γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum

I consider the γW-box correction to superallowed nuclear β decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. The respective correction to the β^{+} spectrum is estimated to be Δ_{R}(E)=(1.6±1.6)×10^{-4}E/MeV assuming a conservative 100% uncertainty. The effect is positive definite and can be observed if a high-precision measurement of the positron spectrum is viable. If only the full rate is observed, it should be included in the calculated Ft values of nuclear decays. I argue that this novel effect should be included in the analyses of nuclear beta decay experiments to ensure the correct extraction of V_{ud} from decay rates, and of the Fierz interference term from precision measurements of decay spectra.