutrino mass and the number of right-handed chiral states from the expectation values of the helicity and chirality transition rates in the weak-field limit.