Lin Guanda, Yang Gang, Zhang Siyuan
School of Physics, Peking University, Beijing 100871, China.
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China.
Phys Rev Lett. 2021 Oct 22;127(17):171602. doi: 10.1103/PhysRevLett.127.171602.
We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and also of a length-3 half-Bogomol'nyi-Prasad-Sommerfield operator in N=4 supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and nonplanar unitarity cuts, and they satisfy the minimal power counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the N=4 SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.
基于色动力学对偶性和壳上幺正性，我们得到了N = 4超对称杨 - 米尔斯（SYM）理论中应力张量超多重态以及一个长度为3的半博戈莫尔尼 - 普拉萨德 - 索末菲算子的全彩三环、三点形状因子。通过所有平面和非平面幺正性截断验证了被积函数结果，并且它们满足圈动量的最小幂次计数和图表对称性。有趣的是，这些三环解虽然体现了所有对偶雅可比关系，但包含大量自由参数；特别是，应力张量超多重态的形状因子有24个自由参数。这种自由度源于与形状因子的算子插入相关的一种新型广义规范变换。我们还进行了数值积分，得到了一致的全彩红外发散和已知的平面余项。我们得到的形状因子可以理解为 QCD 中三环希格斯加三胶子振幅的 N = 4 SYM 对应物，预计将提供后者的最大超越部分。
