Renormalization of QCD in the interpolating momentum subtraction scheme at three loops

We introduce a more general set of kinematic renormalization schemes than the original momentum subtraction schemes of Celmaster and Gonsalves. These new schemes will depend on a parameter $\omega$, which tags the external momentum of one of the legs of the three-point vertex functions in QCD. In each of the three new schemes, we renormalize QCD in the Landau and maximal Abelian gauges and establish the three-loop renormalization group functions in each gauge. For an application, we evaluate two critical exponents at the Banks-Zaks fixed point and demonstrate that their values appear to be numerically scheme independent in a subrange of the conformal window.

Figure 1

Critical exponent $\tilde{\omega }$ at three loops for $SU(2)$ (left panel) and $SU(3)$ (right panel) for the respective iMOMq, iMOMh, and iMOMg schemes.

Figure 2

Critical exponent $\rho$ for $SU(2)$ at two (left panel) and three loops (right panel) for the respective iMOMq, iMOMh, and iMOMg schemes.

Figure 3

Critical exponent $\rho$ for $SU(3)$ at two (left panel) and three loops (right panel) for the respective iMOMq, iMOMh, and iMOMg schemes.

Figure 4

Critical exponents $\tilde{\omega }$ (left panel) and $\rho$ (right panel) for $SU(3)$ in the MAG at three loops for the respective iMOMmq, iMOMmh, and iMOMmg schemes.