Abstract
We introduce a more general set of kinematic renormalization schemes than the original momentum (MOM) 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 $3$-point vertex functions in Quantum Chromodynamics (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. As 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.
Highlights
The renormalization of a renormalizable quantum field theory is a technical exercise which first requires the evaluation of the Feynman diagrams of the relevant divergent n-point Green’s functions of the theory to a specific order in perturbation theory
The only caveat is that we need to distinguish our linear covariant gauge formalism from the corresponding maximal Abelian gauge (MAG) expressions. We do this by denoting the interpolating MOM (iMOM) schemes in the MAG in general by iMOMmi, where the three MAG schemes will be denoted by iMOMmg, iMOMmh, and iMOMmq for the triple off-diagonal gluon, off-diagonal gluon-ghost, and off-diagonal gluon-quark schemes, respectively
We have completed the full renormalization of QCD in a new set of kinematic schemes called iMOM, which extend the momentum subtraction (MOM) schemes of Celmaster and Gonsalves [20,21]
Summary
The renormalization of a renormalizable quantum field theory is a technical exercise which first requires the evaluation of the Feynman diagrams of the relevant divergent n-point Green’s functions of the theory to a specific order in perturbation theory. The determination of the coupling constant renormalization requires the evaluation of one of the three three-point functions in QCD. The main fixed point is the Wilson-Fisher fixed point in the d-dimensional version of the quantum field theory [27,28,29,30] For kinematic schemes, these have been studied in QCD in detail at three loops in Ref. [31], the critical exponents for the three MOM schemes of QCD were examined with the aim of seeing to what extent the renormalization group invariance held as a function of. The renormalization group functions in the iMOM schemes will depend on a parameter ω, which is restricted to 0 < ω < 4 It tags one of the external momenta of the three-point vertices, and the concept was introduced in Refs. Appendix records the tensor bases and projection matrices for each of the three vertices at the interpolating substraction point
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