Verifying the Gell-Mann-Oakes-Renner relation for heavy simulated quarks in quenched lattice QCD
DOI:
https://doi.org/10.64804/849yxn31Keywords:
lattice, Gell-Mann-Oakes-Renner relation, quantum chromodynamics, QCD, quantum field theory, QFT, quenched lattice, simulation, quarks, pion, mass, quenched, C++, GMORAbstract
Since its inception in the 1970s, lattice quantum chromodynamics (QCD) has revolutionized the study of quantum particles by allowing extremely difficult quantum field theory (QFT) calculations to be accomplished computationally and by providing an effective way to compare theoretical predictions with experiment. In this paper, we investigate the application of quenched lattice QCD to verify the Gell-Mann-Oakes-Renner (GMOR) relation, which states that the squared pion mass is proportional to the sum of the up and down quark masses. In our simulation, we restricted ourselves to relatively large simulated quark masses. We conclude that several improvements to the simulation are necessary before it can accurately verify the GMOR relation.
References
B A Berg, Markov Chain Monte Carlo Simulations and Their Statistical Analysis: with Web-based Fortran Code, World Scientific, 2006. DOI: https://doi.org/10.1142/9789812700919_0001
S Chib and E Greenberg, Understanding the Metropolis-Hastings algorithm, The American Statistician 49 (1995), 327–335. DOI: https://doi.org/10.1080/00031305.1995.10476177
S Dürr, Gauge action improvement and smearing, Comput. Phys. Commun. 172 (2005), 163–186. DOI: https://doi.org/10.1016/j.cpc.2005.06.011
C Gattringer and C B Lang, Quantum Chromodynamics on the Lattice: an Introductory Presentation, vol. 788, Springer, 2010. DOI: https://doi.org/10.1007/978-3-642-01850-3
G Guennebaud, B Jacob, et al., Eigen, https://libeigen.gitlab.io, 2010.
S Necco and R Sommer, The Nf = 0 heavy quark potential from short to intermediate distances, Nucl. Phys. B 622 (2002), 328–346. DOI: https://doi.org/10.1016/S0550-3213(01)00582-X
M D Schwartz, Quantum Field Theory and the Standard Model, Cambridge University Press, 2014. DOI: https://doi.org/10.1017/9781139540940
R Sommer, O(a) improved lattice QCD, Nucl. Phys. B 60 (1998), 279–293. DOI: https://doi.org/10.1016/S0920-5632(97)00490-8
A W Thomas, Chiral corrections for lattice QCD, Australian Journal of Physics 44 (1991), 173–180. DOI: https://doi.org/10.1071/PH910173
H A Van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 13 (1992), 631–644. DOI: https://doi.org/10.1137/0913035
Downloads
Published
Data Availability Statement
C++ source code for the lattice QCD simulations is available on Github at https://github.com/DavidPevzner17/pion-correlators
Issue
Section
License
Copyright (c) 2026 Journal of Science & Engineering
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
How to Cite
