Magnetic field driven enhancement of the weak decay width of charged pions

TL;DR

This paper investigates how a strong magnetic field significantly increases the decay rate of charged pions and alters the angular distribution of emitted antineutrinos, using a chiral NJL model.

Contribution

It provides a detailed analysis of magnetic field effects on pion decay constants and decay rates, revealing substantial enhancements and directional asymmetries.

Findings

Decay rate increases by up to three orders of magnitude with magnetic field strength.

The ratio of electronic to muonic decay modes is significantly enhanced.

Antineutrino angular distribution is suppressed along the magnetic field at high field strengths.

Abstract

We study the effect of a uniform magnetic field $\vec B$ on the decays $\pi^-\to l^-\,\bar{\nu}_l$, where $l^-\,=e^-,\,\mu^-$, carrying out a general analysis that includes four $\pi^-$ decay constants. Taking the values of these constants from a chiral effective Nambu-Jona--Lasinio (NJL) model, it is seen that the total decay rate gets strongly increased with respect to the $B=0$ case, with an enhancement factor ranging from $\sim 10$ for $eB=0.1\,\mathrm{GeV}^2$ up to $\sim 10^3$ for $eB=1\,\mathrm{GeV}^2$. The ratio between electronic and muonic decays gets also enhanced, reaching a value of about $1:2$ for $eB=1\,\mathrm{GeV}^2$. In addition, we find that for large $B$ the angular distribution of outgoing antineutrinos shows a significant suppression in the direction of the magnetic field.