Computation of the one-loop spectral QCD running coupling using covariant spectral regularization

The running strong coupling is an important quantity, indicating the strength of the strong force at any given energy. Methods described in the literature for its computation are essentially all defined with respect to the renormalization group equations and these equations are associated with the method of renormalization for dealing with infinities in Feynman integrals. The problem with the renormalization group equations is their prediction of the unphysical Landau pole which for quantum chromodynamics (QCD) occurs at an energy of the order of a few 100[Formula: see text]MeV. The models described in the literature generally interlace high-energy renormalization group predictions with modified low-energy formulations. It would be desirable to have a method for the computation of the running strong coupling which is not ad hoc but is unified over the whole range of energies and is based on a single mathematically rigorous formulation which is guided by physical principles. In this paper, we describe a method using the regularization technique called covariant spectral regularization for which renormalization is not required. We use covariant spectral regularization to compute the spectral QCD vacuum polarization tensor in order to determine and display the (one-loop) spectral QCD running coupling. The densities associated with the quark and gluon bubbles are computed without requiring renormalization and hence the spectral QCD vacuum polarization tensor is determined. We explain why we think these computations are sufficient to determine the QCD running coupling. It is found that the position space spectral QCD running coupling is an analytic function which does not manifest a Landau pole, but instead it manifests what might be called a “Landau peak”, and has the property known as “freezing of [Formula: see text]” in the infrared. On enforcing the agreement of our results with two points in real [Formula: see text] data, we determine a spectral bare strong coupling constant of [Formula: see text] which can be used in higher-order QCD computations (this is to be compared with QCD using renormalization, where the bare strong coupling is infinite). Thus, it seems one can conclude that, when analyzed using covariant spectral regularization, QCD is perturbative at all energies.