Comment on the frozen QCD coupling

TL;DR

This paper introduces a novel, experiment-independent method to define different frozen QCD couplings used in various approximations, providing specific estimates and aligning with existing literature on intercepts.

Contribution

It proposes a new way to define multiple frozen QCD couplings independently of experimental data, distinguishing between DLA and SL approximations.

Findings

DLA coupling with time-like argument is approximately 0.24

DLA coupling with space-like argument is approximately 0.48

SL coupling estimate is around 0.1

Abstract

The frozen QCD coupling is a parameter often used as an effective fixed coupling. It is supposed to mimic both the running coupling effects and the lack of knowledge of alpha_s in the infrared region. Usually the value of the frozen coupling is fixed from the analysis of the experimental data. We present a novel way to define such coupling(s) independently of the experiments. We argue that there are different frozen couplings which are used in the double- (DL) and single- logarithmic (SL) Approximations. We introduce four kinds of the frozen couplings: the coupling used in DLA with a time-like argument (i.e. the coupling present in the non-singlet scattering amplitudes and DIS structure functions) which we find 0.24 approximately; the DLA coupling with a space-like argument (in e+e- -annihilation, in DY processes and in any scattering amplitude in the hard or backward kinematics) which is a factor two larger, namely 0.48. We also show that the frozen coupling in the SL evolution equations like BFKL has to be defined in a way less accurate compared to DLA, and our estimate for this coupling is 0.1. Our estimates for the singlet and non-singlet intercepts are also in a good agreement with the results available in the literature.