We present the first lattice QCD calculation of the universal axial $\gamma W$-box contribution ${\square }_{\gamma W}^{VA}$ to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of $|V_{ud}|$ from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at ${\square }_{\gamma W}^{VA}=3.65(7{)}_{\mathrm{lat}}(1{)}_{\mathrm{PT}}\times {10}^{-3}$. Consequently, this yields a slightly higher value of $|V_{ud}|=0.97386(11{)}_{\exp }(9{)}_{\mathrm{RC}}(27{)}_{\mathrm{NS}}$, reducing the previous $2.1\sigma$ tension with the CKM unitarity to $1.8\sigma$. Additionally, we calculate the vector $\gamma W$-box contribution to the axial charge $g_A$, denoted as ${\square }_{\gamma W}^{VV}$, and explore its potential implications.

中文翻译：

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电弱盒对超允许核和中子 Beta 衰变贡献的晶格 QCD 计算

我们提出了万向轴的第一个晶格 QCD 计算$\gamma 瓦$盒子贡献${\square }_{\gamma 瓦}^{VA}$超允许的核和中子β衰变。这一贡献成为围绕提取的理论不确定性的一个重要组成部分。$|V_{你d}|$来自超级允许的衰变。我们的计算是使用物理π介子质量下的两个畴壁费米子系综进行的。为了构造核子四点相关函数，我们采用随机稀疏场技术。此外，我们使用无限体积重建方法将长距离贡献纳入强子函数。执行连续统外推后，我们得出${\square }_{\gamma 瓦}^{VA}=3.65（7{）}_{\mathrm{拉特}}（1{）}_{\mathrm{PT}}\times {10}^{-3}$。因此，这会产生稍高的值$|V_{你d}|=0.97386（11{）}_{\mathrm{经验值}}（9{）}_{\mathrm{RC}}（27{）}_{\mathrm{NS}}$，减少之前的$2.1\sigma$与 CKM 统一性的张力$1.8\sigma$。另外，我们计算向量$\gamma 瓦$-盒对轴向电荷的贡献$G_A$，表示为${\square }_{\gamma 瓦}^{VV}$，并探讨其潜在影响。