TY - JOUR

T1 - From ten-flavor tests of the β-function to αs at the Z-pole

AU - Fodor, Zoltán

AU - Holland, Kieran

AU - Kuti, Julius

AU - Wong, Chik Him

N1 - Funding Information:
We acknowledge support by the DOE under grant DE-SC0009919, by the NSF under grant 1620845, and by the Deutsche Forschungsgemeinschaft grant SFB-TR 55. Computations for this work were carried out in part on facilities of the USQCD Collaboration, which are funded by the Office of Science of the U.S. Department of Energy. Computational resources were also provided by the DOE INCITE program on the SUMMIT gpu platform at ORNL, by the University of Wuppertal, and by the Juelich Supercomputing Center.
Publisher Copyright:
© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0)

PY - 2022/7/8

Y1 - 2022/7/8

N2 - New tests are applied to two β-functions of the much-discussed BSM model with ten massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The renormalization scheme of the two β-functions is defined on the gauge field gradient flow in respective finite or infinite physical volumes at zero lattice spacing. Recently published results in the ten-flavor theory led to indicators of an infrared fixed point (IRFP) in the finite-volume step β-function in the strong coupling regime of the theory [1]. We analyze our substantially extended set of ten-flavor lattice ensembles at strong renormalized gauge couplings and find no evidence or hint for IRFP in the finite-volume step β-function within controlled lattice reach. We also discuss new ten-flavor tests of the recently introduced lattice definition and algorithmic implementation of the β-function defined on the gradient flow of the gauge field over infinite Euclidean space-time in the continuum. Originally we introduced this new algorithm to match finite-volume step β-functions in massless near-conformal gauge theories with the infinite-volume β-function reached in the chiral limit from small fermion mass deformations of spontaneous chiral symmetry breaking. Results from the lattice analysis of the ten-flavor infinite-volume β-function are consistent with the absence of IRFP from our step β-function based analysis. We make important contact at weak coupling in infinite volume with gradient flow based three-loop perturbation theory, serving as a first pilot study toward the long-term goal of developing alternate approach to the determination of the strong coupling αs at the Z-boson pole in QCD. Without reporting here, our tests of this long-term goal continue in QCD with three massless fermion flavors and in the SU(3) Yang-Mills limit of quenched QCD.

AB - New tests are applied to two β-functions of the much-discussed BSM model with ten massless fermion flavors in the fundamental representation of the SU(3) color gauge group. The renormalization scheme of the two β-functions is defined on the gauge field gradient flow in respective finite or infinite physical volumes at zero lattice spacing. Recently published results in the ten-flavor theory led to indicators of an infrared fixed point (IRFP) in the finite-volume step β-function in the strong coupling regime of the theory [1]. We analyze our substantially extended set of ten-flavor lattice ensembles at strong renormalized gauge couplings and find no evidence or hint for IRFP in the finite-volume step β-function within controlled lattice reach. We also discuss new ten-flavor tests of the recently introduced lattice definition and algorithmic implementation of the β-function defined on the gradient flow of the gauge field over infinite Euclidean space-time in the continuum. Originally we introduced this new algorithm to match finite-volume step β-functions in massless near-conformal gauge theories with the infinite-volume β-function reached in the chiral limit from small fermion mass deformations of spontaneous chiral symmetry breaking. Results from the lattice analysis of the ten-flavor infinite-volume β-function are consistent with the absence of IRFP from our step β-function based analysis. We make important contact at weak coupling in infinite volume with gradient flow based three-loop perturbation theory, serving as a first pilot study toward the long-term goal of developing alternate approach to the determination of the strong coupling αs at the Z-boson pole in QCD. Without reporting here, our tests of this long-term goal continue in QCD with three massless fermion flavors and in the SU(3) Yang-Mills limit of quenched QCD.

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M3 - Conference article

AN - SCOPUS:85134430446

SN - 1824-8039

VL - 396

JO - Proceedings of Science

JF - Proceedings of Science

M1 - 321

T2 - 38th International Symposium on Lattice Field Theory, LATTICE 2021

Y2 - 26 July 2021 through 30 July 2021

ER -