Radiative corrections in neutrino-deuterium disintegration

The radiative corrections of order $\alpha$ for the charged and neutral current neutrino-deuterium disintegration for energies relevant to the SNO experiment are evaluated. Particular attention is paid to the issue of the bremsstrahlung detection threshold. It is shown that the radiative corrections to the total cross section for the charged current reaction are independent of that threshold, as they must be for consistency, and amount to a slowly decreasing function of the neutrino energy $E_{\nu}$, varying from $\sim$ 4% at low energies to $\sim$ 3% at the end of the $^8$B spectrum. The differential cross section corrections, on the other hand, do depend on the bremsstrahlung detection threshold. Various choices of the threshold are discussed. It is shown that for a realistic choice of the threshold, and for the actual electron energy threshold of the SNO detector, the deduced $^8$B $\nu_e$ flux should be decreased by $\sim$ 2%. The radiative corrections to the neutral current reaction are also evaluated.