Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Infrared fixed point in the massless twelve-flavor SU(3) gauge-fermion system (2402.18038v2)

Published 28 Feb 2024 in hep-lat, hep-ph, and hep-th

Abstract: We present strong numerical evidence for the existence of an infrared fixed point in the renormalization group flow of the SU(3) gauge-fermion system with twelve massless fermions in the fundamental representation. Our numerical simulations using nHYP-smeared staggered fermions with Pauli-Villars improvement do not exhibit any first-order bulk phase transition in the investigated parameter region. We utilize an infinite volume renormalization scheme based on the gradient flow transformation to determine the renormalization group $\beta$ function. We identify an infrared fixed point at $g2_{\mathrm{GF}\star}=6.60(62)$ in the GF scheme and calculate the leading irrelevant critical exponent $\gamma_{g}{\star}=0.199(32)$. Our prediction for $\gamma_{g}{\star}$ is consistent with available literature at the $1\mbox{-}2\sigma$ level.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (69)
  1. Thomas A. Ryttov and Robert Shrock, “Higher-loop corrections to the infrared evolution of a gauge theory with fermions,” Phys. Rev. D83, 056011 (2011), arXiv:1011.4542 .
  2. Claudio Pica and Francesco Sannino, “UV and IR Zeros of Gauge Theories at The Four Loop Order and Beyond,” Phys. Rev. D 83, 035013 (2011), arXiv:1011.5917 [hep-ph] .
  3. Thomas A. Ryttov and Robert Shrock, “Infrared Zero of β𝛽\betaitalic_β and Value of γmsubscript𝛾𝑚\gamma_{m}italic_γ start_POSTSUBSCRIPT italic_m end_POSTSUBSCRIPT for an SU(3) Gauge Theory at the Five-Loop Level,” Phys. Rev. D94, 105015 (2016a), arXiv:1607.06866 [hep-th] .
  4. Thomas A. Ryttov and Robert Shrock, “Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories,” Phys. Rev. D94, 125005 (2016b), arXiv:1610.00387 [hep-th] .
  5. Lorenzo Di Pietro and Marco Serone, “Looking through the QCD Conformal Window with Perturbation Theory,” JHEP 07, 049 (2020), arXiv:2003.01742 [hep-th] .
  6. Thomas Appelquist, Anuradha Ratnaweera, John Terning,  and L. C. R. Wijewardhana, “The Phase structure of an SU(N) gauge theory with N(f) flavors,” Phys. Rev. D 58, 105017 (1998), arXiv:hep-ph/9806472 .
  7. A. Bashir, A. Raya,  and J. Rodriguez-Quintero, “QCD: Restoration of Chiral Symmetry and Deconfinement for Large Nfsubscript𝑁𝑓N_{f}italic_N start_POSTSUBSCRIPT italic_f end_POSTSUBSCRIPT,” Phys. Rev. D 88, 054003 (2013), arXiv:1302.5829 [hep-ph] .
  8. Jens Braun and Holger Gies, “Chiral phase boundary of QCD at finite temperature,” JHEP 06, 024 (2006), arXiv:hep-ph/0602226 .
  9. Jens Braun, Christian S. Fischer,  and Holger Gies, “Beyond Miransky Scaling,” Phys. Rev. D 84, 034045 (2011), arXiv:1012.4279 [hep-ph] .
  10. Jong-Wan Lee, “Conformal window from conformal expansion,” Phys. Rev. D 103, 076006 (2021), arXiv:2008.12223 [hep-ph] .
  11. Zhijin Li and David Poland, “Searching for gauge theories with the conformal bootstrap,”   (2020), arXiv:2005.01721 [hep-th] .
  12. Seth Grable and Paul Romatschke, “Elements of Confinement for QCD with Twelve Massless Quarks,”  (2023), arXiv:2310.12203 [hep-th] .
  13. Hee Sok Chung and Daniel Nogradi, “fϱitalic-ϱ\varrhoitalic_ϱ/mϱitalic-ϱ\varrhoitalic_ϱ and fπ𝜋\piitalic_π/mϱitalic-ϱ\varrhoitalic_ϱ ratios and the conformal window,” Phys. Rev. D 107, 074039 (2023), arXiv:2302.06411 [hep-ph] .
  14. Paul Romatschke, “An alternative to perturbative renormalization in 3+1 dimensional field theories,”   (2024), arXiv:2401.06847 [hep-th] .
  15. Thomas Appelquist, George T. Fleming,  and Ethan T. Neil, “Lattice study of the conformal window in QCD-like theories,” Phys.Rev.Lett. 100, 171607 (2008), arXiv:0712.0609 [hep-ph] .
  16. Thomas Appelquist, George T. Fleming,  and Ethan T. Neil, “Lattice Study of Conformal Behavior in SU(3) Yang-Mills Theories,” Phys. Rev. D 79, 076010 (2009), arXiv:0901.3766 [hep-ph] .
  17. C. J. David Lin, Kenji Ogawa, Hiroshi Ohki,  and Eigo Shintani, “Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours,” JHEP 08, 096 (2012), arXiv:1205.6076 [hep-lat] .
  18. C. J. David Lin, Kenji Ogawa,  and Alberto Ramos, “The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box,” JHEP 12, 103 (2015), arXiv:1510.05755 [hep-lat] .
  19. Zoltan Fodor, Kieran Holland, Julius Kuti, Santanu Mondal, Daniel Nogradi,  and Chik Him Wong, “Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group,” Phys. Rev. D94, 091501 (2016), arXiv:1607.06121 [hep-lat] .
  20. Anna Hasenfratz and David Schaich, “Nonperturbative beta function of twelve-flavor SU(3) gauge theory,” JHEP 02, 132 (2018), arXiv:1610.10004 [hep-lat] .
  21. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chik Him Wong, “The twelve-flavor β𝛽\betaitalic_β-function and dilaton tests of the sextet scalar,” EPJ Web Conf. 175, 08015 (2018a), arXiv:1712.08594 [hep-lat] .
  22. A. Hasenfratz, C. Rebbi,  and O. Witzel, “Nonperturbative determination of β𝛽\betaitalic_β functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions,” Phys. Lett. B798, 134937 (2019a), arXiv:1710.11578 [hep-lat] .
  23. Anna Hasenfratz, Claudio Rebbi,  and Oliver Witzel, “Gradient flow step-scaling function for SU(3) with twelve flavors,” Phys. Rev. D100, 114508 (2019b), arXiv:1909.05842 [hep-lat] .
  24. Anna Hasenfratz, “Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions,” Phys. Rev. D 82, 014506 (2010), arXiv:1004.1004 [hep-lat] .
  25. Anna Hasenfratz, “Infrared fixed point of the 12-fermion SU(3) gauge model based on 2-lattice MCRG matching,” Phys. Rev. Lett. 108, 061601 (2012), arXiv:1106.5293 [hep-lat] .
  26. Anna Hasenfratz and Oliver Witzel, “Continuous β𝛽\betaitalic_β function for the SU(3) gauge systems with two and twelve fundamental flavors,” PoS LATTICE2019, 094 (2019), arXiv:1911.11531 [hep-lat] .
  27. A. Deuzeman, M. P. Lombardo,  and E. Pallante, “Evidence for a conformal phase in SU(N) gauge theories,” Phys. Rev. D 82, 074503 (2010), arXiv:0904.4662 [hep-ph] .
  28. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chris Schroeder, “Twelve massless flavors and three colors below the conformal window,” Phys. Lett. B703, 348–358 (2011), arXiv:1104.3124 [hep-lat] .
  29. T. Appelquist, G.T. Fleming, M.F. Lin, E.T. Neil,  and D.A. Schaich, “Lattice Simulations and Infrared Conformality,” Phys.Rev. D84, 054501 (2011), arXiv:1106.2148 [hep-lat] .
  30. Thomas DeGrand, “Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions,” Phys.Rev. D84, 116901 (2011), arXiv:1109.1237 [hep-lat] .
  31. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi, Chris Schroeder,  and Chik Him Wong, “Conformal finite size scaling of twelve fermion flavors,” PoS Lattice 2012, 279 (2012a), arXiv:1211.4238 .
  32. Yasumichi Aoki, Tatsumi Aoyama, Masafumi Kurachi, Toshihide Maskawa, Kei-ichi Nagai, Hiroshi Ohki, Akihiro Shibata, Koichi Yamawaki,  and Takeshi Yamazaki (LatKMI), “Lattice study of conformality in twelve-flavor QCD,” Phys. Rev. D86, 054506 (2012), arXiv:1207.3060 [hep-lat] .
  33. Yasumichi Aoki, Tatsumi Aoyama, Masafumi Kurachi, Toshihide Maskawa, Kei-ichi Nagai, Hiroshi Ohki, Enrico Rinaldi, Akihiro Shibata, Koichi Yamawaki,  and Takeshi Yamazaki (LatKMI), “Light composite scalar in twelve-flavor QCD on the lattice,” Phys. Rev. Lett. 111, 162001 (2013), arXiv:1305.6006 [hep-lat] .
  34. Anqi Cheng, Anna Hasenfratz, Yuzhi Liu, Gregory Petropoulos,  and David Schaich, “Finite size scaling of conformal theories in the presence of a near-marginal operator,” Phys.Rev. D90, 014509 (2014), arXiv:1401.0195 [hep-lat] .
  35. M. P. Lombardo, K. Miura, T. J. Nunes da Silva,  and E. Pallante, “On the particle spectrum and the conformal window,” JHEP 12, 183 (2014), arXiv:1410.0298 [hep-lat] .
  36. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chris Schroeder, “Nearly conformal gauge theories in finite volume,” Phys. Lett. B 681, 353–361 (2009), arXiv:0907.4562 [hep-lat] .
  37. Anqi Cheng, Anna Hasenfratz, Gregory Petropoulos,  and David Schaich, “Scale-dependent mass anomalous dimension from Dirac eigenmodes,” JHEP 1307, 061 (2013), arXiv:1301.1355 [hep-lat] .
  38. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chik Him Wong, “Case studies of near-conformal β𝛽\betaitalic_β-functions,” PoS LATTICE2019, 121 (2019), arXiv:1912.07653 [hep-lat] .
  39. Tiago Nunes da Silva and Elisabetta Pallante, “The strong coupling regime of twelve flavors QCD,” PoS LATTICE2012, 052 (2012), arXiv:1211.3656 [hep-lat] .
  40. Tobias Rindlisbacher, Kari Rummukainen,  and Ahmed Salami, “Bulk-preventing actions for SU(N) gauge theories,” PoS LATTICE2021, 576 (2022), arXiv:2111.00860 [hep-lat] .
  41. Tobias Rindlisbacher, Kari Rummukainen,  and Ahmed Salami, “Bulk-transition-preventing actions for SU(N) gauge theories,” Phys. Rev. D 108, 114511 (2023), arXiv:2306.14319 [hep-lat] .
  42. Felix Springer, David Schaich,  and Enrico Rinaldi (Lattice Strong Dynamics (LSD)), “First-order bulk transitions in large-N𝑁Nitalic_N lattice Yang–Mills theories using the density of states,”   (2023), arXiv:2311.10243 [hep-lat] .
  43. Anna Hasenfratz, Yigal Shamir,  and Benjamin Svetitsky, “Taming lattice artifacts with Pauli-Villars fields,” Phys. Rev. D 104, 074509 (2021), arXiv:2109.02790 [hep-lat] .
  44. Anna Hasenfratz, Ethan T. Neil, Yigal Shamir, Benjamin Svetitsky,  and Oliver Witzel, “Infrared fixed point and anomalous dimensions in a composite Higgs model,” Phys. Rev. D 107, 114504 (2023a), arXiv:2304.11729 [hep-lat] .
  45. Anna Hasenfratz, Ethan T. Neil, Yigal Shamir, Benjamin Svetitsky,  and Oliver Witzel, “Infrared fixed point of the SU(3) gauge theory with Nf=10 flavors,” Phys. Rev. D 108, L071503 (2023b), arXiv:2306.07236 [hep-lat] .
  46. Robert V. Harlander and Tobias Neumann, ‘‘The perturbative QCD gradient flow to three loops,” JHEP 06, 161 (2016), arXiv:1606.03756 [hep-ph] .
  47. R. Narayanan and H. Neuberger, “Infinite N phase transitions in continuum Wilson loop operators,” JHEP 0603, 064 (2006), arXiv:hep-th/0601210 [hep-th] .
  48. Martin Lüscher, “Trivializing maps, the Wilson flow and the HMC algorithm,” Commun.Math.Phys. 293, 899–919 (2010), arXiv:0907.5491 [hep-lat] .
  49. Martin Lüscher, “Properties and uses of the Wilson flow in lattice QCD,” JHEP 1008, 071 (2010), arXiv:1006.4518 [hep-lat] .
  50. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chik Him Wong, “A new method for the beta function in the chiral symmetry broken phase,” EPJ Web Conf. 175, 08027 (2018c), arXiv:1711.04833 [hep-lat] .
  51. Andrea Carosso, Anna Hasenfratz,  and Ethan T. Neil, “Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows,” Phys. Rev. Lett. 121, 201601 (2018), arXiv:1806.01385 [hep-lat] .
  52. Andrea Carosso, ‘‘Stochastic Renormalization Group and Gradient Flow,” JHEP 01, 172 (2020), arXiv:1904.13057 [hep-th] .
  53. Anna Hasenfratz and Oliver Witzel, “Continuous renormalization group β𝛽\betaitalic_β function from lattice simulations,” Phys. Rev. D101, 034514 (2020), arXiv:1910.06408 [hep-lat] .
  54. Anna Hasenfratz, Christopher J. Monahan, Matthew David Rizik, Andrea Shindler,  and Oliver Witzel, “A novel nonperturbative renormalization scheme for local operators,” PoS LATTICE2021, 155 (2022), arXiv:2201.09740 [hep-lat] .
  55. Julius Kuti, Zoltán Fodor, Kieran Holland,  and Chik Him Wong, “From ten-flavor tests of the β𝛽\betaitalic_β-function to αssubscript𝛼𝑠\alpha_{s}italic_α start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT at the Z-pole,” PoS LATTICE2021, 321 (2022), arXiv:2203.15847 [hep-lat] .
  56. 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 (2023c), arXiv:2303.00704 [hep-lat] .
  57. Curtis T. Peterson, Anna Hasenfratz, Jake van Sickle,  and Oliver Witzel, “Determination of the continuous β𝛽\betaitalic_β function of SU(3) Yang-Mills theory,” in 38th International Symposium on Lattice Field Theory (2021) arXiv:2109.09720 [hep-lat] .
  58. Curtis Peterson and Anna Hasenfratz, “Twelve flavor SU(3) gradient flow data for the continuous beta-function,”  (2024).
  59. Anna Hasenfratz and Francesco Knechtli, “Flavor symmetry and the static potential with hypercubic blocking,” Phys. Rev. D64, 034504 (2001), arXiv:hep-lat/0103029 .
  60. Anna Hasenfratz, Roland Hoffmann,  and Stefan Schaefer, “Hypercubic smeared links for dynamical fermions,” JHEP 0705, 029 (2007), arXiv:hep-lat/0702028 [hep-lat] .
  61. Anqi Cheng, Anna Hasenfratz,  and David Schaich, “Novel phase in SU(3) lattice gauge theory with 12 light fermions,” Phys.Rev. D85, 094509 (2012), arXiv:1111.2317 [hep-lat] .
  62. S. Duane, A.D. Kennedy, B.J. Pendleton,  and D. Roweth, “Hybrid Monte Carlo,” Phys.Lett. B195, 216–222 (1987).
  63. J. Osborn and Xiao-Yong Jin, “Introduction to the Quantum EXpressions (QEX) framework,” PoS LATTICE2016, 271 (2017).
  64. Zoltan Fodor, Kieran Holland, Julius Kuti, Daniel Nogradi,  and Chik Him Wong, “The Yang-Mills gradient flow in finite volume,” JHEP 1211, 007 (2012b), arXiv:1208.1051 [hep-lat] .
  65. Peter Lepage, “gvar,”  (2015).
  66. Curtis Peterson, “SwissFit,” https://github.com/ctpeterson/SwissFit.
  67. 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] .
  68. Ethan T. Neil and Jacob W. Sitison, “Improved information criteria for Bayesian model averaging in lattice field theory,” Phys. Rev. D 109, 014510 (2024), arXiv:2208.14983 [stat.ME] .
  69. Ethan T. Neil and Jacob W. Sitison, “Model averaging approaches to data subset selection,” Phys. Rev. E 108, 045308 (2023), arXiv:2305.19417 [stat.ME] .
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