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Exact NLO matching and analyticity in b → sℓℓ
Journal of High Energy Physics ( IF 5.4 ) Pub Date : 2020-04-01 , DOI: 10.1007/jhep04(2020)012
Hrachia M. Asatrian , Christoph Greub , Javier Virto

Exclusive rare decays mediated by b → sll transitions receive contributions from four-quark operators that cannot be naively expressed in terms of local form factors. Instead, one needs to calculate a matrix element of a bilocal operator. In certain kinematic regions, this bilocal operator obeys some type of Operator Product Expansion, with coefficients that can be calculated in perturbation theory. We review the formalism and, focusing on the dominant SM operators O$_{1,2}$, we perform an improved calculation of the NLO matching for the leading dimension-three operators. This calculation is performed completely analytically in the two relevant mass scales (charm-quark mass mc and dilepton squared mass q$^{2}$), and we pay particular attention to the analytic continuation in the complex q$^{2}$ plane. This allows for the first time to study the analytic structure of the non-local form factors at NLO, and to calculate the OPE coefficients far below q$^{2}$ = 0, say $ {q}^2\underset{\sim }{<}-10{\mathrm{GeV}}^2 $. We also provide explicitly the contributions proportional to different charge factors, which obey separate dispersion relations.

中文翻译:

b → sℓℓ 中的精确 NLO 匹配和分析

由 b → sll 跃迁介导的独家稀有衰变接收来自四夸克算子的贡献,不能用局部形状因子天真地表达。相反,需要计算双局部算子的矩阵元素。在某些运动学区域,这个双局部算子服从某种类型的算子乘积扩展,其系数可以在微扰理论中计算。我们回顾了形式主义,并专注于主要的 SM 算子 O$_{1,2}$,我们对领先的三维算子进行了 NLO 匹配的改进计算。这个计算在两个相关的质量标度(粲夸克质量 mc 和双轻子平方质量 q$^{2}$)中完全解析进行,我们特别注意复数 q$^{2}$ 中的解析延拓飞机。这允许第一次研究非局部形状因子在 NLO 的解析结构,并计算远低于 q$^{2}$ = 0 的 OPE 系数,比如 $ {q}^2\underset{\ sim }{<}-10{\mathrm{GeV}}^2 $。我们还明确提供了与不同电荷因子成正比的贡献,它们服从单独的色散关系。
更新日期:2020-04-01
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