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arXiv 2107.07941hep-ph
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辐射喷流函数的重整化

Renormalization of the radiative jet function

Geoffrey T. Bodwin, June-Haak Ee, Jungil Lee, Xiang-Peng Wang

摘要:

我们展示了如何通过一个$b$ -夸克环直接计算出现在$B\to γ\ellν$和$H\to γγ$的因式分解定理中的辐射喷流函数的重整化/演化。我们指出,为了避免重复计算的软贡献,应该使用的因式分解定理减去辐射射流功能,从软贡献已被删除。软贡献减法是软共线有效理论术语中的零仓减法。我们表明,它们可以从辐射射流函数中分解出来,并且由此产生的软减函数引起减辐射射流函数的非局部重整化。这是一个新的例子,其中零仓减法导致非局部性的重正化的减去的量,不存在于重正化的未减去的量。我们证明了使用我们的形式主义通过计算的顺序- $α_s$演变内核减去辐射射流功能。我们的结果与以前利用$B\to γ\ellν$的因式分解定理推导出的结果一致,但这是由于未减辐射喷流函数。

英文摘要:

We show how to compute directly the renormalization/evolution of the radiative jet function that appears in the factorization theorems for $B\to γ\ellν$ and $H\to γγ$ through a $b$-quark loop. We point out that, in order to avoid double counting of soft contributions, one should use in the factorization theorems a subtracted radiative jet function, from which soft contributions have been removed. The soft-contribution subtractions are zero-bin subtractions in the terminology of soft-collinear effective theory. We show that they can be factored from the radiative jet function and that the resulting soft-subtraction function gives rise to a nonlocal renormalization of the subtracted radiative jet function. This is a novel instance in which zero-bin subtractions lead to a nonlocality in the renormalization of a subtracted quantity that is not present in the renormalization of the unsubtracted quantity. We demonstrate the use of our formalism by computing the order-$α_s$ evolution kernel for the subtracted radiative jet function. Our result is in agreement with the result that had been inferred previously by making use of the factorization theorem for $B\to γ\ellν$, but that had been ascribed to the unsubtracted radiative jet function.

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