Coulomb artifacts and bottomonium hyperfine splitting in lattice NRQCD
We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a “na¨ıve” perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show that the correct matching procedure which provides full control over discretization errors is based on the asymptotic expansion of the lattice theory about the continuum limit, which gives M Y(1S) − M ηb (1S) = 52.9 ± 5.5 MeV .
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.
- Particle Data Group collaboration, J. Beringer et al., Review of Particle Physics (RPP), Phys. Rev. D 86 (2012) 010001 [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].