Chiral oscillations in finite time quantum field theory

TL;DR

This paper develops a quantum field theory approach to describe chiral oscillations of massive Dirac fields over finite times, providing a perturbative framework that aligns with existing formulas and explains production and detection processes involving chirality.

Contribution

It introduces a finite-time perturbative method to analyze chiral oscillations in quantum field theory, connecting theoretical predictions with particle production and detection.

Findings

Derived the formula for chiral oscillations at fourth order in perturbation theory.

Showed the framework's consistency with other methods' results.

Illustrated the relevance of chiral oscillations in particle decay processes.

Abstract

We demonstrate how chiral oscillations of a massive Dirac field can be described within quantum field theory using a finite-time interaction picture approach, where the mass term in the Lagrangian is treated as a perturbative coupling between massless fields of definite chirality. We derive the formula for chiral oscillations at the fourth order in the perturbative expansion, obtaining a result consistent with the formula derived by means of other methods. Furthermore, we illustrate how the perturbative framework of chiral oscillations can effectively describe production processes where an electron must exhibit both left chirality and positive helicity, as in decay $\pi^- \to e^- + {\bar \nu}_e$. Finally, we argue that, in this perturbative view, chiral oscillations are also essential for detecting the decay products in such processes.