### Strong-coupling lattice QCD on anisotropic lattices

Philippe de Forcrand (Institut für Theoretische Physik, ETH Zürich, CH-8093 Zürich, Switzerland; CERN, TH Department, CH-1211 Geneva 23, Switzerland) ; Wolfgang Unger (Fakultät für Physik, Universität Bielefeld, Universitätstrasse 25, D33619 Bielefeld, Germany) ; Hélvio Vairinhos ()

Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong-coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalization of the anisotropy coupling in strongly coupled $\mathrm{SU}\left({N}_{c}\right)$ or $U\left({N}_{c}\right)$ lattice QCD with massless staggered fermions. We then compute the renormalized anisotropy, and the strong-coupling analogue of Karsch’s coefficients (the running anisotropy), for ${N}_{c}=3$. We achieve high precision by combining diagrammatic Monte Carlo and multihistogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong-coupling limit at zero temperature.

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"value": "Anisotropic lattice spacings are mandatory to reach the high temperatures where chiral symmetry is restored in the strong-coupling limit of lattice QCD. Here, we propose a simple criterion for the nonperturbative renormalization of the anisotropy coupling in strongly coupled $<mrow><mi>SU</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow>$ or $<mrow><mi>U</mi><mo>(</mo><msub><mrow><mi>N</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>)</mo></mrow>$ lattice QCD with massless staggered fermions. We then compute the renormalized anisotropy, and the strong-coupling analogue of Karsch\u2019s coefficients (the running anisotropy), for $<msub><mi>N</mi><mi>c</mi></msub><mo>=</mo><mn>3</mn>$. We achieve high precision by combining diagrammatic Monte Carlo and multihistogram reweighting techniques. We observe that the mean field prediction in the continuous time limit captures the nonperturbative scaling, but receives a large, previously neglected correction on the unit prefactor. Using our nonperturbative prescription in place of the mean field result, we observe large corrections of the same magnitude to the continuous time limit of the static baryon mass and of the location of the phase boundary associated with chiral symmetry restoration. In particular, the phase boundary, evaluated on different finite lattices, has a dramatically smaller dependence on the lattice time extent. We also estimate, as a byproduct, the pion decay constant and the chiral condensate of massless SU(3) QCD in the strong-coupling limit at zero temperature."
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Published on:
28 February 2018
Publisher:
APS
Published in:
Physical Review D , Volume 97 (2018)
Issue 3
DOI:
https://doi.org/10.1103/PhysRevD.97.034512
arXiv:
1710.00611
Copyrights:
Published by the American Physical Society
Licence:
CC-BY-4.0

Fulltext files: