Study of Scheme Transformations to Remove Higher-Loop Terms in the $\beta$ Function of a Gauge Theory

Understand

Since three-loop and higher-loop terms in the $\beta$ function of a gauge theory are scheme-dependent, one can, at least for sufficiently small coupling, carry out a scheme transformation that removes these terms.

• A basic question concerns the extent to which this can be done at an infrared fixed point of an asymptotically free gauge theory.
• This is important for quantitative analyses of the scheme dependence of such a fixed point.
• Here we study a scheme transformation $S_{R,m}$ with $m \ge 2$ that is constructed so as to remove the terms in the beta function at loop order $\ell=3$ to $\ell=m+1$, inclusive.