Elastic scattering of virtual photons via a quark loop in the 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 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.

“…Calculations in Ref. [15] confirmed the results of Ref. [14] and generalized them on the case of t = 0, and also accounted for the running coupling effects.…”

Section: Introductionsupporting

confidence: 66%

Section: Evolution Equations For Photon-photon Scattering Amplitudesmentioning

confidence: 97%

Section: Evolution Equations For Photon-photon Scattering Amplitudesmentioning

confidence: 99%

“…where f γγ (ω) is defined in Eq. (15). Therefore, F γγ (ω, y 1 ) in kinematics ( 16) is represented in terms of the photonquark amplitudes:…”

Section: B One Of the Photons Is On-shell And The Other Is Off-shellmentioning

confidence: 99%

See 2 more Smart Citations

Light-by-light scattering in double-logarithmic approximation

Ermolaev

Troyan

2018

“…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.…”

Section: Introductory Remarksmentioning

confidence: 99%

Hunting BFKL in semi-hard reactions at the LHC

Celiberto

2021

The agreement between calculations inspired by the resummation of energy logarithms, known as BFKL approach, and experimental data in the semi-hard sector of QCD has become manifest after a wealthy series of phenomenological analyses. However, the contingency that the same data could be concurrently portrayed at the hand of fixed-order, DGLAP-based calculations, has been pointed out recently, but not yet punctually addressed. Taking advantage of the richness of configurations gained by combining the acceptances of CMS and CASTOR detectors, we give results in the full next-to-leading logarithmic approximation of cross sections, azimuthal correlations and azimuthal distributions for three distinct semi-hard processes, each of them featuring a peculiar final-state exclusiveness. Then, making use of disjoint intervals for the transverse momenta of the emitted objects, i.e. $$\kappa $$ κ -windows, we clearly highlight how high-energy resummed and fixed-order driven predictions for semi-hard sensitive observables can be decisively discriminated in the kinematic ranges typical of current and forthcoming analyses at the LHC. The scale-optimization issue is also introduced and explored, while the uncertainty coming from the use of different PDF and FF set is deservedly handled. Finally, a brief overview of , a numerical tool recently developed, suited for the computation of inclusive semi-hard reactions is provided.

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

Ermolaev

Troyan

2020

Interest in studying the inclusive photon induced processes of Deep-Inelastic Scattering (DIS) and Diffractive DIS (DDIS) at high energies includes their experimental investigation and thorough theoretical description. The conventional instrument for theoretical investigation of DIS at large x and large Q 2 in Collinear Factorization is DGLAP. It describes the Q 2 -evolution of the DIS structure functions. Description of DIS at large Q 2 in the small x-region requires accounting for the both Q 2 and x -evolution at the same time. Combining DGLAP with total resummation of double logarithms of x and Q 2 , we present a description of F1 at large Q 2 and arbitrary x. Making use of the necessity of the shift of Q 2 in order to regulate infrared singularities, we obtain an expression for F1 valid at arbitrary x and Q 2 . The obtained expressions coincide with the DLA expressions at small x and at the same time coincide with the DGLAP result at large x and large Q 2 . Accounting for virtuality k 2 of the external partons allows us to obtain expressions for F1 in KT -Factorization, which are valid at arbitrary Q 2 and arbitrary relations between Q 2 and k 2 . Expressions for F1 in all forms of QCD factorization exhibit the small-x asymptotics of the Pomeron type. This Pomeron is revealed by the high-energy asymptotics of amplitudes of the 2 → 2 parton-parton forward scattering. These amplitudes are calculated in DLA, so their asymptotics have nothing to do with the BFKL Pomeron. We demonstrate that the parton-parton amplitudes can be used in the DDIS models at experimentally available energies which are not asymptotic instead of BFKL Pomeron or combinations of hard and soft Pomerons. This modification allows us to describe DDIS at high but not asymptotically high energies and automatically ensures the Pomerons asymptotics, which simplifies and makes more consistent theory of DDIS.