Brüser R, Dlapa C, Henn J M, Yan K
Theoretische Physik 1, Naturwissenschaftlich-Technische Fakultät, Universität Siegen, 57068 Siegen, Germany.
Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, 80805 München, Germany.
Phys Rev Lett. 2021 Jan 15;126(2):021601. doi: 10.1103/PhysRevLett.126.021601.
The angle-dependent cusp anomalous dimension governs divergences coming from soft gluon exchanges between heavy particles, such as top quarks. We focus on the matter-dependent contributions and compute the first truly nonplanar terms. They appear at four loops and are proportional to a quartic Casimir operator in color space. Specializing our general gauge theory result to U(1), we obtain the full QED four-loop angle-dependent cusp anomalous dimension. While more complicated functions appear at intermediate steps, the analytic answer depends only on multiple polylogarithms with singularities at fourth roots of unity. It can be written in terms of four rational structures and contains functions of up to maximal transcendental weight seven. Despite this complexity, we find that numerically the answer is tantalizingly close to the appropriately rescaled one-loop formula, over most of the kinematic range. We take several limits of our analytic result, which serves as a check and allows us to obtain new, power-suppressed terms. In the antiparallel lines limit, which corresponds to production of two massive particles at threshold, we find that the subleading power correction vanishes. Finally, we compute the quartic Casimir contribution for scalars in the loop. Taking into account a supersymmetric decomposition, we derive the first nonplanar corrections to the quark antiquark potential in maximally supersymmetric gauge theory.
与角度相关的尖点反常维数控制着重粒子（如顶夸克）之间软胶子交换产生的发散。我们关注与物质相关的贡献，并计算出首个真正的非平面项。它们出现在四圈阶，且与色空间中的四次卡西米尔算符成正比。将我们的一般规范理论结果专门应用于U(1)，我们得到了完整的量子电动力学四圈与角度相关的尖点反常维数。虽然在中间步骤会出现更复杂的函数，但解析答案仅取决于在单位四次根处有奇点的多重多项对数。它可以用四种有理结构表示，并且包含最高超越权重为七的函数。尽管有这种复杂性，但我们发现，在数值上，在大多数运动学范围内，答案惊人地接近适当重标度的一圈公式。我们对解析结果取了几个极限，这既作为一种检验，又使我们能够得到新的、幂次压低的项。在反平行线极限下，这对应于在阈值处产生两个大质量粒子，我们发现次主导幂次修正消失。最后，我们计算了圈中标量的四次卡西米尔贡献。考虑到超对称分解，我们推导了最大超对称规范理论中夸克 - 反夸克势的首个非平面修正。
