标题： 重夸克有效理论在小速度下的重整化 显示英文标题

标题： Renormalization of the effective theory for heavy quarks at small velocity

摘要： Isgur-Wise函数在归一化点$\xi^{(1)}(1)$处的斜率是提取自exclusive半轻子衰变数据中$CKM$矩阵元$V_{cb}$的基本参数之一。 在格点上测量这个参数的方法是重夸克小速度有效理论$v$。 该理论是重夸克有效理论的一种变体，在其中夸克的运动被当作微扰来处理。 在本工作中，我们研究了慢速重夸克有效理论的格点重整化。 我们表明$\xi^{(1)}(1)$的重整化不受紫外幂发散的影响，意味着不需要进行困难的非微扰减除。 因此，使用这种方法进行$\xi^{(1)}(1)$的格点计算在原则上是可行的。 有效理论中慢重夸克的一环重整化常数在$v^2$阶计算完成，同时计算了$\xi^{(1)}(1)$的格点-连续重整化常数。 我们证明了在重夸克速度展开可以正确地再现原始（未展开）理论的红外结构，每一阶都如此。 我们还计算了慢重夸克有效理论在$v^2$更高阶的单环重整化常数以及$\xi$函数的高阶导数的格点-连续重整化常数。 不幸的是，高阶导数的重整化常数受到紫外幂发散的影响，这意味着需要数值上的非微扰减去。 因此，Isgur-Wise 函数的高阶导数的格点计算似乎存在问题。 显示英文摘要

摘要： The slope of the Isgur-Wise function at the normalization point, $\xi^{(1)}(1)$,is one of the basic parameters for the extraction of the $CKM$ matrix element $V_{cb}$ from exclusive semileptonic decay data. A method for measuring this parameter on the lattice is the effective theory for heavy quarks at small velocity $v$. This theory is a variant of the heavy quark effective theory in which the motion of the quark is treated as a perturbation. In this work we study the lattice renormalization of the slow heavy quark effective theory. We show that the renormalization of $\xi^{(1)}(1)$ is not affected by ultraviolet power divergences, implying no need of difficult non-perturbative subtractions. A lattice computation of $\xi^{(1)}(1)$ with this method is therefore feasible in principle. The one-loop renormalization constants of the effective theory for slow heavy quarks are computed to order $v^2$ together with the lattice-continuum renormalization constant of $\xi^{(1)}(1)$ . We demonstrate that the expansion in the heavy-quark velocity reproduces correctly the infrared structure of the original (non-expanded) theory to every order. We compute also the one-loop renormalization constants of the slow heavy quark effective theory to higher orders in $v^2$ and the lattice-continuum renormalization constants of the higher derivatives of the $\xi$ function. Unfortunately, the renormalization constants of the higher derivatives are affected by ultraviolet power divergences, implying the necessity of numerical non-perturbative subtractions. The lattice computation of higher derivatives of the Isgur-Wise function seems therefore problematic.