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arXiv 2004.13193hep-phnucl-th
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内禀横动量与加权自旋不对称性的演化

Intrinsic Transverse Momentum and Evolution in Weighted Spin Asymmetries

Jian-Wei Qiu, Ted C. Rogers, Bowen Wang

摘要:

横向动量相关(TMD)和共线高扭理论因式分解是描述自旋相关硬截面的常用方法。特别感兴趣的是与目标束缚态相关的小横向动量的贡献。在唯象学应用中,这种贡献经常使用横向动量加权积分来研究,该积分可以急剧调节大的横向动量贡献,例如高斯参数化。由于结果是一种混合的TMD和共线(包括)的治疗,重要的是要建立如果和如何的形式主义是相关的加权积分可观的应用。例如,对大的横向动量尾的抑制可能会影响适用的演化类型。我们发现,一个天真的版本广泛使用的身份有关的$k_T^2$加权和集成Sivers TMD功能的重整化扭曲3功能具有强烈的模糊紫外贡献,它的修正不一定是微扰抑制。我们讨论了应用的影响,特别是认为,相关的演变横向动量加权和积分截面与尖锐的有效大横向动量截止的TMD形式,而不是标准的重整化群共线关联函数的演变。

英文摘要:

The transverse momentum dependent (TMD) and collinear higher twist theoretical factorization frameworks are the most frequently used approaches to describing spin dependent hard cross sections weighted by and integrated over transverse momentum. Of particular interest is the contribution from small transverse momentum associated with the target bound state. In phenomenological applications, this contribution is often investigated using transverse momentum weighted integrals that sharply regulate the large transverse momentum contribution, for example with Gaussian parametrizations. Since the result is a kind of hybrid of TMD and collinear (inclusive) treatments, it is important to establish if and how the formalisms are related in applications to weighted integral observables. The suppression of a large transverse momentum tail, for example, can potentially affect the type of evolution that is applicable. We find that a naive version of a widely used identity relating the $k_T^2$-weighted and integrated Sivers TMD function to a renormalized twist-3 function has strongly ambiguous ultraviolet contributions, and that corrections to it are not necessarily perturbatively suppressed. We discuss the implications for applications, arguing in particular that the relevant evolution for transverse momentum weighted and integrated cross sections with sharp effective large transverse momentum cutoffs is of the TMD form rather than the standard renormalization group evolution of collinear correlation functions.

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