Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory

Abstract

We present a scheme-independent calculation of the infrared value of the anomalous dimension of the fermion bilinear, ${\gamma }_{\bar{\psi }\psi ,IR}$ 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 ${\gamma }_{\bar{\psi }\psi ,IR}$ 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.

Comments: 5 page latex, 1 figure