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Radiative Corrections to the Neutrino-Deuteron Reactions

The $O(α)$ QED and electroweak radiative corrections to neutrino deuteron reactions is investigated with particular emphasis given to the constant terms, which have not been treated properly in the literature. This problem is related to the definition of the axial-vector coupling constant $g_{A}$ as to the inclusion of radiative corrections. After proper calculations of the constants for the Fermi and Gamow-Teller transitions, we find the radiative correction to the neutral current induced reaction, with the usually adopted definition of $g_{A}$, is 1.017 for the Higgs boson mass $m_{H}=1.5 m_{Z}$. This value is close to that given by Kurylov et al., but this is due to an accidental cancellation of the errors, between those caused by putative identification of constant terms for the Fermi and Gamow-Teller transitions for the charged current reactions and minor errors in their treatment of the constant terms for the neutral current induced reactions.