The BFKL pomeron with running coupling constant: how much of its hard nature survives?

Abstract

We discuss the BFKL equation with a running gauge coupling and identify in its solutions the contributions originating from different transverse momentum scales. We show that for a running coupling constant the distribution of the gluons making up the BFKL Pomeron shifts to smaller transverse momenta so that the dominant part of Pomeron can have a nonperturbative origin. It is demonstrated how this soft physics enters into the BFKL solution through the boundary condition. We consider two kinematical regimes leading to different behaviour of the rapidity and transverse momentum dependence of the gluon distribution. In the diffusion approximation to the BFKL kernel with running αs, we find a sequence of poles which replaces the cut for fixed αs. The second regime corresponds to the singular part of the kernel, which gives the dominant contribution in the limit of very large transverse momenta. Finally, a simple more general picture is obtained for the QCD Pomeron in hard processes: it is of soft, nonperturbative nature, but has hard ends of DGLAP-type.

Geometric Scaling from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi Evolution

“…However, this running-coupling GS can also be obtained using the running-coupling version of Eq. (9) [10,11] FIG. 2 (color online).…”

An anomalous dimension for small x evolution

“…A traditionally delicate point of the small-x resummation is the treatment of the running of the coupling [23][24][25][26][27][28]. While it has been known for some time [29] that running coupling effects can be included perturbatively order by order at small x, in a recent paper [30] we have shown that an all-order resummation of running coupling effects at small x is desirable and can in fact be accomplished.…”

Reanalysis of the BFKL Pomeron at the next-to-leading logarithmic accuracy

“…So, the next-to-leading order (NLO) correction to the BFKL equation is very important, which can be obtained by the resummation of α s [α s ln s] n terms. One may expect to achieve a reasonable intercept with the higherorder corrections at the next-to-leading logarithmic (NLL) accuracy [5][6][7][8][9][10][11][12][13]. The Pomeron intercept has also been analyzed in N = 4 super symmetry theory [14,15].…”