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 \(\mathcal{O}\)(an) 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.
Similar content being viewed by others
References
K. Symanzik, Nucl. Phys. B 226, 187 (1983)
K. Symanzik, Nucl. Phys. B 226, 205 (1983)
S. Naik, Nucl. Phys. B 316, 238 (1989)
F. Karsch, E. Laermann, A. Peikert, Nucl. Phys. B 605, 579 (2001)
B. Sheikholeslami, R. Wohlert, Nucl. Phys. B 259, 572 (1985)
P. Hasenfratz, F. Niedermayer, Nucl. Phys. B 414, 785 (1994)
P. Hasenfratz, S. Hauswirth, K. Holland, T. Jorg, F. Niedermayer, U. Wenger, Int. J. Mod. Phys. C 12, 691 (2001)
W. Bietenholz, U.-J. Wiese, Nucl. Phys. B 464, 319 (1996)
G. Boyd, J. Engels, F. Karsch, E. Laermann, C. Legeland, M. Lütgemeier, B. Petersson, Nucl. Phys. B 469, 419 (1996)
B. Beinlich, F. Karsch, E. Laermann, A. Peikert, Eur. Phys. J. C 6, 133 (1999)
C.R. Allton, S. Ejiri, S.J. Hands, O. Kaczmarek, F. Karsch, E. Laermann, C. Schmidt, Phys. Rev. D 68, 014507 (2003)
MILC Collaboration, C. Bernard et al., Phys. Rev. D 71, 034504 (2005)
MILC Collaboration, C. Bernard et al., Phys. Rev. D 77, 014503 (2008)
W. Bietenholz, U.-J. Wiese, Phys. Lett. B 426, 114 (1998)
C. Gattringer, L. Liptak, Phys. Rev. D 76, 054502 (2007)
P. Hasenfratz, F. Karsch, Phys. Lett. B 125, 308 (1983)
H.-T. Elze, K. Kajantie, J. Kapusta, Nucl. Phys. B 304, 832 (1988)
W. Bietenholz, R. Brower, S. Chandrasekharan, U.-J. Wiese, Nucl. Phys. Proc. Suppl. 53, 921 (1997)
S. Shcheredin, E. Laermann, PoS LAT2006, 146 (2006)
D.H. Adams, Nucl. Phys. Proc. Suppl. 129/130, 513 (2004)
R. Narayanan, H. Neuberger, Phys. Lett. B 302, 62 (1993)
R. Narayanan, H. Neuberger, Nucl. Phys. B 443, 305 (1995)
Y. Shamir, Nucl. Phys. B 406, 90 (1993)
D. Kaplan, Phys. Lett. B 417, 141 (1998)
S. Capitani, Phys. Rep. 382, 113 (2003), for a recent review
UKQCD Collaboration, G. Aarts, J. Foley, JHEP 0702, 062 (2007)
G.T. Fleming, Nucl. Phys. Proc. Suppl. 94, 393 (2001)
H. Neuberger, Phys. Rev. D 57, 5417 (1998)
R.G. Edwards, U.M. Heller, Phys. Rev. D 63, 094505 (2001)
N. Christ, private communication.
Author information
Authors and Affiliations
Corresponding author
Additional information
PACS
11.15.Ha; 11.10.Wx; 12.38.Gc; 12.38.Mh
Rights and permissions
About this article
Cite this article
Hegde, P., Karsch, F., Laermann, E. et al. Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential. Eur. Phys. J. C 55, 423–437 (2008). https://doi.org/10.1140/epjc/s10052-008-0613-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s10052-008-0613-7