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arXiv 2302.05856hep-ph
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SCET位置空间表述中辐射喷注函数的规范不变性

Gauge invariance of radiative jet functions in the position-space formulation of SCET

Geoffrey T. Bodwin, June-Haak Ee, Daekyoung Kang, Xiang-Peng Wang

AI总结:

本文研究SCET位置空间表述中次领头幂次拉格朗日量的规范不变性问题,发现硬-共线扇区因规范变换导致动量跨扇区移动而破坏规范不变性,并通过加入软夸克运动方程项构造出对任意夸克质量均成立的规范不变拉格朗日量。

摘要:

在软-共线有效理论(SCET)的次领头幂次中,拉格朗日量包含软夸克与硬-共线夸克之间的耦合。这些耦合的硬-共线部分矩阵元是辐射喷注函数。在SCET的位置空间表述中,拉格朗日量由看似规范不变的算符构造而成。然而,我们发现硬-共线扇区中会出现规范不变性的破坏,因为规范变换可以将硬-共线夸克场的动量从硬-共线扇区移到软扇区,而根据定义,硬-共线场在软扇区没有支撑。规范不变性的破坏在硬-共线扇区的微扰论中表现为某些费曼图的缺失,而这些图在完整QCD中是存在的。这些图缺失的一个后果是,直接从位置空间拉格朗日量得到的辐射喷注函数不是规范不变的,我们通过低阶微扰论中的显式计算证明了这一点。我们通过在现有位置空间拉格朗日量中加入正比于软夸克运动方程的各项,得到了规范不变的拉格朗日量。这些规范不变的拉格朗日量对非零夸克质量以及零夸克质量均适用。我们还简要评述了在SCET的标签-动量表述中已构造的某些拉格朗日量的规范不变性。

英文摘要:

In subleading powers of soft-collinear effective theory (SCET), the Lagrangian contains couplings between soft quarks and hard-collinear quarks. Matrix elements of the hard-collinear parts of these couplings are radiative jet functions. In the position-space formulation of SCET, the Lagrangians are constructed from operators that appear to be gauge invariant. Nevertheless, we find violations of gauge invariance arise in the hard-collinear sector because gauge transformations can shift the momentum of a hard-collinear quark field from the hard-collinear sector to the soft sector, where the hard-collinear fields, by definition, have no support. The violations of gauge invariance are manifested in perturbation theory in the hard-collinear sector through the absence of certain Feynman diagrams that would be present in full QCD. A consequence of the absence of these diagrams is that the radiative jet functions that follow directly from the position-space Lagrangians are not gauge invariant, and we demonstrate this through explicit calculations in lower-order perturbation theory. We obtain gauge-invariant Lagrangians by adding to existing position-space Lagrangians terms that are proportional to the soft-quark equation of motion. These gauge-invariant Lagrangians are valid for nonzero, as well as zero, quark masses. We also remark briefly on the gauge invariance of certain Lagrangians that have been constructed in the label-momentum formulation of SCET.

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