Grand Canonical Potential for a Static Quark-Antiquark Pair at finite chemical potential

The grand canonical potential for a static quark-antiquark pair at non-vanishing chemical potential was determined at several temperatures. The dynamical staggered simulations were carried out with 2+1 physical quarks along the Lines of Constant Physiscs (LCP). c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. Forces among infinitely heavy quarks separated by distance r are of significance both at T = 0 and when they are surrounded by an interacting medium. This paper is an extension of [1], where a reweighting technique was used to compute the grand canonical potential of a q ¯ q pair surrounded by a medium of finite chemical potential µ along the transition line. In this work two other temperatures, one above and one below the transition temperature, will be examined. All simulations were carried out for 2+1 flavours with physical quark masses along a line of constant physics (LCP). As we want to perform all our finite temperature simulations on lattices of size 4 × 12 3 , we have to control the temperature T = 1/(4a) by the lattice spacing a. But on changing a it is also necessary to tune the mass parametersˆm u,d andˆm s accordingly, where the hat denotes the quantities in lattice units. To determine this so called line of constant physics, we carried out zero temperature simulations for several values of the gauge coupling β and of the mass parameters (see Table 1). We used 2 + 1 flavours with dynamical staggered fermions. A few hundred configurations were generated for each parameter set using the R-algorithm and setting the microcanonical stepsize to half of the light quark mass. We measuredˆm π , ˆ m ρ , ˆ m K , ˆ r 0 andˆσ at 3 quark masses for each β in β ˆ m u,d ˆ m s Table 1: Parameters used for the zero temperature simulations. order to extrapolate to physical masses. The lattice sizes ranged from 24 × 12 3 for coarse lattices over 32 × 16 3 to 48 × 24 3 for finer lattices, so that even for the lightest quark masses m π L > 4, where L is the spatial extent of the lattice. The ratio m π /m ρ was set to its physical value (0.179) in order to fixˆm u,d as a function of β and m π /m K was set to …