Abstract
We apply the relative weights method to SU(3) gauge theory with staggered fermions of mass 695 MeV at a set of temperatures in the range $151 \le T \le 267$ MeV, to obtain an effective Polyakov line action at each temperature. We then apply a mean-field method to search for phase transitions in the effective theory at finite densities. The result is a transition line in the plane of temperature and chemical potential, with an endpoint at high temperature, as expected, but also a second endpoint at a lower temperature. We cannot rule out the possibilities that a transition line reappears at temperatures lower than the range investigated, or that the second endpoint is absent for light quarks.
Highlights
The effective Polyakov line action (PLA) of a lattice gauge theory is the theory which results from integrating out all of the degrees of freedom of the theory, subject to the condition that the Polyakov lines are held fixed, and it is hoped that this effective theory is more tractable than the underlying lattice gauge theory (LGT) when confronting the sign problem at finite density
Whether a transition line reappears at still lower temperatures, outside the range we have investigated, or whether the second transition point disappears for lighter quarks, or whether this second transition point is instead indicative of some deficiency in our ansatz for the PLA, remains to be seen
With KðRÞ determined by the procedure just outlined, we find h by simulating the PLA in Eq (11) at μ 1⁄4 0 with a series of trial values of the h parameter, until hPi computed in the PLA agrees with the value computed in the LGT up to error bars
Summary
The effective Polyakov line action (PLA) of a lattice gauge theory is the theory which results from integrating out all of the degrees of freedom of the theory, subject to the condition that the Polyakov lines are held fixed, and it is hoped that this effective theory is more tractable than the underlying lattice gauge theory (LGT) when confronting the sign problem at finite density. Given the PLA at some fixed temperature T, we can apply a mean field method to search for phase transitions at finite chemical potential μ. This is the strategy which we have outlined in some detail in [6], where some preliminary results for finite densities were presented. For exploratory work, an ansatz for the PLA inspired first by the success of the relative weights method applied to pure gauge theories [5], and second by the form of the PLA obtained for heavy-dense quarks. A result for a recently introduced observable ξ=ξ2nd [10], which is sensitive to excitations above the lowest lying excitation, is presented in Appendix
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