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

Hasenfratz, Anna; Peterson, Curtis T.

doi:10.1103/PhysRevD.109.114507

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

Journal Article · 09 June 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.109.114507 · OSTI ID:2474652

;

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 $β$ function. The gradient flow $β$ function exhibits a zero at $g_{GF ⋆}^{2} = 6.60 (62)$ , implying that the system is infrared conformal. We calculate the leading irrelevant critical exponent $γ_{g}^{⋆} = 0.199 (32)$ . Our prediction for $γ_{g}^{⋆}$ is consistent with available literature at the $1 − 2 σ$ level. Published by the American Physical Society 2024

View Journal Article

Cite

Export

Save

Research Organization:: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)

Sponsoring Organization:: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: AC02-07CH11359; SC0010005

OSTI ID:: 2474652

Report Number(s):: FERMILAB-PUB--24-0098-V; arXiv:2402.18038; 114507

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 11 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (74)

Stochastic renormalization group and gradient flow Carosso, Andrea Journal of High Energy Physics, Vol. 2020, Issue 1 https://doi.org/10.1007/JHEP01(2020)172	journal	January 2020
Nonperturbative β function of twelve-flavor SU(3) gauge theory Hasenfratz, Anna; Schaich, David Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)132	journal	February 2018
Searching for gauge theories with the conformal bootstrap Li, Zhijin; Poland, David Journal of High Energy Physics, Vol. 2021, Issue 3 https://doi.org/10.1007/JHEP03(2021)172	journal	March 2021
The perturbative QCD gradient flow to three loops Harlander, Robert V.; Neumann, Tobias Journal of High Energy Physics, Vol. 2016, Issue 6 https://doi.org/10.1007/JHEP06(2016)161	journal	June 2016
Scale-dependent mass anomalous dimension from Dirac eigenmodes Cheng, Anqi; Hasenfratz, Anna; Petropoulos, Gregory Journal of High Energy Physics, Vol. 2013, Issue 7 https://doi.org/10.1007/JHEP07(2013)061	journal	July 2013
Looking through the QCD conformal window with perturbation theory Di Pietro, Lorenzo; Serone, Marco Journal of High Energy Physics, Vol. 2020, Issue 7 https://doi.org/10.1007/JHEP07(2020)049	journal	July 2020
Properties and uses of the Wilson flow in lattice QCD Lüscher, Martin Journal of High Energy Physics, Vol. 2010, Issue 8 https://doi.org/10.1007/JHEP08(2010)071	journal	August 2010
Lattice study of infrared behaviour in SU(3) gauge theory with twelve massless flavours Lin, C. -J. David; Ogawa, Kenji; Ohki, Hiroshi Journal of High Energy Physics, Vol. 2012, Issue 8 https://doi.org/10.1007/JHEP08(2012)096	journal	August 2012
The Yang-Mills gradient flow in finite volume Fodor, Zoltan; Holland, Kieran; Kuti, Julius Journal of High Energy Physics, Vol. 2012, Issue 11 https://doi.org/10.1007/JHEP11(2012)007	journal	November 2012
On the particle spectrum and the conformal window Lombardo, M. P.; Miura, K.; Nunes da Silva, T. J. Journal of High Energy Physics, Vol. 2014, Issue 12 https://doi.org/10.1007/JHEP12(2014)183	journal	December 2014
The Yang-Mills gradient flow and SU(3) gauge theory with 12 massless fundamental fermions in a colour-twisted box Lin, C. -J. David; Ogawa, Kenji; Ramos, Alberto Journal of High Energy Physics, Vol. 2015, Issue 12 https://doi.org/10.1007/JHEP12(2015)103	journal	December 2015
Trivializing Maps, the Wilson Flow and the HMC Algorithm Lüscher, Martin Communications in Mathematical Physics, Vol. 293, Issue 3 https://doi.org/10.1007/s00220-009-0953-7	journal	November 2009
Hybrid Monte Carlo Duane, Simon; Kennedy, A. D.; Pendleton, Brian J. Physics Letters B, Vol. 195, Issue 2 https://doi.org/10.1016/0370-2693(87)91197-X	journal	September 1987
Monte Carlo errors with less errors Wolff, Ulli Computer Physics Communications, Vol. 156, Issue 2 https://doi.org/10.1016/S0010-4655(03)00467-3	journal	January 2004
pyerrors: A python framework for error analysis of Monte Carlo data Joswig, Fabian; Kuberski, Simon; Kuhlmann, Justus T. Computer Physics Communications, Vol. 288 https://doi.org/10.1016/j.cpc.2023.108750	journal	July 2023
Critical slowing down and error analysis in lattice QCD simulations Schaefer, Stefan; Sommer, Rainer; Virotta, Francesco Nuclear Physics B, Vol. 845, Issue 1 https://doi.org/10.1016/j.nuclphysb.2010.11.020	journal	April 2011
Nearly conformal gauge theories in finite volume Fodor, Zoltan; Holland, Kieran; Kuti, Julius Physics Letters B, Vol. 681, Issue 4 https://doi.org/10.1016/j.physletb.2009.10.040	journal	November 2009
Twelve massless flavors and three colors below the conformal window Fodor, Zoltán; Holland, Kieran; Kuti, Julius Physics Letters B, Vol. 703, Issue 3 https://doi.org/10.1016/j.physletb.2011.07.037	journal	September 2011
The bulk transition of QCD with twelve flavors and the role of improvement Deuzeman, Albert; Lombardo, Maria Paola; Nunes da Silva, Tiago Physics Letters B, Vol. 720, Issue 4-5 https://doi.org/10.1016/j.physletb.2013.02.030	journal	March 2013
Extended investigation of the twelve-flavor β -function Fodor, Zoltán; Holland, Kieran; Kuti, Julius Physics Letters B, Vol. 779 https://doi.org/10.1016/j.physletb.2018.02.008	journal	April 2018
Nonperturbative determination of β functions for SU(3) gauge theories with 10 and 12 fundamental flavors using domain wall fermions Hasenfratz, A.; Rebbi, C.; Witzel, O. Physics Letters B, Vol. 798 https://doi.org/10.1016/j.physletb.2019.134937	journal	November 2019
The twelve-flavor β-function and dilaton tests of the sextet scalar Fodor, Zoltan; Holland, Kieran; Kuti, Julius EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817508015	journal	January 2018
A new method for the beta function in the chiral symmetry broken phase Fodor, Zoltan; Holland, Kieran; Kuti, Julius EPJ Web of Conferences, Vol. 175 https://doi.org/10.1051/epjconf/201817508027	journal	January 2018
Infinite N phase transitions in continuum Wilson loop operators Narayanan, Rajamani; Neuberger, Herbert Journal of High Energy Physics, Vol. 2006, Issue 03 https://doi.org/10.1088/1126-6708/2006/03/064	journal	March 2006
Chiral phase boundary of QCD at finite temperature Braun, Jens; Gies, Holger Journal of High Energy Physics, Vol. 2006, Issue 06 https://doi.org/10.1088/1126-6708/2006/06/024	journal	June 2006
Hypercubic smeared links for dynamical fermions Hasenfratz, Anna; Hoffmann, Roland; Schaefer, Stefan Journal of High Energy Physics, Vol. 2007, Issue 05 https://doi.org/10.1088/1126-6708/2007/05/029	journal	May 2007
Gradient flow and the Wilsonian renormalization group flow Makino, Hiroki; Morikawa, Okuto; Suzuki, Hiroshi Progress of Theoretical and Experimental Physics, Vol. 2018, Issue 5 https://doi.org/10.1093/ptep/pty050	journal	May 2018
Gradient flow step-scaling function for SU(3) with twelve flavors Hasenfratz, A.; Rebbi, C.; Witzel, O. Physical Review D, Vol. 100, Issue 11 https://doi.org/10.1103/PhysRevD.100.114508	journal	December 2019
Continuous renormalization group β function from lattice simulations Hasenfratz, Anna; Witzel, Oliver Physical Review D, Vol. 101, Issue 3 https://doi.org/10.1103/PhysRevD.101.034514	journal	February 2020
Conformal window from conformal expansion Lee, Jong-Wan Physical Review D, Vol. 103, Issue 7 https://doi.org/10.1103/PhysRevD.103.076006	journal	April 2021
Bayesian model averaging for analysis of lattice field theory results Jay, William I.; Neil, Ethan T. Physical Review D, Vol. 103, Issue 11 https://doi.org/10.1103/PhysRevD.103.114502	journal	June 2021
Taming lattice artifacts with Pauli-Villars fields Hasenfratz, Anna; Shamir, Yigal; Svetitsky, Benjamin Physical Review D, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevD.104.074509	journal	October 2021
fϱ/mϱ and fπ/mϱ ratios and the conformal window Chung, Hee Sok; Nogradi, Daniel Physical Review D, Vol. 107, Issue 7 https://doi.org/10.1103/PhysRevD.107.074039	journal	April 2023
Infrared fixed point and anomalous dimensions in a composite Higgs model Hasenfratz, Anna; Neil, Ethan T.; Shamir, Yigal Physical Review D, Vol. 107, Issue 11 https://doi.org/10.1103/PhysRevD.107.114504	journal	June 2023
Λ parameter of the SU(3) Yang-Mills theory from the continuous β function Hasenfratz, Anna; Peterson, Curtis T.; van Sickle, Jake Physical Review D, Vol. 108, Issue 1 https://doi.org/10.1103/PhysRevD.108.014502	journal	July 2023
Bulk-transition-preventing actions for SU(N) gauge theories Rindlisbacher, Tobias; Rummukainen, Kari; Salami, Ahmed Physical Review D, Vol. 108, Issue 11 https://doi.org/10.1103/PhysRevD.108.114511	journal	December 2023
Infrared fixed point of the SU(3) gauge theory with Nf=10 flavors Hasenfratz, Anna; Neil, Ethan T.; Shamir, Yigal Physical Review D, Vol. 108, Issue 7 https://doi.org/10.1103/PhysRevD.108.L071503	journal	October 2023
Improved information criteria for Bayesian model averaging in lattice field theory Neil, Ethan T.; Sitison, Jacob W. Physical Review D, Vol. 109, Issue 1 https://doi.org/10.1103/PhysRevD.109.014510	journal	January 2024
Phase structure of an SU ( N ) gauge theory with N f flavors Appelquist, Thomas; Ratnaweera, Anuradha; Terning, John Physical Review D, Vol. 58, Issue 10 https://doi.org/10.1103/PhysRevD.58.105017	journal	October 1998
Flavor symmetry and the static potential with hypercubic blocking Hasenfratz, Anna; Knechtli, Francesco Physical Review D, Vol. 64, Issue 3 https://doi.org/10.1103/PhysRevD.64.034504	journal	July 2001
Lattice study of conformal behavior in SU(3) Yang-Mills theories Appelquist, Thomas; Fleming, George T.; Neil, Ethan T. Physical Review D, Vol. 79, Issue 7 https://doi.org/10.1103/PhysRevD.79.076010	journal	April 2009
Conformal or walking? Monte Carlo renormalization group studies of S U ( 3 ) gauge models with fundamental fermions Hasenfratz, Anna Physical Review D, Vol. 82, Issue 1 https://doi.org/10.1103/PhysRevD.82.014506	journal	July 2010
Evidence for a conformal phase in SU ( N ) gauge theories Deuzeman, A.; Lombardo, M. P.; Pallante, E. Physical Review D, Vol. 82, Issue 7 https://doi.org/10.1103/PhysRevD.82.074503	journal	October 2010
Ultraviolet and infrared zeros of gauge theories at the four-loop order and beyond Pica, Claudio; Sannino, Francesco Physical Review D, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevD.83.035013	journal	February 2011
Higher-loop corrections to the infrared evolution of a gauge theory with fermions Ryttov, Thomas A.; Shrock, Robert Physical Review D, Vol. 83, Issue 5 https://doi.org/10.1103/PhysRevD.83.056011	journal	March 2011
Beyond Miransky scaling Braun, Jens; Fischer, Christian S.; Gies, Holger Physical Review D, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevD.84.034045	journal	August 2011
Lattice simulations and infrared conformality Appelquist, T.; Fleming, G. T.; Lin, M. F. Physical Review D, Vol. 84, Issue 5 https://doi.org/10.1103/PhysRevD.84.054501	journal	September 2011
Finite-size scaling tests for spectra in SU(3) lattice gauge theory coupled to 12 fundamental flavor fermions DeGrand, Thomas Physical Review D, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevD.84.116901	journal	December 2011
Novel phase in SU(3) lattice gauge theory with 12 light fermions Cheng, Anqi; Hasenfratz, Anna; Schaich, David Physical Review D, Vol. 85, Issue 9 https://doi.org/10.1103/PhysRevD.85.094509	journal	May 2012
Lattice study of conformality in twelve-flavor QCD Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi Physical Review D, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevD.86.054506	journal	September 2012
QCD: Restoration of chiral symmetry and deconfinement for large N f Bashir, A.; Raya, A.; Rodríguez-Quintero, J. Physical Review D, Vol. 88, Issue 5 https://doi.org/10.1103/PhysRevD.88.054003	journal	September 2013
Finite size scaling of conformal theories in the presence of a near-marginal operator Cheng, Anqi; Hasenfratz, Anna; Liu, Yuzhi Physical Review D, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevD.90.014509	journal	July 2014
Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group Fodor, Zoltan; Holland, Kieran; Kuti, Julius Physical Review D, Vol. 94, Issue 9 https://doi.org/10.1103/PhysRevD.94.091501	journal	November 2016
Infrared zero of β and value of γ m for an SU(3) gauge theory at the five-loop level Ryttov, Thomas A.; Shrock, Robert Physical Review D, Vol. 94, Issue 10 https://doi.org/10.1103/PhysRevD.94.105015	journal	November 2016
Scheme-independent series expansions at an infrared zero of the beta function in asymptotically free gauge theories Ryttov, Thomas A.; Shrock, Robert Physical Review D, Vol. 94, Issue 12 https://doi.org/10.1103/PhysRevD.94.125005	journal	December 2016
Higher-order scheme-independent series expansions of γ ψ ¯ ψ , IR and β IR ′ in conformal field theories Ryttov, Thomas A.; Shrock, Robert Physical Review D, Vol. 95, Issue 10 https://doi.org/10.1103/PhysRevD.95.105004	journal	May 2017
Model averaging approaches to data subset selection Neil, Ethan T.; Sitison, Jacob W. Physical Review E, Vol. 108, Issue 4 https://doi.org/10.1103/PhysRevE.108.045308	journal	October 2023
Lattice Study of the Conformal Window in QCD-like Theories Appelquist, Thomas; Fleming, George T.; Neil, Ethan T. Physical Review Letters, Vol. 100, Issue 17 https://doi.org/10.1103/PhysRevLett.100.171607	journal	April 2008
Infrared Fixed Point of the 12-Fermion SU(3) Gauge Model Based on 2-Lattice Monte Carlo Renomalization-Group Matching Hasenfratz, Anna Physical Review Letters, Vol. 108, Issue 6 https://doi.org/10.1103/PhysRevLett.108.061601	journal	February 2012
Light Composite Scalar in Twelve-Flavor QCD on the Lattice Aoki, Yasumichi; Aoyama, Tatsumi; Kurachi, Masafumi Physical Review Letters, Vol. 111, Issue 16 https://doi.org/10.1103/PhysRevLett.111.162001	journal	October 2013
Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows Carosso, Andrea; Hasenfratz, Anna; Neil, Ethan T. Physical Review Letters, Vol. 121, Issue 20 https://doi.org/10.1103/PhysRevLett.121.201601	journal	November 2018
Strong dynamics, composite Higgs and the conformal window Nogradi, Daniel; Patella, Agostino International Journal of Modern Physics A, Vol. 31, Issue 22 https://doi.org/10.1142/S0217751X1643003X	journal	August 2016
Bulk and finite- temperature transitions in SU(3) gauge theories with many light fermions Schaich, David; Cheng, Anqi; Hasenfratz, Anna Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012) https://doi.org/10.22323/1.164.0028	conference	December 2012
The Strong coupling regime of twelve flavours QCD Nunes da Silva, Tiago; Pallante, Elisabetta Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012) https://doi.org/10.22323/1.164.0052	conference	December 2012
Conformal finite size scaling of twelve fermion flavors Fodor, Zoltan; Holland, Kieran; Kuti, Julius Proceedings of The 30th International Symposium on Lattice Field Theory — PoS(Lattice 2012) https://doi.org/10.22323/1.164.0279	conference	December 2012
Introduction to the Quantum EXpressions (QEX) framework Osborn, James C.; Jin, Xiao-yong Proceedings of 34th annual International Symposium on Lattice Field Theory — PoS(LATTICE2016) https://doi.org/10.22323/1.256.0271	conference	February 2017
Continuous $\beta$ function for the SU(3) gauge systems with two and twelve fundamental flavors Hasenfratz, Anna; Witzel, Oliver Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019) https://doi.org/10.22323/1.363.0094	conference	August 2020
Case studies of near-conformal beta-functions Fodor, Zoltan; Holland, Kieran; Kuti, Julius Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019) https://doi.org/10.22323/1.363.0121	conference	August 2020
Automatic Differentiation for error analysis Ramos, Alberto Proceedings of Tools for High Energy Physics and Cosmology — PoS(TOOLS2020) https://doi.org/10.22323/1.392.0045	conference	May 2021
A novel nonperturbative renormalization scheme for local operators Monahan, Chris; Hasenfratz, Anna; Rizik, Matthew David Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0155	conference	May 2022
Determination of the continuous $\beta$ function of SU(3) Yang-Mills theory Peterson, Curtis; Hasenfratz, Anna; van Sickle, Jake Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0174	conference	May 2022
From ten-flavor tests of the $\beta$-function to $\alpha_s$ at the Z-pole Kuti, Julius; Fodor, Zoltan; Holland, Kieran Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0321	conference	May 2022
Bulk-preventing actions for SU(N) gauge theories Rindlisbacher, Tobias; Rummukainen, Kari; Salami, Ahmed Proceedings of The 38th International Symposium on Lattice Field Theory — PoS(LATTICE2021) https://doi.org/10.22323/1.396.0576	conference	May 2022
Toward a novel determination of the strong QCD coupling at the Z-pole Wong, Chik Him; Borsanyi, Szabolcs; Fodor, Zoltan Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022) https://doi.org/10.22323/1.430.0043	conference	January 2023