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

## TL;DR

This paper develops a unified theoretical framework combining DGLAP and small-x resummation techniques to accurately describe inclusive photon-induced processes in DIS across all x and Q^2 ranges, improving the understanding of high-energy scattering.

## Contribution

It introduces a novel approach that merges DGLAP evolution with double logarithm resummation, providing expressions valid at arbitrary x and Q^2, and offers a new perspective on Pomeron contributions in high-energy QCD.

## Key findings

- Derived expressions for F_1 valid at all x and Q^2.
- Unified description matching DGLAP and small-x limits.
- Parton-parton amplitudes can replace BFKL Pomeron in models.

## Abstract

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 is DGLAP. It describes the Q^2-evolution. Description of DIS 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 structure function F_1 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 F_1 valid at arbitrary x and Q^2. The obtained expressions coincide with the DLA expressions at small x and at the same time coincides with the DGLAP result at large x and large Q^2. Accounting for virtualities k^2 of the external partons allows us to obtain expressions for F_1 in K_T-Factorization, which are valid at arbitrary Q^2 and arbitrary relations between Q^2 and k^2. Expressions for F_1 in all types of QCD factorization exhibit the small-x asymptotics of the Pomeron type. This Pomeron is generated 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 instead of BFKL Pomeron or combinations of hard and soft Pomerons at non-asymptotic energies. On the other hand, this modification automatically ensures the Pomerons asymptotics, which simplifies and makes more consistent theory of DDIS.