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arXiv · 2606.05643

$\gamma W$-exchange correction beyond the forward-angle limit in neutron $\beta$ decay

Hui-Yun Cao·Hai-Qing Zhou
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Abstract

In this work, we discuss the $\gamma W$-exchange contributions in neutron $\beta$ decay with an elastic intermediate state, beyond the forward-angle limit (FAL). By decomposing the one-$W$-exchange and $\gamma W$-exchange amplitudes in terms of $16$ independent Pauli-spinor structures, we calculate the $\gamma W$-exchange corrections to the relevant coefficients. Our numerical results show that the relative corrections to the Fermi Born term $C_{\text{Born}}^{\text{F}}$ and the Gamow-Teller Born term $C_{\text{Born}}^{\text{GT}}$ are enhanced by about 8\% and 18\%, respectively. In particular, we find a non-zero contribution to $C_{\text{Born}}^{\text{GT}}$ from the axial-vector current, which is identically zero in the FAL. The corresponding effect on the extracted $V_{ud}$ from the neutron lifetime is also analyzed, and we find the correction to be at the $10^{-4}$ level.

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Hui-Yun Cao, Hai-Qing Zhou. 2026-06-04. $\gamma W$-exchange correction beyond the forward-angle limit in neutron $\beta$ decay. https://arxiv.org/abs/2606.05643

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