Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

Abstract

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to O(a^n) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show, that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations.

arXiv comment19 pages, 7 plots

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Cited by in corpus (17)

• The chiral and deconfinement aspects of the QCD transition
• Equation of state and QCD transition at finite temperature
• The QCD equation of state from the lattice
• The physics of eight flavours
• QCD Thermodynamics from the Lattice
• Diagonal and off-diagonal quark number susceptibilities at high temperatures
• QCD Phase Diagram: Phase Transition, Critical Point and Fluctuations
• Equation of State in 2+1 Flavor QCD at High Temperatures
• Quark number susceptibilities at high temperatures
• Two-color quark matter: U(1)_A restoration, superfluidity, and quarkyonic phase
• The finite temperature QCD using 2+1 flavors of domain wall fermions at N_t = 8
• The phase structure of QCD
• Brillouin improvement for Wilson fermions
• Thermodynamics of the ideal overlap quarks on the lattice
• Cutoff effects of Wilson fermions on the QCD equation of state to O(g^2)
• Thermodynamics of free Domain Wall fermions
• Finite isospin density probe for conformality