Generalized scheme transformations for the elimination of higher-loop terms in the beta function of a gauge theory

We construct and study a generalized one-parameter class of scheme transformations, denoted SR,m,k1 with m≥2, with the property that an SR,m,k1 scheme transformation eliminates the -loop terms in the beta function of a gauge theory from loop order =3 to order =m+1, inclusive. These scheme transformations are applied to the higher-loop calculation of the infrared zero of the beta function of an asymptotically free gauge theory with multiple fermions. We show that scheme transformations in this generalized class satisfy a set of criteria for physical acceptability over a larger range of numbers of fermions than previously studied scheme transformations. We also present an interesting modification of a different type of scheme transformation that removes the three-loop term in the beta function.