Collinearly-improved BK evolution meets the HERA data

Abstract

In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order corrections to the BK equation which are enhanced by (single or double) collinear logarithms. We then use numerical solutions to this equation to fit the HERA data for the electron-proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q^2=400 GeV^2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran-Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.Comment: 15 pages, 3 figures; minor corrections to fit results and few comments adde

Use of a running coupling in the NLO calculation of forward hadron production

“…The explicit calculations of the one-loop RC corrections to the BK equation [11,[37][38][39] 39] or the fastest apparent convergence [19]. Still, one should be rather careful with some choices: for example, for certain values of the dipole sizes the Balitsky prescription takes unphysically small values, and one may question if the contribution from the respective phase space is properly computed (see the discussion in [19]).…”

Initial conditions in AA and pA collisions

“…The equation as originally derived is unstable [24] due to large transverse momentum logarithms. Recently a way to resum these logarithms was developed [25,26], leading to a stable solution of the whole equation at NLO accuracy. It turns out [27] that with a suitable choice of a constant under the log, one can arrange so that most of the NLO corrections are included in the resummation and the remaining finite NLO terms are small.…”

Balitsky-Kovchegov equation at next-to-leading order accuracy with a resummation of large logarithms

“…[37]. The resummation is done at leading log accuracy, and the α 2 s contribution of the resummed logarithms is included exactly in the kernel K 2 .…”

“…The origin of this problem was traced back to so called non-conformal double logarithm [35] modifying the leading order part of the BK kernel. Later, a resummation scheme to resum large logarithmic contributions to all orders has been developed [36,37]. The first solution to the NLO BK equation improved with these resummations was presented in Ref.…”