Papers
Topics
Authors
Recent
2000 character limit reached

Static force from generalized Wilson loops on the lattice using the gradient flow (2312.17231v3)

Published 28 Dec 2023 in hep-lat, hep-ph, hep-th, and nucl-th

Abstract: The static QCD force from the lattice can be used to extract $\Lambda_{\overline{\textrm{MS}}}$, which determines the running of the strong coupling. Usually, this is done with a numerical derivative of the static potential. However, this introduces additional systematic uncertainties; thus, we use another observable to measure the static force directly. This observable consists of a Wilson loop with a chromoelectric field insertion. We work in the pure SU(3) gauge theory. We use gradient flow to improve the signal-to-noise ratio and to address the field insertion. We extract $\Lambda_{\overline{\textrm{MS}}}{n_f=0}$ from the data by exploring different methods to perform the zero-flow-time limit. We obtain the value $\sqrt{8t_0} \Lambda_{\overline{\textrm{MS}}}{n_f=0} =0.629{+22}_{-26}$, where $t_0$ is a flow-time reference scale. We also obtain precise determinations of several scales: $r_0/r_1$, $\sqrt{8 t_0}/r_0$, $\sqrt{8 t_0}/r_1$ and we compare these to the literature. The gradient flow appears to be a promising method for calculations of Wilson loops with chromoelectric and chromomagnetic insertions in quenched and unquenched configurations

Definition Search Book Streamline Icon: https://streamlinehq.com
References (72)
  1. Y. Aoki et al. (Flavour Lattice Averaging Group (FLAG)), “FLAG Review 2021,” Eur. Phys. J. C 82, 869 (2022), arXiv:2111.09849 [hep-lat] .
  2. D. d’Enterria et al., “The strong coupling constant: State of the art and the decade ahead,”   (2022), arXiv:2203.08271 [hep-ph] .
  3. Mattia Dalla Brida, Roman Höllwieser, Francesco Knechtli, Tomasz Korzec, Alessandro Nada, Alberto Ramos, Stefan Sint,  and Rainer Sommer (ALPHA), “Determination of αs⁢(mZ)subscript𝛼𝑠subscript𝑚𝑍\alpha_{s}(m_{Z})italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT ( italic_m start_POSTSUBSCRIPT italic_Z end_POSTSUBSCRIPT ) by the non-perturbative decoupling method,” Eur. Phys. J. C 82, 1092 (2022), arXiv:2209.14204 [hep-lat] .
  4. Silvia Necco and Rainer Sommer, “The N(f) = 0 heavy quark potential from short to intermediate distances,” Nucl. Phys. B 622, 328–346 (2002), arXiv:hep-lat/0108008 .
  5. Marco Guagnelli, Rainer Sommer,  and Hartmut Wittig (ALPHA), “Precision computation of a low-energy reference scale in quenched lattice QCD,” Nucl. Phys. B 535, 389–402 (1998), arXiv:hep-lat/9806005 .
  6. R. Sommer, “A New way to set the energy scale in lattice gauge theories and its applications to the static force and αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT in SU(2) Yang-Mills theory,” Nucl. Phys. B 411, 839–854 (1994), arXiv:hep-lat/9310022 .
  7. Gunnar S. Bali and Klaus Schilling, “Running coupling and the Lambda parameter from SU(3) lattice simulations,” Phys. Rev. D 47, 661–672 (1993), arXiv:hep-lat/9208028 .
  8. S. P. Booth, D. S. Henty, A. Hulsebos, A. C. Irving, Christopher Michael,  and P. W. Stephenson (UKQCD), “The Running coupling from SU(3) lattice gauge theory,” Phys. Lett. B 294, 385–390 (1992), arXiv:hep-lat/9209008 .
  9. Nora Brambilla, Xavier Garcia i Tormo, Joan Soto,  and Antonio Vairo, “Precision determination of r0⁢ΛM⁢S−subscript𝑟0superscriptsubscriptΛ𝑀𝑆r_{0}\Lambda_{MS}^{-}italic_r start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT roman_Λ start_POSTSUBSCRIPT italic_M italic_S end_POSTSUBSCRIPT start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT from the QCD static energy,” Phys. Rev. Lett. 105, 212001 (2010), [Erratum: Phys.Rev.Lett. 108, 269903 (2012)], arXiv:1006.2066 [hep-ph] .
  10. Nikolai Husung, Mateusz Koren, Philipp Krah,  and Rainer Sommer, “SU(3) Yang Mills theory at small distances and fine lattices,” EPJ Web Conf. 175, 14024 (2018), arXiv:1711.01860 [hep-lat] .
  11. Nikolai Husung, Peter Marquard,  and Rainer Sommer, “Asymptotic behavior of cutoff effects in Yang–Mills theory and in Wilson’s lattice QCD,” Eur. Phys. J. C 80, 200 (2020), arXiv:1912.08498 [hep-lat] .
  12. Karl Jansen, Felix Karbstein, Attila Nagy,  and Marc Wagner (ETM), “ΛM⁢S¯subscriptΛ¯𝑀𝑆\Lambda_{\bar{MS}}roman_Λ start_POSTSUBSCRIPT over¯ start_ARG italic_M italic_S end_ARG end_POSTSUBSCRIPT from the static potential for QCD with nf=2subscript𝑛𝑓2n_{f}=2italic_n start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT = 2 dynamical quark flavors,” JHEP 01, 025 (2012), arXiv:1110.6859 [hep-ph] .
  13. Alexei Bazavov, Nora Brambilla, Xavier Garcia i Tormo, Peter Petreczky, Joan Soto,  and Antonio Vairo, “Determination of αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT from the QCD static energy,” Phys. Rev. D 86, 114031 (2012), arXiv:1205.6155 [hep-ph] .
  14. Alexei Bazavov, Nora Brambilla, Xavier Garcia Tormo, I, Peter Petreczky, Joan Soto,  and Antonio Vairo, “Determination of αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT from the QCD static energy: An update,” Phys. Rev. D 90, 074038 (2014), [Erratum: Phys.Rev.D 101, 119902 (2020)], arXiv:1407.8437 [hep-ph] .
  15. Alexei Bazavov, Nora Brambilla, Xavier Garcia i Tormo, Péter Petreczky, Joan Soto, Antonio Vairo,  and Johannes Heinrich Weber (TUMQCD), “Determination of the QCD coupling from the static energy and the free energy,” Phys. Rev. D 100, 114511 (2019), arXiv:1907.11747 [hep-lat] .
  16. Cesar Ayala, Xabier Lobregat,  and Antonio Pineda, “Determination of α⁢(Mz)𝛼subscript𝑀𝑧\alpha(M_{z})italic_α ( italic_M start_POSTSUBSCRIPT italic_z end_POSTSUBSCRIPT ) from an hyperasymptotic approximation to the energy of a static quark-antiquark pair,” JHEP 09, 016 (2020), arXiv:2005.12301 [hep-ph] .
  17. Nora Brambilla, Antonio Pineda, Joan Soto,  and Antonio Vairo, “The Infrared behavior of the static potential in perturbative QCD,” Phys. Rev. D 60, 091502 (1999), arXiv:hep-ph/9903355 .
  18. Antonio Pineda and Joan Soto, “The Renormalization group improvement of the QCD static potentials,” Phys. Lett. B 495, 323–328 (2000), arXiv:hep-ph/0007197 .
  19. Nora Brambilla, Xavier Garcia i Tormo, Joan Soto,  and Antonio Vairo, “The Logarithmic contribution to the QCD static energy at N**4 LO,” Phys. Lett. B 647, 185–193 (2007), arXiv:hep-ph/0610143 .
  20. Nora Brambilla, Antonio Vairo, Xavier Garcia i Tormo,  and Joan Soto, “The QCD static energy at NNNLL,” Phys. Rev. D 80, 034016 (2009), arXiv:0906.1390 [hep-ph] .
  21. Alexander V. Smirnov, Vladimir A. Smirnov,  and Matthias Steinhauser, “Three-loop static potential,” Phys. Rev. Lett. 104, 112002 (2010), arXiv:0911.4742 [hep-ph] .
  22. Antonio Vairo, “A low-energy determination of αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT at three loops,” EPJ Web Conf. 126, 02031 (2016a), arXiv:1512.07571 [hep-ph] .
  23. Antonio Vairo, “Strong coupling from the QCD static energy,” Mod. Phys. Lett. A 31, 1630039 (2016b).
  24. Nora Brambilla, Antonio Pineda, Joan Soto,  and Antonio Vairo, “The QCD potential at O(1/m),” Phys. Rev. D 63, 014023 (2001), arXiv:hep-ph/0002250 .
  25. Nora Brambilla, Viljami Leino, Owe Philipsen, Christian Reisinger, Antonio Vairo,  and Marc Wagner, “Lattice gauge theory computation of the static force,” Phys. Rev. D 105, 054514 (2022a), arXiv:2106.01794 [hep-lat] .
  26. R. Narayanan and H. Neuberger, “Infinite N phase transitions in continuum Wilson loop operators,” JHEP 03, 064 (2006), arXiv:hep-th/0601210 .
  27. Martin Lüscher, “Trivializing maps, the Wilson flow and the HMC algorithm,” Commun. Math. Phys. 293, 899–919 (2010a), arXiv:0907.5491 [hep-lat] .
  28. Martin Lüscher, “Properties and uses of the Wilson flow in lattice QCD,” JHEP 08, 071 (2010b), [Erratum: JHEP 03, 092 (2014)], arXiv:1006.4518 [hep-lat] .
  29. Andreas Risch, Stefan Schaefer,  and Rainer Sommer, “The influence of gauge field smearing on discretisation effects,” PoS LATTICE2022, 384 (2023), arXiv:2212.04000 [hep-lat] .
  30. Andreas Risch, “Gauge field smearing and controlled continuum extrapolations,” in 40th International Symposium on Lattice Field Theory (2023) arXiv:2310.06587 [hep-lat] .
  31. Masanori Okawa and Antonio Gonzalez-Arroyo, ‘‘String tension from smearing and Wilson flow methods,” PoS LATTICE2014, 327 (2014), arXiv:1410.7862 [hep-lat] .
  32. Alexei Bazavov, Daniel Hoying, Olaf Kaczmarek, Rasmus N. Larsen, Swagato Mukherjee, Peter Petreczky, Alexander Rothkopf,  and Johannes Heinrich Weber, “Un-screened forces in Quark-Gluon Plasma?”   (2023), arXiv:2308.16587 [hep-lat] .
  33. Alexei Bazavov and Thomas Chuna, “Efficient integration of gradient flow in lattice gauge theory and properties of low-storage commutator-free Lie group methods,”  (2021), arXiv:2101.05320 [hep-lat] .
  34. Nora Brambilla, Hee Sok Chung, Antonio Vairo,  and Xiang-Peng Wang, “QCD static force in gradient flow,” JHEP 01, 184 (2022b), arXiv:2111.07811 [hep-ph] .
  35. Viljami Leino, Nora Brambilla, Julian Mayer-Steudte,  and Antonio Vairo, “The static force from generalized Wilson loops using gradient flow,” EPJ Web Conf. 258, 04009 (2022), arXiv:2111.10212 [hep-lat] .
  36. Julian Mayer-Steudte, Nora Brambilla, Viljami Leino,  and Antonio Vairo, “Implications of gradient flow on the static force,” PoS LATTICE2022, 353 (2023), arXiv:2212.12400 [hep-lat] .
  37. Kenneth G. Wilson, “Confinement of Quarks,” Phys. Rev. D 10, 2445–2459 (1974).
  38. Martin Luscher, “Topology, the Wilson flow and the HMC algorithm,” PoS LATTICE2010, 015 (2010), arXiv:1009.5877 [hep-lat] .
  39. Martin Luscher and Peter Weisz, “Perturbative analysis of the gradient flow in non-abelian gauge theories,” JHEP 02, 051 (2011), arXiv:1101.0963 [hep-th] .
  40. Patrick Fritzsch and Alberto Ramos, “The gradient flow coupling in the Schrödinger Functional,” JHEP 10, 008 (2013), arXiv:1301.4388 [hep-lat] .
  41. Sundance O. Bilson-Thompson, Derek B. Leinweber,  and Anthony G. Williams, “Highly improved lattice field strength tensor,” Annals Phys. 304, 1–21 (2003), arXiv:hep-lat/0203008 .
  42. G. Peter Lepage and Paul B. Mackenzie, “On the viability of lattice perturbation theory,” Phys. Rev. D 48, 2250–2264 (1993), arXiv:hep-lat/9209022 .
  43. C. Christensen and M. Laine, “Perturbative renormalization of the electric field correlator,” Phys. Lett. B 755, 316–323 (2016), arXiv:1601.01573 [hep-lat] .
  44. Nora Brambilla, Viljami Leino, Julian Mayer-Steudte,  and Peter Petreczky (TUMQCD), “Heavy quark diffusion coefficient with gradient flow,” Phys. Rev. D 107, 054508 (2023), arXiv:2206.02861 [hep-lat] .
  45. Luis Altenkort, Alexander M. Eller, Olaf Kaczmarek, Lukas Mazur, Guy D. Moore,  and Hai-Tao Shu, “Heavy quark momentum diffusion from the lattice using gradient flow,” Phys. Rev. D 103, 014511 (2021), arXiv:2009.13553 [hep-lat] .
  46. Johannes Heinrich Weber, Alexei Bazavov,  and Peter Petreczky, “Equation of state in (2+1) flavor QCD at high temperatures,” PoS Confinement2018, 166 (2019), arXiv:1811.12902 [hep-lat] .
  47. Patrick Fritzsch, Alberto Ramos,  and Felix Stollenwerk, “Critical slowing down and the gradient flow coupling in the Schrödinger functional,” PoS Lattice2013, 461 (2014), arXiv:1311.7304 [hep-lat] .
  48. William I. Jay and Ethan T. Neil, “Bayesian model averaging for analysis of lattice field theory results,” Phys. Rev. D 103, 114502 (2021), arXiv:2008.01069 [stat.ME] .
  49. Zoltan Fodor, Kieran Holland, Julius Kuti, Santanu Mondal, Daniel Nogradi,  and Chik Him Wong, “The lattice gradient flow at tree-level and its improvement,” JHEP 09, 018 (2014), arXiv:1406.0827 [hep-lat] .
  50. Claude W. Bernard, Tom Burch, Kostas Orginos, Doug Toussaint, Thomas A. DeGrand, Carleton E. DeTar, Steven A. Gottlieb, Urs M. Heller, James E. Hetrick,  and Bob Sugar, “The Static quark potential in three flavor QCD,” Phys. Rev. D 62, 034503 (2000), arXiv:hep-lat/0002028 .
  51. Rainer Sommer, “Scale setting in lattice QCD,” PoS LATTICE2013, 015 (2014), arXiv:1401.3270 [hep-lat] .
  52. Mattia Bruno and Rainer Sommer (ALPHA), “On the Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT-dependence of gluonic observables,” PoS LATTICE2013, 321 (2014), arXiv:1311.5585 [hep-lat] .
  53. Masayuki Asakawa, Tetsuo Hatsuda, Takumi Iritani, Etsuko Itou, Masakiyo Kitazawa,  and Hiroshi Suzuki, “Determination of Reference Scales for Wilson Gauge Action from Yang–Mills Gradient Flow,”   (2015), arXiv:1503.06516 [hep-lat] .
  54. A. Francis, O. Kaczmarek, M. Laine, T. Neuhaus,  and H. Ohno, “Critical point and scale setting in SU(3) plasma: An update,” Phys. Rev. D 91, 096002 (2015), arXiv:1503.05652 [hep-lat] .
  55. Marco Cè, Cristian Consonni, Georg P. Engel,  and Leonardo Giusti, “Non-Gaussianities in the topological charge distribution of the SU(3) Yang–Mills theory,” Phys. Rev. D 92, 074502 (2015), arXiv:1506.06052 [hep-lat] .
  56. Norihiko Kamata and Shoichi Sasaki, “Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory,” Phys. Rev. D 95, 054501 (2017), arXiv:1609.07115 [hep-lat] .
  57. Francesco Knechtli, Tomasz Korzec, Björn Leder,  and Graham Moir (ALPHA), “Power corrections from decoupling of the charm quark,” Phys. Lett. B 774, 649–655 (2017), arXiv:1706.04982 [hep-lat] .
  58. Leonardo Giusti and Martin Lüscher, “Topological susceptibility at T>Tc𝑇subscript𝑇cT>T_{\rm c}italic_T > italic_T start_POSTSUBSCRIPT roman_c end_POSTSUBSCRIPT from master-field simulations of the SU(3) gauge theory,” Eur. Phys. J. C 79, 207 (2019), arXiv:1812.02062 [hep-lat] .
  59. Mattia Dalla Brida and Alberto Ramos, “The gradient flow coupling at high-energy and the scale of SU(3) Yang–Mills theory,” Eur. Phys. J. C 79, 720 (2019), arXiv:1905.05147 [hep-lat] .
  60. Yoshiaki Koma, Miho Koma,  and Hartmut Wittig, “Relativistic corrections to the static potential at O(1/m) and O(1/m**2),” PoS LATTICE2007, 111 (2007), arXiv:0711.2322 [hep-lat] .
  61. Antonio Gonzalez-Arroyo and Masanori Okawa, “The string tension from smeared Wilson loops at large N,” Phys. Lett. B 718, 1524–1528 (2013), arXiv:1206.0049 [hep-th] .
  62. Biagio Lucini, Michael Teper,  and Urs Wenger, “The High temperature phase transition in SU(N) gauge theories,” JHEP 01, 061 (2004), arXiv:hep-lat/0307017 .
  63. B. Beinlich, F. Karsch, E. Laermann,  and A. Peikert, “String tension and thermodynamics with tree level and tadpole improved actions,” Eur. Phys. J. C 6, 133–140 (1999), arXiv:hep-lat/9707023 .
  64. Stefano Capitani, Martin Lüscher, Rainer Sommer,  and Hartmut Wittig, “Non-perturbative quark mass renormalization in quenched lattice QCD,” Nucl. Phys. B 544, 669–698 (1999), [Erratum: Nucl.Phys.B 582, 762–762 (2000)], arXiv:hep-lat/9810063 .
  65. M. Gockeler, R. Horsley, A. C. Irving, D. Pleiter, P. E. L. Rakow, G. Schierholz,  and H. Stuben, “A Determination of the Lambda parameter from full lattice QCD,” Phys. Rev. D 73, 014513 (2006), arXiv:hep-ph/0502212 .
  66. Ken-Ichi Ishikawa, Issaku Kanamori, Yuko Murakami, Ayaka Nakamura, Masanori Okawa,  and Ryoichiro Ueno, “Non-perturbative determination of the ΛΛ\Lambdaroman_Λ-parameter in the pure SU(3) gauge theory from the twisted gradient flow coupling,” JHEP 12, 067 (2017), arXiv:1702.06289 [hep-lat] .
  67. Masakiyo Kitazawa, Takumi Iritani, Masayuki Asakawa, Tetsuo Hatsuda,  and Hiroshi Suzuki, “Equation of State for SU(3) Gauge Theory via the Energy-Momentum Tensor under Gradient Flow,” Phys. Rev. D 94, 114512 (2016), arXiv:1610.07810 [hep-lat] .
  68. Chik Him Wong, Szabolcs Borsanyi, Zoltan Fodor, Kieran Holland,  and Julius Kuti, “Toward a novel determination of the strong QCD coupling at the Z-pole,” PoS LATTICE2022, 043 (2023), arXiv:2301.06611 [hep-lat] .
  69. Anna Hasenfratz, Curtis Taylor Peterson, Jake van Sickle,  and Oliver Witzel, “ΛΛ\Lambdaroman_Λ parameter of the SU(3) Yang-Mills theory from the continuous β𝛽\betaitalic_β function,” Phys. Rev. D 108, 014502 (2023), arXiv:2303.00704 [hep-lat] .
  70. K. G. Chetyrkin, Johann H. Kuhn,  and M. Steinhauser, “RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses,” Comput. Phys. Commun. 133, 43–65 (2000), arXiv:hep-ph/0004189 .
  71. Barbara Schmidt and Matthias Steinhauser, “CRunDec: a C++ package for running and decoupling of the strong coupling and quark masses,” Comput. Phys. Commun. 183, 1845–1848 (2012), arXiv:1201.6149 [hep-ph] .
  72. Florian Herren and Matthias Steinhauser, “Version 3 of RunDec and CRunDec,” Comput. Phys. Commun. 224, 333–345 (2018), arXiv:1703.03751 [hep-ph] .
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now

Whiteboard

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up for Free