Infrared Zero of $β$ and Value of $γ_m$ for an SU(3) Gauge Theory at the Five-Loop Level

Thomas A. Ryttov, Robert Shrock

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We calculate the value of the coupling at the infrared zero of the beta function of an asymptotically free SU(3) gauge theory at the five-loop level as a function of the number of fermions. Both a direct analysis of the beta function and analyses of Pad\'e approximants are used for this purpose. We then calculate the value of the five-loop anomalous dimension, $\gamma_m$, of the fermion bilinear at this IR zero of the beta function.