The zero-temperature static potential

In this module are methods related to the zero-temperature static potential. This potential is sometimes used to renormalize Polyakov-loop observables, to extract reference scales like \(r_0\), or to improve short-distance lattice spacings at tree-level.

Tree-level improved distances

Short distances calculated directly from multiplying the separation by the lattice spacing are plagued by lattice artifacts. Therefore if one is interested in how an observable depends on \(r\), they should use tree-level improved distances for small \(r\). This calculation depends on \(N_s\). Given a maximum squared distance to improve r2max, the method

impdist(Ns,r2max)

returns a list of improved distances.

Zero temperature quark potential

The method

V_Teq0(r)

takes a distance \(r\) in fm and returns \(V\) in MeV. The potential comes from a three-parameter Levenberg-Marquardt fit of the data in Fig. 14 here to the form \(V(r)=a/r+b*r+c\), which is the Cornell parameterization.

There are also fit functions like fitV_Teq0, which can be used to extract fit parameters using a Cornell ansatz. Other possibilities include a parameterization including one-loop and two-loop corrections to the Coulomb part.