QCD Cusp Anomalous Dimension: Current Status
International journal of modern physics A(2023)
摘要
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 $\gamma_h$ is known up to 4 loops. The cusp anomalous dimension $\Gamma(\varphi)$ is known up to 3 loops, and its small-angle and large-angle asymptotics -- up to 4 loops. Some (but not all) color structures at 4 loops are known with the full $\varphi$ dependence. Some simple contributions are known at higher loops. For the $\varphi\to\infty$ asymptotics of $\Gamma(\varphi)$ (the light-like cusp anomalous dimension) and the $\varphi^2$ term of the small-$\varphi$ expansion (the Bremsstrahlung function), the $\mathcal{N}=4$ SYM results are equal to the highest-weight parts of the QCD results. There is an interesting conjecture about the structure of $\Gamma(\varphi)$ which holds up to 3 loops; at 4 loops it holds for some color structures and breaks down for other ones. In cases when it holds it related highly non-trivial functions of $\varphi$, and it cannot be accidental; however, the reasons of this conjecture and its failures are not understood. The cusp anomalous dimension at Euclidean angle $\phi\to\pi$ 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 $\beta$ function. Some new results are also presented. Using the recent 4-loop result for $\gamma_h$, here we obtain analytical expressions for some terms in the 4-loop on-shell renormalization constant of the massive quark field $Z_Q^{\text{os}}$ which were previously known only numerically. We also present 2 new contribution to $\gamma_h$, $\Gamma(\varphi)$ at 5 loops and to the quark-antiquark potential at 4 loops.
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