Analytic and numerical treatment of an effective lattice theory for heavy QCD at zero and finite density

  • We discuss aspects of the phase structure of a three-dimensional effective lattice theory of Polyakov loops derived from QCD by strong coupling and hopping parameter expansions. The theory is valid for the thermodynamics of heavy quarks where it shows all qualitative features of nuclear physics emerging from QCD. In particular, the SU(3) pure gauge effective theory also exhibits a first-order thermal deconfinement transition due to spontaneous breaking of its global Z₃ center symmetry. The presence of heavy dynamical quarks breaks this symmetry explicitly and consequently, the transition weakens with decreasing quark mass until it disappears at a critical endpoint. At non-zero baryon density, the effective theory can be evaluated either analytically by the so-called high-temperature expansion which does not suffer from the sign problem, or numerically by standard Monte-Carlo methods due to its mild sign problem. The first part of this work devotes to a systematic derivation of the effective theory up to the 6th order in the hopping parameter κ. This method combined with the SU(3) link update algorithm provides a way to simulate the O(κ⁶) effective theory. The second part involves a study of the deconfinement transition of the pure gauge effective theory, with and without static quarks, at all chemical potentials with help of the high-temperature expansion. Our estimate of the deconfinement transition and its critical endpoint as a function of quark mass and all chemical potentials agrees well with recent Monte-Carlo simulations. In the third part, we investigate the N ſ ∈ {1,2} effective theory with zero chemical potential up to O(κ⁴). We determine the location of the critical hopping parameter at which the first-order deconfinement phase transition terminates and changes to a crossover. Our results for the critical endpoint of the O(κ²) effective theory are in excellent agreement with the determinations from simulations of four-dimensional QCD with a hopping expanded determinant by the WHOT-QCD collaboration. For the O(κ⁴) effective theory, our estimate suggests that the critical quark mass increases as the order of κ-contributions increases. We also compare with full lattice QCD with N ſ = 2 degenerate standard Wilson fermions and thus obtain a measure for the validity of both the strong coupling and the hopping expansion in this regime.

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Author:Anh Quang PhamORCiDGND
Place of publication:Frankfurt am Main
Referee:Owe PhilipsenORCiDGND, Dirk H. RischkeORCiDGND
Document Type:Doctoral Thesis
Date of Publication (online):2022/06/12
Year of first Publication:2022
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2022/06/09
Release Date:2022/06/27
Page Number:137
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):License LogoDeutsches Urheberrecht