Abstract
We compute analytically the matter-dependent contributions to the quartic Casimir term of the four-loop lightlike cusp anomalous dimension in QCD, with n_{f} fermion and n_{s} scalar flavors. The result is extracted from the double pole of a scalar form factor. We adopt a new strategy for the choice of master integrals with simple analytic and infrared properties, which significantly simplifies our calculation. To this end, we first identify a set of integrals for which the integrands have a d log form, and are hence expected to have uniform transcendental weight. We then perform a systematic analysis of the soft and collinear regions of loop integration and build linear combinations of integrals with a simpler infrared pole structure. In this way, only integrals with ten or fewer propagators are needed for obtaining the cusp anomalous dimension. These integrals are then computed via the method of differential equations through the addition of an auxiliary scale. Combining our result with that of a parallel paper, we obtain the complete n_{f} dependence of the four-loop cusp anomalous dimension in QCD. Finally, using known numerical results for the gluonic contributions, we obtain an improved numerical prediction for the cusp anomalous dimension in N=4 super Yang-Mills theory.
Highlights
Introduction.—The cusp anomalous dimension is a universal quantity appearing in QCD
Further interest comes from the fact that these are the first truly nonplanar terms in N 1⁄4 4 super YangMills (SYM) theory
The planar cusp anomalous dimension is known from integrability [13], and it remains an open question whether integrability extends to the nonplanar sector
Summary
The quartic Casimir terms appear for the first time at four loops and, as a consequence of renormalizability, they come with a 1=ε2 pole (for which the coefficient is the cusp anomalous dimension). In order to take advantage of this fact, we classify the pure functions according to their soft and collinear divergence properties [23,27,28] In this way, we can arrange integrals having many propagators into linear combinations that have only 1=ε2 or better pole structure, and are irrelevant for the determination of the cusp anomalous dimension. We can arrange integrals having many propagators into linear combinations that have only 1=ε2 or better pole structure, and are irrelevant for the determination of the cusp anomalous dimension In this way, only a subset of form factor integrals is needed. We are interested in the four-loop contribution to F with the quartic Casimir structure [33]
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