2017/03/24 by Thomas A. Ryttov, Robert Shrock
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Computer science #Geology #Mathematical analysis #Mathematics #Order (exchange) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #Scheme (mathematics) #Series (stratigraphy) #Speech recognition #Stress (linguistics) #hep-lat #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.95.105004
published as Phys. Rev. D 95, 105004 (2017) · 40 pages, latex, 12 figures
arxiv created 2017/03/24 · openalex publication_date 2017/05/26 · arxiv updated 2017/05/30 · openalex created_date 2017/06/05 · openalex updated_date 2026/08/06
We study a vectorial asymptotically free gauge theory, with gauge group G and Nf massless fermions in a representation R of this group, that exhibits an infrared (IR) zero in its beta function, \ensuremathβ, at the coupling \ensuremathα=\ensuremathαIR in the non-Abelian Coulomb phase. For general G and R, we calculate the scheme-independent series expansions of (i) the anomalous dimension of the fermion bilinear, \ensuremathγ_\ensuremathψ\ensuremathψ,IR, to O(\mathrm\ensuremathΔf4) and (ii) the derivative \ensuremathβ^\ensuremath'=d\ensuremathβ/d\ensuremathα, to O(\mathrm\ensuremathΔf5), both evaluated at \ensuremathαIR, where \mathrm\ensuremathΔf is an Nf-dependent expansion variable. These are the highest orders to which these expansions have been calculated. We apply these general results to theories with G=SU(Nc) and R equal to the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. It is shown that for all of these representations, \ensuremathγ_\ensuremathψ\ensuremathψ,IR, calculated to the order \mathrm\ensuremathΔfp, with 1\ensuremath≤p\ensuremath≤4, increases monotonically with decreasing Nf and, for fixed Nf, is a monotonically increasing function of p. Comparisons of our scheme-independent calculations of \ensuremathγ_\ensuremathψ\ensuremathψ,IR and \ensuremathβIR^\ensuremath' are made with our earlier higher n-loop values of these quantities, and with lattice measurements. For R=F, we present results for the limit Nc\ensuremath→\ensuremath∞ and Nf\ensuremath→\ensuremath∞ with Nf/Nc fixed. We also present expansions for \ensuremathαIR calculated to O(\mathrm\ensuremathΔf4).