Renormalization-group Calculation of Color-Coulomb Potential

I report on some recent work done in collaboration with E. de Rafael on the connection between ultraviolet renormalons in QCD and Nambu-Jona-Lasinio-like Lagrangians as its effective description at low energies.

We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of nonconformal {\beta_i}-terms, and reveals a special degeneracy of the terms in the perturbative coefficients. It allows us to systematically determine the argument of the running coupling order by order in pQCD in a form which can be readily automatiz...

The vNRQCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization group improved computations of scalar-antiscalar bound state energies and production rates at next-to-next-to-leading-logarithmic (NNLL) order.

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It is shown that at any loop level the relevant $\beta$ function has the universal behaviors at small and large values of the invariant charge. Due to this feature the new analytic running coupling possesses the universal asymptotics both in th...

We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the beta-function of the renormalization-group equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the determination of the pole mass m_b when we use perturbative expansions. We demonstrate the existence of these uncertainties for the Richardson potential explicitly and then discus...

The long standing problem of a non-perturbative renormalization of a gauge field theoretical Hamiltonian is addressed and explicitly carried out within an (effective) light-cone Hamiltonian approach to QCD. The procedure is in line with the conventional ideas: The Hamiltonian is first regulated by suitable cut-off functions, and subsequently renormalized by suitable counter terms to make it cut-off independent. Emphasized is the considerable freedom in the cut-off function wh...

The Coulomb plus linear potential is widely used in QCD. However, in this paper we show that the Coulomb potential of the form $\frac{1}{r}$ is not a part of the QCD potential. This is because the form $\frac{g^2}{r}$ is for abelian theory (not QCD) and the form $\frac{g^2(\mu)}{r}$ in QCD at short distance is not of the Coulomb form $\frac{1}{r}$ because $g(\mu)$ depends on the mass/length scale $\mu$. Similarly at long distance the QCD potential corresponds to the potential...

Based on a simple but effective regularization-renormalization method (RRM), the running coupling constants (RCC) of fermions with masses in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are calculated by renormalization group equation (RGE). Starting at Q=0 ($Q$ being the momentum transfer), the RCC in QED increases with the increase of $Q$ whereas the RCCs for different flavors of quarks with masses in QCD are different and they increase with the decrease o...

A fictitious discussion is taken as a point of origin to present novel physical insight into the nature of gauge theory and the potential energy of QCD and QED at short distance. Emphasized is the considerable freedom in the cut-off function which eventually can modify the Coulomb potential of two charges at sufficiently small distances. Emphasized is also that the parameters of the regularization function (the ``cut-off scale'') should not be driven to infinity but kept cons...

We study renormalization of Coulomb-gauge QCD within the Lagrangian second-order formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analyses, we show that, in the strict Coulomb gauge, g^2D^{00} is invariant under renormalization. (D^{00} is the time-time component of the gluon propagator.)