Chiral oscillations in finite time quantum field theory

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 \(\pi ^- \rightarrow e^- + {\bar{\nu }}_e\). Finally, we argue that, in this perturbative view, chiral oscillations are also essential for detecting the decay products in such processes.