Additional time-dependent phase in the flavor-conversion formulas

TL;DR

This paper investigates the impact of second-order energy corrections on flavor oscillation formulas, revealing an additional time-dependent phase that affects oscillation patterns, especially in non-relativistic regimes.

Contribution

It introduces a detailed analysis of second-order corrections in wave-packet models, highlighting a previously overlooked time-dependent phase in flavor oscillations.

Findings

Extra time-dependent phase arises from second-order energy corrections.

Phase effects persist non-relativistically, influencing oscillation patterns.

Modifications are small but relevant in precise flavor oscillation measurements.

Abstract

In the framework of intermediate wave-packets for treating flavor oscillations, we quantify the modifications which appear when we assume a strictly peaked momentum distribution and consider the second-order corrections in a power series expansion of the energy. By following a sequence of analytic approximations, we point out that an extra time-dependent phase is merely the residue of second-order corrections. Such phase effects are usually ignored in the relativistic wave-packet treatment, but they do not vanish non-relativistically and can introduce some small modifications to the oscillation pattern even in the ultra-relativistic limit.