Higher-Order Scheme-Independent Calculations of Physical Quantities in the Conformal Phase of a Gauge Theory

Preprint number: CP3-Origins-2017-5 DNRF90
Authors: Thomas A. Ryttov (CP3-Origins & DIAS) and Robert Shrock (C. N. Yang Institute for Theoretical Physics)
External link: arXiv.org

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We consider an asymptotically free vectorial SU($N_c$) gauge theory with
$N_f$ massless fermions in a representation $R$, having an infrared fixed
point (IRFP) of the renormalization group at $alpha_{IR}$ in the conformal
non-Abelian Coulomb phase. The cases with $R$ equal to the fundamental,
adjoint, and symmetric rank-2 tensor representation are considered. We
present scheme-independent calculations of the anomalous dimension
$gamma_{barpsipsi,IR}$ to $O(Delta_f^4)$ and $beta’_{IR}$ to
$O(Delta_f^5)$ at this IRFP, where $Delta_f$ is an $N_f$-dependent
expansion parameter. Comparisons are made with conventional $n$-loop
calculations and lattice measurements. As a test of the accuracy of the
$Delta_f$ expansion, we calculate $gamma_{barpsipsi,IR}$ to
$O(Delta_f^3)$ in ${cal N}=1$ SU($N_c$) supersymmetric quantum
chromodynamics and find complete agreement, to this order, with the exactly
known expression. The $Delta_f$ expansion also avoids a problem in which
an IRFP may not be manifest as an IR zero of a higher $n$-loop beta
function.