The static quark potential in three flavor QCD

TL;DR

The paper investigates how dynamical quarks affect the static quark potential at short distances by comparing quenched and three-flavor QCD on matched lattices using improved actions. The static potential is extracted from Wilson-loop data in Coulomb gauge and fit to a Coulomb-plus-linear form $V(r)=C-\alpha/r+\sigma r$, with $r_0$ and $r_1$ derived from the fit; the results are then used to solve a nonrelativistic Schrödinger equation to estimate wavefunctions at the origin and related heavy-quark observables. The study finds that sea quarks deepen the short-distance potential, increasing $\Psi(0)$ and altering dimensionless scales like $r_0\sqrt{\sigma}$ and $r_1\sqrt{\sigma}$, with effects visible even for fairly heavy sea quarks. Crude Schrödinger-based estimates suggest increased heavy-light decay constants $f_B$, $f_{B_S}$ and larger quarkonium hyperfine splittings, though quantitative results depend on the scale definition ($r_0$, $r_1$, or $\sigma$). Overall, the work clarifies how dynamical quarks modify short-distance QCD dynamics and informs lattice-scale setting and phenomenology of heavy-quark systems.

Abstract

We study the effects of dynamical quarks on the static quark potential at distances shorter than those where string breaking is expected. Quenched calculations and calculations with three flavors of dynamical quarks are done on sets of lattices with the lattice spacings matched within about one percent. The effect of the sea quarks on the shape of the potential is clearly visible. We investigate the consequences of these effects in a very crude model, namely solving Schroedinger's equation in the resulting potential.

Figures (8)

• Figure 1: Accuracy of a lattice spacing determination from the static potential as a function of the distance at which the force is determined. The square is the point where $r^2 F(r)=1.65$ and the octagon the point where $r^2 F(r)=1$. The arrow is the accuracy of a string tension determination.
• Figure 2: The static quark potential in quenched QCD, with $10/g^2_{imp}=8.0$. Octagons are from time separation four to five, and diamonds from time separation three to four. The solid line is the Coulomb plus linear fit to the potential. Insets show the remaining lattice artifacts, as explained in the text. A constant has been subtracted from the potential to set $V(r_1)=0$. The vertical lines are at $r_1$ and $r_0$.
• Figure 3: The short distance part of the static quark potential in quenched QCD for two different lattice spacings. Octagons are from the $10/g^2=8.0$ run, and diamonds from the $10/g^2=8.4$ run. The solid lines are the Coulomb plus linear fit to the potentials, plotted in units of $r_1$. The upper two sets of vertical lines show the lattice spacings --- $a$, $2a$ … --- for the two runs, and the lower set is at spacings of $0.1$ fm, where the overall length scale was set by $r_0=0.50$ fm.
• Figure 4: The static quark potential for quenched (octagons) and three flavor (diamonds) QCD, in units of $r_1$. The solid lines are fits to the Coulomb plus constant plus linear form. The lattice spacing was matched using $r_1$ as described in the text. As in Fig. \ref{['POT_ASQ_FIG']}, the upper two rulers show the lattice spacing in the two runs, and the lower one shows units of $0.1$ fm. The inset expands the area shown by the box.
• Figure 5: Effects of dynamical quarks on the shape of the potential. Here we plot $r_0 \sqrt{\sigma}$ as a function of the quark mass. The quenched points are at the right, with the octagon coming from the $10/g^2=8.0$ run and the cross from the $10/g^2=8.4$ run. The remaining octagons are full QCD runs with three degenerate flavors, and the squares are full QCD runs with two light flavors and one heavy.