Abstract
A major problem with periodic boundary condition on the gauge fields used in current lattice gauge theory simulations is the trapping of topological charge in a particular sector as the continuum limit is approached. To overcome this problem open boundary condition in the temporal direction has been proposed recently. One may ask whether open boundary condition can reproduce the observables calculated with periodic boundary condition. In this work we find that the extracted lowest glueball mass using open and periodic boundary conditions at the same lattice volume and lattice spacing agree for the range of lattice scales explored in the range 3 GeV ≤ \( \frac{1}{a} \) ≤ 5 GeV. The problem of trapping is overcome to a large extent with open boundary and we are able to extract the glueball mass at even larger lattice scale ≈ 5.7 GeV. To smoothen the gauge fields we have used recently proposed Wilson flow which, compared to HYP smearing, exhibits better systematics in the extraction of glueball mass. The extracted glueball mass shows remarkable insensitivity to the lattice spacings in the range explored in this work, 3 GeV ≤ \( \frac{1}{a} \) ≤ 5.7 GeV.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. Lüscher, Topology, the Wilson flow and the HMC algorithm, PoS(LATTICE2010)015 [arXiv:1009.5877] [INSPIRE].
M. Lüscher and S. Schaefer, Lattice QCD without topology barriers, JHEP 07 (2011) 036 [arXiv:1105.4749] [INSPIRE].
M. Lüscher and S. Schaefer, Lattice QCD with open boundary conditions and twisted-mass reweighting, Comput. Phys. Commun. 184 (2013) 519 [arXiv:1206.2809] [INSPIRE].
M. Grady, Connecting phase transitions between the 3 − D O(4) Heisenberg model and 4 − D SU(2) lattice gauge theory, arXiv:1104.3331 [INSPIRE].
E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson, Nucl. Phys. B 156 (1979) 269 [INSPIRE].
G. Veneziano, U(1) Without Instantons, Nucl. Phys. B 159 (1979) 213 [INSPIRE].
E. Seiler, Some more remarks on the Witten-Veneziano formula for the eta-prime mass, Phys. Lett. B 525 (2002) 355 [hep-th/0111125] [INSPIRE].
L. Del Debbio, L. Giusti and C. Pica, Topological susceptibility in the SU(3) gauge theory, Phys. Rev. Lett. 94 (2005) 032003 [hep-th/0407052] [INSPIRE].
S. Dürr, Z. Fodor, C. Hölbling and T. Kurth, Precision study of the SU(3) topological susceptibility in the continuum, JHEP 04 (2007) 055 [hep-lat/0612021] [INSPIRE].
M. Lüscher and F. Palombi, Universality of the topological susceptibility in the SU(3) gauge theory, JHEP 09 (2010) 110 [arXiv:1008.0732] [INSPIRE].
A. Chowdhury, A. Harindranath, J. Maiti and P. Majumdar, Topological susceptibility in lattice Yang-Mills theory with open boundary condition, JHEP 02 (2014) 045 [arXiv:1311.6599] [INSPIRE].
C.J. Morningstar and M.J. Peardon, Efficient glueball simulations on anisotropic lattices, Phys. Rev. D 56 (1997) 4043 [hep-lat/9704011] [INSPIRE].
C.J. Morningstar and M.J. Peardon, The Glueball spectrum from an anisotropic lattice study, Phys. Rev. D 60 (1999) 034509 [hep-lat/9901004] [INSPIRE].
Y. Chen, A. Alexandru, S.J. Dong, T. Draper, I. Horvath et al., Glueball spectrum and matrix elements on anisotropic lattices, Phys. Rev. D 73 (2006) 014516 [hep-lat/0510074] [INSPIRE].
M.J. Teper, Glueball masses and other physical properties of SU(N ) gauge theories in D = (3 + 1): A Review of lattice results for theorists, hep-th/9812187 [INSPIRE].
G.S. Bali, ‘Glueballs’: Results and perspectives from the lattice, hep-ph/0110254 [INSPIRE].
UKQCD collaboration, G.S. Bali et al., A Comprehensive lattice study of SU(3) glueballs, Phys. Lett. B 309 (1993) 378 [hep-lat/9304012] [INSPIRE].
A. Vaccarino and D. Weingarten, Glueball mass predictions of the valence approximation to lattice QCD, Phys. Rev. D 60 (1999) 114501 [hep-lat/9910007] [INSPIRE].
G. Parisi, Prolegomena to any future computer evaluation of the QCD mass spectrum, in Progress in gauge field theory: proceedings, G. ’t Hooft, A. Jaffe, H. Lehmann, P.K. Mitter, I. M. Singer, R. Stora eds., Plenum Press, 1984.
APE collaboration, M. Albanese et al., Glueball Masses and String Tension in Lattice QCD, Phys. Lett. B 192 (1987) 163 [INSPIRE].
A. Hasenfratz and F. Knechtli, Flavor symmetry and the static potential with hypercubic blocking, Phys. Rev. D 64 (2001) 034504 [hep-lat/0103029] [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].
M. Lüscher, Trivializing maps, the Wilson flow and the HMC algorithm, Commun. Math. Phys. 293 (2010) 899 [arXiv:0907.5491] [INSPIRE].
M. Lüscher, Properties and uses of the Wilson flow in lattice QCD, JHEP 08 (2010) 071 [arXiv:1006.4518] [INSPIRE].
M. Lüscher and P. Weisz, Perturbative analysis of the gradient flow in non-abelian gauge theories, JHEP 02 (2011) 051 [arXiv:1101.0963] [INSPIRE].
M.F. Atiyah and R. Bott, The Yang-Mills Equations over Riemann Surfaces, in Philosophical Transactions of the Royal Society of London, series A, Mathematical and Physical Sciences, vol. 308, no. 1505, Mar. 17, 1983, pg. 523.
M. Nakahara, Geometry, Topology and Physics, second edition, Taylor and Francis, 2003.
S.K. Donaldson and P.B. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, U.S.A., 1997.
B. Berg, Plaquette-plaquette Correlations in the SU(2) Lattice Gauge Theory, Phys. Lett. B 97 (1980) 401 [INSPIRE].
B. Berg and A. Billoire, Glueball Spectroscopy in Four-dimensional SU(3) Lattice Gauge Theory. 2., Nucl. Phys. B 226 (1983) 405 [INSPIRE].
ALPHA collaboration, M. Guagnelli, R. Sommer and H. Wittig, Precision computation of a low-energy reference scale in quenched lattice QCD, Nucl. Phys. B 535 (1998) 389 [hep-lat/9806005] [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].
S. Borsányi, S. Dürr, Z. Fodor, C. Hölbling, S.D. Katz et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [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: 1402.7138
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
Chowdhury, A., Harindranath, A. & Maiti, J. Open boundary condition, Wilson flow and the scalar glueball mass. J. High Energ. Phys. 2014, 67 (2014). https://doi.org/10.1007/JHEP06(2014)067
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2014)067