Abstract
A three-dimensional effective lattice theory of Polyakov loops is derived from QCD by expansions in the fundamental character of the gauge action, u, and the hopping parameter, \kappa, whose action is correct to \kappa^n u^m with n+m=4. At finite baryon density, the effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes. The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential. In its region of convergence, it is moreover amenable to perturbative calculations in the small effective couplings. In this work we study the challenging cold and dense regime. We find unambiguous evidence for the nuclear liquid gas transition once the baryon chemical potential approaches the baryon mass, and calculate the nuclear equation of state. In particular, we find a negative binding energy per nucleon causing the condensation, whose absolute value decreases exponentially as mesons get heavier. For decreasing meson mass, we observe a first order liquid gas transition with an endpoint at some finite temperature, as well as gap between the onset of isospin and baryon condensation.
Highlights
The effective theory has a sign problem which meets all criteria to be simulated by complex Langevin as well as by Monte Carlo on small volumes
The theory is valid for the thermodynamics of heavy quarks, where its predictions agree with simulations of full QCD at zero and imaginary chemical potential
The phase diagram of QCD at finite temperature and baryon density is still largely unknown today, because lattice QCD suffers from a severe sign problem when chemical potential for baryon number is non-vanishing
Summary
The phase diagram of QCD at finite temperature and baryon density is still largely unknown today, because lattice QCD suffers from a severe sign problem when chemical potential for baryon number is non-vanishing. In this work we further elaborate on an effective theory approach [8,9,10,11], where analytic strong coupling and hopping expansion methods are used to derive an effective lattice action whose numerical simulation is feasible in the cold and dense regime. The effective theory is unsuitable for long range correlation functions, but it gives accurate results for bulk thermodynamic quantities and phase transitions [12] It has already provided predictions with better than 10% accuracy for the critical couplings of SU(2), SU(3) Yang-Mills [8], the critical quark masses where the deconfinement transition changes to a crossover [9] and the tricritical point of the deconfinement transition at imaginary chemical potential [13]. Readers not interested in the technical aspects of the derivation and simulation may skip sections 2, 4 and read sections 3, 5 only
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