Light-by-light scattering in double-logarithmic approximation

Abstract

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 doublelogarithmic (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.

Combining the small-x evolution and DGLAP for description of inclusive photon induced processes

“…The parton-parton amplitudes h rr ′ (ω) in DLA with both fixed and running α s were also obtained in Ref. [13]. The explicit expressions for them can be found in Appendix A.…”

“…Amplitudes T (col) q.g in region B Amplitudes T (col) q,g in region B were calculated in Ref. [13] with DL accuracy and with both fixed and running α s . They were represented in terms of the parton-parton amplitudes h rr ′ :…”

“…( 9), we obtain expressions for the photoproduction amplitudes in the Mellin space: Expressions for the Mellin amplitudes F q,g (ω, y) and f γq (ω), f γg (ω) in DLA with fixed and running QCD coupling were obtained in Ref. [13], where they are represented in terms of the Mellin amplitudes h rr ′ (ω) :…”

“…Expressions for amplitudes T (col) q,g at small-x were obtained in double-logarithmic approximation (DLA) in Ref. [13] where these amplitudes were represented in terms of the on-shell parton-parton amplitudes A rr ′ (r, r ′ = q, g) depicted in Fig. 2, and explicit expressions for them are presented in Appendix A.…”

Hunting BFKL in semi-hard reactions at the LHC

“…Although being recognized as a privileged channel for the manifestation of the BFKL dynamics, comparisons between the large number of BFKL predictions [72][73][74][75][76][77][78][79] with the only available data from the LEP2 Cern experiment were ineffective due to the relatively low center-of-mass energy and the limited accuracy of the detector. Quite recently [80,81], the amplitude for the light-by-light elastic scattering via a single-quark loop was calculated in the so-called double-logarithmic approximation (DLA). This approach 2 accounts for the resummation of those contributions proportional to (α s ln s ln s) n that, at variance with gluon interactions in the BFKL ladder, appear in the quark-antiquark exchange [92][93][94][95][96][97][98], giving rise to a different asymptotic behavior in the power of s with respect to the single-logarithmic trend of the BFKL Pomeron (for more details, see Refs.…”