Full Angle Dependence of the Four-Loop Cusp Anomalous Dimension in QED

Webs are sets of Feynman diagrams which manifest soft gluon exponentiation in gauge theory scattering amplitudes: individual webs contribute to the logarithm of the amplitude and their ultraviolet renormalization encodes its infrared structure. In this paper, we consider the particular class of boomerang webs, consisting of multiple gluon exchanges, but where at least one gluon has both of its endpoints on the same Wilson line. First, we use the replica trick to prove that diagrams involving self-energy insertions along the Wilson line do not contribute to the web, i.e. their exponentiated colour factor vanishes. Consequently boomerang webs effectively involve only integrals where boomerang gluons straddle one or more gluons that connect to other Wilson lines. Next we classify and calculate all boomerang webs involving semi-infinite non-lightlike Wilson lines up to three-loop order, including a detailed discussion of how to regulate and renormalize them. Furthermore, we show that they can be written using a basis of specific harmonic polylogarithms, that has been conjectured to be sufficient for expressing all multiple gluon exchange webs. However, boomerang webs differ from other gluon-exchange webs by featuring a lower and non-uniform transcendental weight. We cross-check our results by showing how certain boomerang webs can be determined by the so-called collinear reduction of previously calculated webs. Our results are a necessary ingredient of the soft anomalous dimension for non-lightlike Wilson lines at three loops.

“…(5.18) 10 We point out that prior to performing this integral we observed the same regularisation of the double pole at the x = 1 2 endpoint as in eq. (3.11).…”

Section: The (123) Websupporting

confidence: 60%

Section: Jhep12(2021)018 7 Discussionmentioning

confidence: 99%

“…In particular, a richer structure was found in the full angle-dependent cusp anomalous dimension in QCD at three loops in refs. [8,9] and also in QED at four loops [10].…”

Section: Jhep12(2021)018mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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