Light-by-light scattering in Double-Logarithmic Approximation

In the present paper we consider the elastic 2 -> 2 -scattering of virtual photons at high energies in the forward kinematics at zero and non-zero values of t. Accounting for both gluon and quark double-logarithmic (DL) contributions to all orders in the QCD coupling, we obtain explicit expressions for amplitudes of this process in Double-Logarithmic Approximation (DLA). First we keep the QCD coupling fixed and then account for running coupling effects. Applying the saddle-point method to the obtained expressions for the scattering amplitude, we calculate the high-energy asymptotics of the amplitude, which proved to be of the Regge form. The Reggeon bears the vacuum quantum numbers and therefore it is a new, DL contribution to Pomeron. Comparison of the DL Pomeron to the BFKL Pomeron shows that contribution of the DL Pomeron to the high-energy asymptotics is of the same order as contribution of the BFKL Pomeron, so the DL Pomeron should be taken into account together with the BFKL Pomeron. We estimate the applicability region for the asymptotics of the light-by-light scattering amplitude, where the the DL Pomeron can reliably represent the parent amplitude.Comment: 16 pages, 4 figures. Multiple errors are corrected, 2 figs are added, comparizon to BFKL is done in more detai

Comment on the recent COMPASS data on the spin structure function g_1

We examine the recent COMPASS data on the spin structure function g_1 singlet. We show that it is rather difficult to use the data in the present form in order to draw conclusions on the initial parton densities. However, our tentative estimate is that the data better agree with positive rather than negative initial gluon densities.Comment: 8 pages, 1 figur

Comment on the frozen QCD coupling

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.Comment: 11 pages, 3 figure