From deconfinement to nuclear matter: mean-field approaches for effective Polyakov loop theories of lattice QCD

A bstract Numerical studies of the QCD phase diagram at finite baryon chemical potential μ B on the lattice are impeded by a sign problem. Effective Polyakov loop theories derived from lattice QCD via combined strong-coupling and hopping expansions are valid for heavy quarks only, but tractable with a significantly less severe sign problem. In this work, we apply three mean-field approximations to these effective theories, each incorporating local fluctuations to different degrees. We compare their predictions against Monte Carlo results for the deconfinement transition at high temperatures and for the baryon onset transition at low temperatures. In agreement with earlier effective theory simulations, we find a first-order nuclear liquid-gas transition with a critical end point for very low temperatures and moderately heavy quarks. While the location of fluctuation-dominated critical end points is expectedly inaccurate, the phase diagram of lattice QCD with heavy quarks can be determined qualitatively with entirely analytical methods.