Hard to Soft Pomeron Transition in Small-xDeep Inelastic Scattering Data Using Optimal Renormalization

Abstract

We show that it is possible to describe the effective Pomeron intercept, determined from the HERA deep inelastic scattering data at small values of Bjorken x, by using next-to-leading order Balitsky-Fadin-Kuraev-Lipatov evolution together with collinear improvements. To obtain a good description over the whole range of Q(2), we use a non-Abelian physical renormalization scheme with the Brodsky-Lepage-Mackenzie optimal scale, combined with a parametrization of the running coupling in the infrared region.

The high-energy radiation pattern from BFKLex with double-log collinear contributions

“…Phenomenological applications of this resummation, not using a Monte Carlo approach, show agreement with experimental results and good perturbative convergence [27][28][29][30][31][32][33][34][35].…”

Single bottom quark production in k ⊥-factorisation

“…We will use in this study the fit of refs. [14,15] which achieves a successful description of F 2 and F L HERA data with a very simple ansatz for the proton impact factor with three independent parameters.…”

“…While the unintegrated gluon density extracted from [14,15] does not provide a detailed discussion of experimental uncertainties (unlike e.g. [38]), it is the only currently available unintegrated gluon density which is subject to BFKL evolution at NLL accuracy including a resummation of large logarithms at the level of the next-to-leading order BFKL kernel.…”

“…Bottom quarks can generally be produced via gluon splitting, g → bb in proton-proton collisions. Since our main purpose here is to test the unintegrated gluon density from the HERA fit [14,15] and to compare it to theoretical predictions from collinear factorization at small x, we concentrate in the following on bottom quark production in the forward region of one of the protons. In this way the heavy quark -as an incoming parton -will be fixed at relatively large x, while the second parton -a gluon -is forced into the smallx region.…”

“…A simple way for that to be realized and act as a proof of concept is to use an unintegrated gluon density from HERA fits into a phenomenological study of an LHC process. Recently, there were successful attempts for the detailed description of the Q 2 and x dependence of the structure functions F 2 and F L by making use of a collinearly-improved BFKL equation at next-to-leading logarithmic (NLx) accuracy [14,15]. 1 Within high energy factorization, the description of any hard process requires three ingredients: the universal BFKL gluon Green's function which resums high energy logarithms and two process dependent impact factors which describe the coupling of scattering particles to the gluon Green's function.…”