Scheme-Independent Calculation of $gamma_{barpsipsi,IR}$ for an SU(3) Gauge Theory

Preprint number: CP3-Origins-2016-34 DNRF90
Authors: Thomas A. Ryttov (CP3-Origins & DIAS) and Robert Shrock (C. N. Yang Institute for Theoretical Physics, Stony Brook University)
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We present a scheme-independent calculation of the infrared value of
the anomalous dimension of the fermion bilinear,
$gamma_{barpsipsi,IR}$ in an SU(3) gauge theory as a function of
the number of fermions, $N_f$, via a series expansion in powers of
$Delta_f$, where $Delta_f=(16.5-N_f)$, to order $Delta_f^4$.
We perform an extrapolation to obtain the first determination of the
exact $gamma_{barpsipsi,IR}$ from continuum field theory.
The results are compared with calculations of the $n$-loop values of
this anomalous dimension from series in powers of the coupling
and from lattice measurements.