Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry
Scale-dependence of the $B$-meson LCDA beyond leading order from conformal symmetry
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DOI：
10.22323/1.375.0037
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
V. Braun;Yao Ji;A. Manashov
中科院分区：
文献类型：
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作者：
V. Braun;Yao Ji;A. Manashov
我们论证了B -介子光锥分布振幅（LCDA）的尺度依赖演化核可以在微扰理论的所有阶数上，用一种修正理论的特殊共形变换的产生器来表示：在非整数d\ neq4维中临界耦合的QCD。导出了演化核的特征函数的显式表达式，该表达式同样适用于所有阶。从实践者的角度来看，这种表示的效用在于，它允许“节省一个循环”，并从低一阶的保形异常计算中获得给定阶的扰动理论的演化核，直至常数项。通过双回路水平的显式计算验证了这种结构。
We argue that the evolution kernel for the scale-dependence of the $B$-meson light-cone distribution amplitude (LCDA) can be written, to all orders in perturbation theory, in terms of the generator of special conformal transformations in a modified theory: QCD at critical coupling in non-integer $d\neq 4$ dimensions. Explicit expression for the eigenfunctions of the evolution kernel is derived that is valid, again, to all orders. From a practitioner's point of view the utility of this representation is that it allows to "save one loop" and obtain the evolution kernel to a given order of perturbation theory, up to a constant term, from the calculation of the conformal anomaly at one order less. This construction is verified by explicit calculation at two-loop level.