Abstract
A previously derived three-dimensional effective lattice theory describing the thermodynamics of QCD with heavy quarks in the cold and dense region is extended through order ∼ u 5 κ 8 in the combined character and hopping expansion of the original four-dimensional Wilson action. The systematics of the effective theory is investigated to determine its range of validity in parameter space. We demonstrate the severe cut-off effects due to lattice saturation, which afflict any lattice results at finite baryon density independent of the sign problem or the quality of effective theories, and which have to be removed by continuum extrapolation. We then show how the effective theory can be solved analytically by means of a linked cluster expansion, which is completely unaffected by the sign problem, in quantitative agreement with numerical simulations. As an application, we compute the cold nuclear equation of state of heavy QCD. Our continuum extrapolated result is consistent with a polytropic equation of state for non-relativistic fermions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. de Forcrand, Simulating QCD at finite density, PoS(LAT2009)010 [arXiv:1005.0539] [INSPIRE].
G. Aarts, L. Bongiovanni, E. Seiler, D. Sexty and I.-O. Stamatescu, Controlling complex Langevin dynamics at finite density, Eur. Phys. J. A 49 (2013) 89 [arXiv:1303.6425] [INSPIRE].
D. Sexty, Simulating full QCD at nonzero density using the complex Langevin equation, Phys. Lett. B 729 (2014) 108 [arXiv:1307.7748] [INSPIRE].
G. Aarts, E. Seiler, D. Sexty and I.-O. Stamatescu, Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion, Phys. Rev. D 90 (2014) 114505 [arXiv:1408.3770] [INSPIRE].
P. de Forcrand, J. Langelage, O. Philipsen and W. Unger, Lattice QCD Phase Diagram In and Away from the Strong Coupling Limit, Phys. Rev. Lett. 113 (2014) 152002 [arXiv:1406.4397] [INSPIRE].
E.T. Tomboulis, Chiral symmetry in SU(N c ) gauge theories at high density, Int. J. Mod. Phys. A 29 (2014) 1445004 [arXiv:1403.0664] [INSPIRE].
M. Fromm, J. Langelage, S. Lottini and O. Philipsen, The QCD deconfinement transition for heavy quarks and all baryon chemical potentials, JHEP 01 (2012) 042 [arXiv:1111.4953] [INSPIRE].
M. Fromm, J. Langelage, S. Lottini, M. Neuman and O. Philipsen, Onset Transition to Cold Nuclear Matter from Lattice QCD with Heavy Quarks, Phys. Rev. Lett. 110 (2013) 122001 [arXiv:1207.3005] [INSPIRE].
J. Langelage, M. Neuman and O. Philipsen, Heavy dense QCD and nuclear matter from an effective lattice theory, JHEP 09 (2014) 131 [arXiv:1403.4162] [INSPIRE].
P. Scior and L. von Smekal, Baryonic Matter Onset in Two-Color QCD with Heavy Quarks, Phys. Rev. D 92 (2015) 094504 [arXiv:1508.00431] [INSPIRE].
P.M. Lo, B. Friman and K. Redlich, Polyakov loop fluctuations and deconfinement in the limit of heavy quarks, Phys. Rev. D 90 (2014) 074035 [arXiv:1406.4050] [INSPIRE].
C.S. Fischer, J. Luecker and J.M. Pawlowski, Phase structure of QCD for heavy quarks, Phys. Rev. D 91 (2015) 014024 [arXiv:1409.8462] [INSPIRE].
M. Wortis, Linked Cluster Expansion, in Phase Transitions and Critical Phenomena. Volume 3. Series Expansions for Lattice Models, C. Domb and M.S. Green eds., Academic Press, New York U.S.A. (1974) [INSPIRE].
J. Langelage, S. Lottini and O. Philipsen, Centre symmetric 3d effective actions for thermal SU(N ) Yang-Mills from strong coupling series, JHEP 02 (2011) 057 [Erratum ibid. 07 (2011) 014] [arXiv:1010.0951] [INSPIRE].
T. Rindlisbacher and P. de Forcrand, Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry, JHEP 02 (2016) 051 [arXiv:1509.00087] [INSPIRE].
G. Bergner, J. Langelage and O. Philipsen, Effective lattice Polyakov loop theory vs. full SU(3) Yang-Mills at finite temperature, JHEP 03 (2014) 039 [arXiv:1312.7823] [INSPIRE].
G. Bergner, J. Langelage and O. Philipsen, Numerical corrections to the strong coupling effective Polyakov-line action for finite T Yang-Mills theory, JHEP 11 (2015) 010 [arXiv:1505.01021] [INSPIRE].
J. Smit, Introduction to quantum fields on a lattice: A robust mate, Cambridge Lect. Notes Phys. 15 (2002) 1 [INSPIRE].
S. Necco and R. Sommer, The N f = 0 heavy quark potential from short to intermediate distances, Nucl. Phys. B 622 (2002) 328 [hep-lat/0108008] [INSPIRE].
ALPHA collaboration, J. Heitger and R. Sommer, Nonperturbative heavy quark effective theory, JHEP 02 (2004) 022 [hep-lat/0310035] [INSPIRE].
J. Langelage and O. Philipsen, The deconfinement transition of finite density QCD with heavy quarks from strong coupling series, JHEP 01 (2010) 089 [arXiv:0911.2577] [INSPIRE].
J. Langelage, G. Münster and O. Philipsen, Strong coupling expansion for finite temperature Yang-Mills theory in the confined phase, JHEP 07 (2008) 036 [arXiv:0805.1163] [INSPIRE].
J. Langelage and O. Philipsen, The pressure of strong coupling lattice QCD with heavy quarks, the hadron resonance gas model and the large-N limit, JHEP 04 (2010) 055 [arXiv:1002.1507] [INSPIRE].
A.J. Guttman, Asymptotic Analysis of Power-Series Expansions, in Phase Transitions and Critical Phenomena. Volume 13, C. Domb and J.L. Lebowitz eds., Academic Press, London U.K. (1989).
I. Montvay and G. Münster, Quantum fields on a lattice, Cambridge monographs on mathematical physics, Cambridge University Press, Cambridge U.K. (1994).
M. Creutz, On invariant integration over SU(N ), J. Math. Phys. 19 (1978) 2043 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1512.05195
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Glesaaen, J., Neuman, M. & Philipsen, O. Equation of state for cold and dense heavy QCD. J. High Energ. Phys. 2016, 100 (2016). https://doi.org/10.1007/JHEP03(2016)100
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2016)100