Renormalization group analysis of the QCD quark potential to order v^2

Abstract

A one-loop renormalization group analysis of the order v^2 relativistic corrections to the static QCD potential is presented. The velocity renormalization group is used to simultaneously sum ln(m/mv) and ln(m/mv^2) terms. The results are compared to previous calculations in the literature.

Figures (3)

• Figure 1: QCD diagrams for tree level matching.
• Figure 2: The Compton scattering diagrams (a,b,c) generate the soft gluon coupling (d) in the effective theory. Diagrams analogous to (c) but with external ghosts or massless quarks generate the soft ghost and massless soft quark couplings in Eq. (\ref{['Lsoft']}).
• Figure 3: Soft contributions to the running of the potential. The loop includes soft gluons, ghosts, and massless quarks. Graphs with two $\sigma=0$ vertices from Eq. (\ref{['Lsoft']}) gives the running of the coefficient ${\cal V}_c^{(T)}$. Graphs with one $\sigma=0$ and one $\sigma=1$ vertex vanish, while those with one $\sigma=0$ and one $\sigma=2$, or two $\sigma=1$ vertices contribute to the running of the order $v^2$ corrections to the potential.