论文标题
$ b_c^*$准确的衰减常数最多可至$ \ mathcal {o}（α_s^3）$
Decay constant of $B_c^*$ accurate up to $\mathcal{O}(α_s^3)$
论文作者
论文摘要
在本文中，我们评估了QCD临近到领先的订单，即$ b_c^*$衰减常数，在非递归QCD（NRQCD）框架内，该常数被分解为短途距离系数（SDC）的乘积和长距离固定矩阵元素。 NRQCD矢量电流的重新归一化常数和异常维度由$ c \ bar {b} $组成，它是Charm Quark Mass $ M_C $的功能，底部Quark Mass $ M_B $和分析级别$μ__}以$ \ n Mathcal Calcal Calcal cancal cancal c $}（分析）。 $ \ MATHCAL {O}（α_s^3）$。 SDC在扰动扩展中最多可计算出$ \ MATHCAL {O}（α_s^3）$。 Explicitly, the $\mathcal{O}(α_s^2)$ correction to the SDC is analytically calculated in terms of logarithmic and polylogarithmic functions of $r\equiv m_b/m_c$, and the $\mathcal{O}(α_s^3)$ correction to the SDC is numerically calculated at a series of values of $r$,从$ 2.1 $到$ 4.0 $不等。令人惊讶的是，我们发现SDC的非平凡部分是$ \ Mathcal {o}（α_s^3）$可以通过$ r $的线性函数很好地估计。此外，我们发现$ \ MATHCAL {O}（α_s^2）$和$ \ MATHCAL {O}（α_s^3）$对衰减常数的校正和衰减宽度相当大且非常重要，这表明对逆向扩张的融合非常差。
In this paper, we evaluate, up to QCD next-to-next-to-next-to-leading order, the $B_c^*$ decay constant, which, within the nonrelativistic QCD (NRQCD) framework, is factorized as the product of the short-distance coefficient (SDC) and the long-distance matrix element. For the first time, the renormalization constant and the anomalous dimension for the NRQCD vector current composed of $c\bar{b}$, which are functions of the charm quark mass $m_c$, the bottom quark mass $m_b$ and the factorization scale $μ_Λ$, are obtained analytically at $\mathcal{O}(α_s^2)$ and $\mathcal{O}(α_s^3)$. The SDC is calculated up to $\mathcal{O}(α_s^3)$ in perturbative expansion. Explicitly, the $\mathcal{O}(α_s^2)$ correction to the SDC is analytically calculated in terms of logarithmic and polylogarithmic functions of $r\equiv m_b/m_c$, and the $\mathcal{O}(α_s^3)$ correction to the SDC is numerically calculated at a series of values of $r$, ranging from $2.1$ to $4.0$. Surprisingly, we find that the nontrivial part of the SDC at $\mathcal{O}(α_s^3)$ can be well estimated by a linear function of $r$. In addition, We find that the $\mathcal{O}(α_s^2)$ and $\mathcal{O}(α_s^3)$ corrections to the decay constant and decay width are considerable and very significant, which indicates a very poor convergence for the perturbative expansion.
