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

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 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.

Logarithmic Regge Pole

“…The fitting procedures considering only energies above 1.0 TeV result in a pomeron intercept compatible with the double-pomeron value, α P ≈ 1.04 ∼ 1.05. This value corroborates the Double-Logarithmic contributions, where the higher accuracy of calculations, the lower is the intercept, resulting in the best value is given by the intercept close to 1 [41,42].…”

Logarithmic Regge pole

“…As is well-known, the LHC result at TeV is GeV [31], in accordance with the value predicted here. In contrast, starting from the TO-TEM result, one cannot reproduce, for example, the unexpected value for the slope encountered by the E710 Collaboration at TeV, GeV [40].…”

“…In general, the slope is obtained considering very small ranges of , which implies Coulomb and Nuclear contributions to the scattering amplitude. For example, for the E710 Collaboration [40], the interval for t is GeV and for the TOTEM Collaboration, one has GeV [31]. Then, these experimental values may carry some dependence on the momentum transfer.…”

Rise of the DIS structure function FL at small x caused by double-logarithmic corrections

“…[38,43] and used for the structute function F 1 in ref. [52] that such a generalization is achieved with replacement of Q 2 by Q 2 + µ 2 . When this shift has been done, F where A and A stand for the running QCD couplings as shown in ref.…”