Radiative correction to electron-neutrino correlation inΛβdecay

The order-$\alpha$ radiative correction for the $\beta$-decay process $\Lambda \to \mathrm{pe}\overline{\nu }$ is studied in order to meet the needs of high-precision experiments which measure the electron-neutrino angular distribution. The relative correction is tabulated for the decay distribution in terms of the electron energy $E_e$ and ${cos\theta }_{e\overline{\nu }}$. The one-variable distribution with respect to ${cos\theta }_{e\overline{\nu }}$ is decomposed in terms of the form-factor combinations $f_1^2$, $f_1{f}_2$, etc., and the radiative correction is evaluated for each term. For the electron-neutrino correlation parameter ${\alpha }_{e\nu }$, a huge relative correction is found due to its small value in the lowest order.