Abstract
We develop an improved lattice action for heavy quarks based on Brillouintype fermions, that have excellent energy-momentum dispersion relation. The leading discretization errors of O(a) and O(a 2) are eliminated at tree-level. We carry out a scaling study of this improved Brillouin fermion action on quenched lattices by calculating the charmonium energy-momentum dispersion relation and hyperfine splitting. We present a comparison to standard Wilson fermions and domain-wall fermions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
HPQCD, UKQCD collaboration, E. Follana et al., Highly improved staggered quarks on the lattice, with applications to charm physics, Phys. Rev. D 75 (2007) 054502 [hep-lat/0610092] [INSPIRE].
HPQCD, UKQCD collaboration, E. Follana, C.T.H. Davies, G.P. Lepage and J. Shigemitsu, High Precision determination of the π, K, D and D(s) decay constants from lattice QCD, Phys. Rev. Lett. 100 (2008) 062002 [arXiv:0706.1726] [INSPIRE].
C.T.H. Davies et al., Update: precision D s decay constant from full lattice QCD using very fine lattices, Phys. Rev. D 82 (2010) 114504 [arXiv:1008.4018] [INSPIRE].
C. McNeile, C.T.H. Davies, E. Follana, K. Hornbostel and G.P. Lepage, High-precision \( {f_B}_{{}_s} \) and HQET from relativistic lattice QCD, Phys. Rev. D 85 (2012) 031503 [arXiv:1110.4510] [INSPIRE].
H. Na, C.T.H. Davies, E. Follana, G.P. Lepage and J. Shigemitsu, The D → K, lν semileptonic decay scalar form factor and |V cs | from Lattice QCD, Phys. Rev. D 82 (2010) 114506 [arXiv:1008.4562] [INSPIRE].
H. Na et al., D → π, lν semileptonic decays, |V cd | and 2 nd row unitarity from lattice QCD, Phys. Rev. D 84 (2011) 114505 [arXiv:1109.1501] [INSPIRE].
K. Symanzik, Continuum limit and improved action in lattice theories. 1. Principles and ϕ 4 theory, Nucl. Phys. B 226 (1983) 187 [INSPIRE].
K. Symanzik, Continuum limit and improved action in lattice theories. 2. O(N ) nonlinear σ-model in perturbation theory, Nucl. Phys. B 226 (1983) 205 [INSPIRE].
B. Sheikholeslami and R. Wohlert, Improved continuum limit lattice action for QCD with Wilson fermions, Nucl. Phys. B 259 (1985) 572 [INSPIRE].
T. Eguchi and N. Kawamoto, Improved lattice action for Wilson fermion, Nucl. Phys. B 237 (1984) 609 [INSPIRE].
H.W. Hamber and C.M. Wu, Some predictions for an improved fermion action on the lattice, Phys. Lett. B 133 (1983) 351 [INSPIRE].
M.G. Alford, T.R. Klassen and G.P. Lepage, Improving lattice quark actions, Nucl. Phys. B 496 (1997) 377 [hep-lat/9611010] [INSPIRE].
S. Dürr and G. Koutsou, Brillouin improvement for Wilson fermions, Phys. Rev. D 83 (2011) 114512 [arXiv:1012.3615] [INSPIRE].
R.C. Brower, H. Neff and K. Orginos, The Möbius domain wall fermion algorithm, arXiv:1206.5214 [INSPIRE].
P.H. Ginsparg and K.G. Wilson, A remnant of chiral symmetry on the lattice, Phys. Rev. D 25 (1982) 2649 [INSPIRE].
H. Neuberger, Exactly massless quarks on the lattice, Phys. Lett. B 417 (1998) 141 [hep-lat/9707022] [INSPIRE].
H. Neuberger, More about exactly massless quarks on the lattice, Phys. Lett. B 427 (1998) 353 [hep-lat/9801031] [INSPIRE].
M. Creutz, T. Kimura and T. Misumi, Index theorem and overlap formalism with naive and minimally doubled fermions, JHEP 12 (2010) 041 [arXiv:1011.0761] [INSPIRE].
W. Bietenholz and I. Hip, The scaling of exact and approximate Ginsparg-Wilson fermions, Nucl. Phys. B 570 (2000) 423 [hep-lat/9902019] [INSPIRE].
W. Bietenholz, Approximate Ginsparg-Wilson fermions for QCD, hep-lat/0007017 [INSPIRE].
C. Gattringer, A new approach to Ginsparg-Wilson fermions, Phys. Rev. D 63 (2001) 114501 [hep-lat/0003005] [INSPIRE].
C. Gattringer, I. Hip and C.B. Lang, Approximate Ginsparg-Wilson fermions: a first test, Nucl. Phys. B 597 (2001) 451 [hep-lat/0007042] [INSPIRE].
H. Ikeda and S. Hashimoto, O(a 2) improvement of the overlap-Dirac operator, PoS(LAT2009)082 [arXiv:0912.4119] [INSPIRE].
S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].
C. Morningstar and M.J. Peardon, Analytic smearing of SU(3) link variables in lattice QCD, Phys. Rev. D 69 (2004) 054501 [hep-lat/0311018] [INSPIRE].
S. Hashimoto et al., Residual mass in five-dimensional fermion formulations, PoS(LATTICE 2013)431.
UKQCD collaboration, M. Foster and C. Michael, Quark mass dependence of hadron masses from lattice QCD, Phys. Rev. D 59 (1999) 074503 [hep-lat/9810021] [INSPIRE].
A.X. El-Khadra, A.S. Kronfeld and P.B. Mackenzie, Massive fermions in lattice gauge theory, Phys. Rev. D 55 (1997) 3933 [hep-lat/9604004] [INSPIRE].
T.A. DeGrand, One loop matching coefficients for a variant overlap action: And some of its simpler relatives, Phys. Rev. D 67 (2003) 014507 [hep-lat/0210028] [INSPIRE].
QCD-TARO collaboration, S. Choe et al., Quenched charmonium spectrum, JHEP 08 (2003) 022 [hep-lat/0307004] [INSPIRE].
C. Lehner, Automated lattice perturbation theory and relativistic heavy quarks in the Columbia formulation, PoS(LATTICE 2012)126 [arXiv:1211.4013] [INSPIRE].
G. Cossu et al., JLQCD IroIro++ lattice code on BG/Q, arXiv:1311.0084 [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: 1504.01630
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
Cho, YG., Hashimoto, S., Jüttner, A. et al. Improved lattice fermion action for heavy quarks. J. High Energ. Phys. 2015, 72 (2015). https://doi.org/10.1007/JHEP05(2015)072
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2015)072