QCD cusp anomalous dimension: Current status

Abstract

Calculation results for the HQET field anomalous dimension and the QCD cusp anomalous dimension, as well as their properties, are reviewed. The HQET field anomalous dimension [Formula: see text] is known up to four loops. The cusp anomalous dimension [Formula: see text] is known up to three loops, and its small-angle and large-angle asymptotics up to four loops. Some (but not all) color structures at four loops are known with the full [Formula: see text]-dependence. Some simple contributions are known at higher loops. For the [Formula: see text] asymptotics of [Formula: see text] (the light-like cusp anomalous dimension) and the [Formula: see text]-term of the small-[Formula: see text] expansion (the Bremsstrahlung function), the [Formula: see text] SYM results are equal to the highest-weight parts of the QCD results. There is an interesting conjecture about the structure of [Formula: see text] which holds up to three loops; at four loops it holds for some color structures and breaks down for other ones. In the cases when it holds, it related highly nontrivial functions of [Formula: see text], and it cannot be accidental; however, the reasons of this conjecture and its failures are not understood. The cusp anomalous dimension at the Euclidean angle [Formula: see text] is related to the static quark–antiquark potential due to conformal symmetry; in QCD, this relation is broken by an anomalous term proportional to the [Formula: see text]-function. Some new results are also presented. Using the recent four-loop result for [Formula: see text], here we obtain analytical expressions for some terms in the four-loop on-shell renormalization constant of the massive quark field [Formula: see text] which were previously known only numerically. We also present two new contributions to [Formula: see text], [Formula: see text] at five loops and to the quark–antiquark potential at four loops.