AI 中文总结
该研究在vNRQCD框架下直接计算$B_c^{(*)}$衰变味改变非相对论流的两圈反常维度，结果与匹配计算一致且可约化为等质量夸克偶素极限，明确了超软诱导混合算符的作用。
AI 中文摘要
我们给出了vNRQCD（非相对论有效场论）对主导味改变非相对论流的两圈反常维度的直接计算，这类流支配$B_c$和$B_c^*$介子的轻子衰变。该计算在匹配标度$\nu=1$下完成，此处反常维度是抵消全QCD短距离系数剩余红外极点所需的紫外抵消项。与从这些红外极点的常规提取方式不同，我们直接在有效理论中确定流的重整化常数。赝标量和矢量道由一个自旋统一公式得到，自旋依赖通过$S(S+1)$引入。我们还阐明了不等质量理论中超软诱导混合算符的作用：它们对$\nu=1$以下的全速度跑动是必不可少的，但它们的威尔逊系数在匹配点处为零，不会改变本文报道的固定阶流反常维度。所得结果与已知的匹配计算一致，且平滑地约化为等质量夸克偶素极限。
英文摘要
We present a direct vNRQCD calculation of the two-loop anomalous dimensions of the leading flavor-changing nonrelativistic currents that govern the leptonic decays of the $B_c$ and $B_c^*$ mesons. The calculation is performed at the matching scale $ν=1$, where the anomalous dimensions are the ultraviolet counterterms required to cancel the residual infrared poles of the full-QCD short-distance coefficients. In contrast to the conventional extraction from those infrared poles, we determine the current renormalization constants directly in the effective theory. The pseudoscalar and vector channels are obtained from one spin-unified formula, with the spin dependence entering through $S(S+1)$. We also clarify the role of ultrasoft-induced mixing operators in the unequal-mass theory: they are essential for the full velocity running below $ν=1$, but their Wilson coefficients vanish at the matching point and do not alter the fixed-order current anomalous dimensions reported here. The results agree with the known matching calculations and reduce smoothly to the equal-mass quarkonium limits.
Comments12 pages, 2 figures
