The static potential in QCD to two loops

TL;DR

This work provides an analytic, gauge-compatible recalculation of the two-loop static QCD potential, determining the coefficient a2 with an independent method and identifying a significant correction to the pure gluonic contribution relative to prior results. Using a generalized Tarasov reduction to a small set of master integrals and a careful renormalization in ${ m ar{MS}}$, the authors reconcile the fermionic parts with previous findings while uncovering a 2π^2 discrepancy in the gluonic piece. They trace the discrepancy to a delta-function contribution from specific diagrams and show that the corrected a2 reduces the corresponding $\beta_2^{V}$ in the V-scheme, notably by about a factor of two for SU(3) with $n_f=5$. The results have direct implications for precision threshold studies, including top-antitop production and heavy quark mass definitions, where accurate two-loop potentials influence the derived observables.

Abstract

We evaluate the static QCD potential to two--loop order. Compared to a previous calculation a sizable reduction of the two--loop coefficient $a_2$ is found.

Figures (1)

• Figure 1: Classes of two--loop diagrams contributing to the static potential. Double, wiggly, dotted and solid lines denote source, gluon, ghost and (light) fermion propagators, respectively. A blob on a gluon line stands for one--loop self--energy corrections.