Abstract
By studying an explicit analytical solution of the Schrödinger equation with the Coulomb potential on the lattice we demonstrate a breakdown of perturbative matching for the description of the Coulomb artifacts in lattice NRQCD, which leads to a large systematic error in the predictions for the heavy quarkonium spectrum. The breakdown is a result of a fine interplay between the short and long distance effects specific to the lattice regularization of NRQCD. We show how the problem can be solved by matching the lattice and continuum results for the solution of the full Schrödinger equation without the expansion in the Coulomb interaction.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W.E. Caswell and G.P. Lepage, Effective Lagrangians for Bound State Problems in QED, QCD and Other Field Theories, Phys. Lett. 167B (1986) 437 [INSPIRE].
G.T. Bodwin, E. Braaten and G.P. Lepage, Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium, Phys. Rev. D 51 (1995) 1125 [Erratum ibid. D 55 (1997) 5853] [hep-ph/9407339] [INSPIRE].
B.A. Thacker and G.P. Lepage, Heavy quark bound states in lattice QCD, Phys. Rev. D 43 (1991) 196 [INSPIRE].
G.P. Lepage, L. Magnea, C. Nakhleh, U. Magnea and K. Hornbostel, Improved nonrelativistic QCD for heavy quark physics, Phys. Rev. D 46 (1992) 4052 [hep-lat/9205007] [INSPIRE].
HPQCD collaboration, R.J. Dowdall et al., The Upsilon spectrum and the determination of the lattice spacing from lattice QCD including charm quarks in the sea, Phys. Rev. D 85 (2012) 054509 [arXiv:1110.6887] [INSPIRE].
T. Liu, A.A. Penin and A. Rayyan, Coulomb Artifacts and Bottomonium Hyperfine Splitting in Lattice NRQCD, JHEP 02 (2017) 084 [arXiv:1609.07151] [INSPIRE].
A.A. Kvitsinsky, Exact solution of the Coulomb problem on a lattice, J. Phys. A 25 (1992) 65.
R.J. Hill and G.P. Lepage, Order (α2Γ, α3Γ) binding effects in orthopositronium decay, Phys. Rev. D 62 (2000) 111301 [hep-ph/0003277] [INSPIRE].
E. Hairer, S.P. Nørsett and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, Springer Berlin Heidelberg (2008).
G.S. Bali and P. Boyle, A Lattice potential investigation of quark mass and volume dependence of the Upsilon spectrum, Phys. Rev. D 59 (1999) 114504 [hep-lat/9809180] [INSPIRE].
HPQCD collaboration, R.J. Dowdall et al., Bottomonium hyperfine splittings from lattice nonrelativistic QCD including radiative and relativistic corrections, Phys. Rev. D 89 (2014) 031502 [Erratum ibid. D 92 (2015) 039904] [arXiv:1309.5797] [INSPIRE].
T.C. Hammant, A.G. Hart, G.M. von Hippel, R.R. Horgan and C.J. Monahan, Radiative improvement of the lattice NRQCD action using the background field method and application to the hyperfine splitting of quarkonium states, Phys. Rev. Lett. 107 (2011) 112002 [Erratum ibid. 115 (2015) 039901] [arXiv:1105.5309] [INSPIRE].
B.A. Kniehl, A.A. Penin, A. Pineda, V.A. Smirnov and M. Steinhauser, M(eta(b)) and α s from nonrelativistic renormalization group, Phys. Rev. Lett. 92 (2004) 242001 [Erratum ibid. 104 (2010) 199901] [hep-ph/0312086] [INSPIRE].
T.C. Hammant, A.G. Hart, G.M. von Hippel, R.R. Horgan and C.J. Monahan, Radiative improvement of the lattice nonrelativistic QCD action using the background field method with applications to quarkonium spectroscopy, Phys. Rev. D 88 (2013) 014505 [Erratum ibid. D 92 (2015) 119904] [arXiv:1303.3234] [INSPIRE].
M. Baker, A.A. Penin, D. Seidel and N. Zerf, Bottomonium Hyperfine Splitting on the Lattice and in the Continuum, Phys. Rev. D 92 (2015) 054502 [arXiv:1504.05979] [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: 1710.03244
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
Penin, A.A., Rayyan, A. Coulomb artifacts and breakdown of perturbative matching in lattice NRQCD. J. High Energ. Phys. 2017, 7 (2017). https://doi.org/10.1007/JHEP12(2017)007
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2017)007