Renormalization-group Calculation of Color-Coulomb Potential

We propose a new strategy for the determination of the QCD coupling. It relies on a coupling computed in QCD with $N_{\rm f} \geq 3$ degenerate heavy quarks at a low energy scale $\mu_{\rm dec}$, together with a non-perturbative determination of the ratio $\Lambda/\mu_{\rm dec}$ in the pure gauge theory. We explore this idea using a finite volume renormalization scheme for the case of $N_{\rm f} = 3$ QCD, demonstrating that a precise value of the strong coupling $\alpha_s$ ca...

The large-beta_0 limit of QCD is discussed, with the emphasize on simple technical methods of calculating various quantities at the order 1/\beta_0. Many examples, mainly from heavy quark physics, are considered. Some QCD results based on renormalization group (and not restricted to the large-\beta_0 limit) are also discussed.

We try to review the main current ideas and points of view on the running coupling constant in QCD. We begin by recalling briefly the classic analysis based on the Renormalization Group with some emphasis on the exact solutions of the RG equation for a given number of loops, in comparison with the usual approximate expressions. We give particular attention to the problem of eliminating the unphysical Landau singularities, and of defining a coupling that remains significant at...

The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale, together with an arbitrary range. This {\it ad hoc} assignment of the renormalization scale causes the coefficients of the QCD running coupling at each perturbative order to be strongly dependent on the choice of both the renormalization scale and the renormalization scheme. However, such ambiguities are not necessary, since as a basic requiremen...

In this work we consider the possibility of representing the perturbative series for renormalization group invariant quantities in QCD in the form of their decomposition in powers of the conformal anomaly $\beta(\alpha_s)/\alpha_s$ in the ${\rm{\overline{MS}}}$-scheme. We remind that such expansion is possible for the Adler function of the process of $e^+e^-$ annihilation into hadrons and the coefficient function of the Bjorken polarized sum rule for the deep-inelastic electr...

The quark-antiquark potential is constructed by making use of a new analytic running coupling in QCD. This running coupling arises under ``analytization'' of the renormalization group equation. The rising behavior of the quark-antiquark potential at large distances, which provides the quark confinement, is shown explicitly. At small distances, the standard behavior of this potential originating in the QCD asymptotic freedom is revealed. The higher loop corrections and the sch...

The problem of precise evaluation of perturbative QCD predictions at moderate energies is addressed. In order to improve stability of the predictions with respect to change of the renormalization scheme it is proposed to replace the sequence of conventional renormalization group improved approximants by a sequence of modified approximants, involving a modified running coupling constant, which is free from Landau singularity and much less renormalization scheme depenedent than...

Renormalization Group Equations (RGEs) are indispensable tool to know the behavior of physical parameters at different energy scales. They are also extremely crucial if we want to extend our known Standard Model gauge group by some extra gauge groups and the $\beta$-functions are the soul of these RGEs. In literature although it is quite common to find long, final expressions of the RGEs, unfortunately it is difficult to find any pedagogical review to calculate these $\beta$-...

Recently, the QCD renormalization group (RG) equation at higher orders in MS-like renormalization schemes has been solved for the running coupling as a series expansion in powers of the exact 2-loop order coupling. In this work, we prove that the power series converges to all orders in perturbation theory. Solving the RG equation at higher orders, we determine the running coupling as an implicit function of the 2-loop order running coupling. Then we analyze the singularity st...

We present a one-loop calculation of a gauge invariant QCD beta function. Using both momentum and temperature renormalization group equations we investigate the running coupling in the magnetic sector as a function of temperature and momentum scale. At fixed momentum scale we find that, in contrast to $\lambda\phi^4$ or QED, high-temperature QCD is strongly coupled, even after renormalization group improvement. However, if the momentum scale is changed simultaneously with tem...