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

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.