Equation of state for cold and dense heavy QCD

Abstract

A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order $\sim u^5{\kappa }^8$ in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.

30 pages, 16 figure; figures updated for readability, caption fig 10 updated

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• A new dual representation for staggered lattice QCD
• Complex spectrum of finite-density lattice QCD with static quarks at strong coupling
• Beyond Complex Langevin Equations: positive representation of a class of complex measures
• Positive Representations of a Class of Complex Measures
• The SU(3) spin model with chemical potential by series expansion techniques
• Towards a theoretical description of dense QCD
• Strong coupling methods in QCD thermodynamics
• QCD at high temperature and density: selected highlights