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 $eB=0.1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$ up to $\sim {10}^3$ for $eB=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. The ratio between electronic and muonic decays gets also enhanced, reaching a value of about $1:2$ for $eB=1{\mathrm{G}\mathrm{e}\mathrm{V}}^2$. 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.