Pion-to-vacuum vector and axial vector amplitudes and weak decays of pions in a magnetic field

TL;DR

This paper develops a model-independent framework to parametrize pion-to-vacuum matrix elements of vector and axial vector currents in magnetic fields, analyzing implications for weak pion decays under external magnetic influences.

Contribution

It introduces a gauge covariant Lorentz structure-based parametrization for hadronic matrix elements in magnetic fields, applicable to weak decay processes.

Findings

Provides general expressions for pion decay amplitudes in magnetic fields

Analyzes limits under strong and weak magnetic field conditions

Offers a framework for future theoretical and experimental studies

Abstract

We propose a model-independent parametrization for the one-pion-to-vacuum matrix elements of the vector and axial vector hadronic currents in the presence of an external uniform magnetic field. It is shown that, in general, these hadronic matrix elements can be written in terms of several gauge covariant Lorentz structures and form factors. Within this framework we obtain a general expression for the weak decay $\pi^- \to l\,\bar\nu_l$ and discuss the corresponding limits of strong and weak external magnetic fields.