论文标题
QCD跟踪异常及其应用的三环校正和GLUON分解
Three-loop corrections to the quark and gluon decomposition of the QCD trace anomaly and their applications
论文作者
论文摘要
在QCD Energy-Momentum Tensor $ t^{μν} $中，对物理矩阵元素的术语表示为量规不变性夸克部分和gluon部分的总和。由于夸克和胶子之间的相互作用，每个部分都经过重新归一化，尽管由于能量和动量的保护，总张量$ t^{μν} $未重新归一化。我们表明，通过重新规定，$ t^{μν} $的每个夸克和gluon部分都会收到一定量的异常痕量贡献，因此它们的总和复制了众所周知的QCD痕量痕量异常。我们提供了一个程序，以在扰动理论中的所有订单中为每个Quark/Gluon部分获得此类异常的痕量贡献，并在$ \ edline {\ rm MS} $方案中获得相应的显式公式，最高为三环订单。我们应用痕量异常的夸克/Gluon分解的三环公式来计算核子和亲核的异常质量结构。我们三环公式的另一个应用是对核子扭曲四重力形式的约束的定量分析，$ \ bar {c} _ {q，g} $。
In the QCD energy-momentum tensor $T^{μν}$, the terms that contribute to physical matrix elements are expressed as the sum of the gauge-invariant quark part and gluon part. Each part undergoes the renormalization due to the interactions among quarks and gluons, although the total tensor $T^{μν}$ is not renormalized thanks to conservation of energy and momentum. We show that, through the renormalization, each of the quark and gluon parts of $T^{μν}$ receives a definite amount of anomalous trace contribution, such that their sum reproduces the well-known QCD trace anomaly. We provide a procedure to derive such anomalous trace contribution for each quark/gluon part to all orders in perturbation theory, and obtain the corresponding explicit formulas up to three-loop order in the $\overline{\rm MS}$ scheme in the dimensional regularization. We apply our three-loop formulas of the quark/gluon decomposition of the trace anomaly to calculate the anomaly-induced mass structure of nucleons as well as pions. Another application of our three-loop formulas is a quantitative analysis for the constraints on the twist-four gravitational form factors of the nucleon, $\bar{C}_{q,g}$.
