Conformal symmetry assisted perturbative calculations in QCD

本课题研究利用共形对称性计算量子色动力学（QCD）中的高阶微扰修正。这种宣传的方法分离了相关的量，比如在“保形部分”中重整化群方程的异常维数，以及与QCD β函数成比例的附加修正。这可以通过考虑非整数维的QCD来形式化，d = 4 - 2epsilon，在所谓的消失β函数的Banks-Zaks临界点处，这里的关键兴趣量是光线算子的共形异常。该方法已成功地应用于推导出QCD中风味非单重态下次至次阶广义部子分布的演化方程。提出的项目寻求共形对称性的帮助，以计算在次至次至前阶的广义部分子分布的味道单重态异常维，以及深度虚拟康普顿散射的系数函数。它的目的是在Banks-Zaks临界点处建立微扰QCD，作为更大类可观测值的计算工具。

The project pursues the computation of higher order perturbative corrections in QuantumChromodynamics (QCD) by utilizing conformal symmetry. The advertised approach separates the relevant quantities such as anomalous dimensions for renormalization group equations in a "conformal part" and additional corrections proportional to the QCD beta-function. This can be formalized by considering QCD in non-integer dimensions, d = 4 - 2epsilon, at the so-called Banks-Zaks critical point for a vanishing beta-function with the quantity of key interest here being the conformal anomaly of light-ray operators. The approach has already been successfully applied to derive the evolution equations for generalized parton distributions at the next-to-next-toleading order in QCD in the flavor non-singlet case. The proposed project seeks assistance from conformal symmetry to compute also the flavor singlet anomalous dimensions of generalized parton distributions at the next-to-next-to-leading order as well as the coefficient functions for deeply-virtual Compton scattering. It aims at establishing perturbative QCD at the Banks-Zaks critical point as a computational tool for larger classes of observables.