Resumming double logarithms in the QCD evolution of color dipoles

Abstract

The higher-order perturbative corrections, beyond leading logarithmic accuracy, to the BFKL evolution in QCD at high energy are well known to suffer from a severe lack-of-convergence problem, due to radiative corrections enhanced by double collinear logarithms. Via an explicit calculation of Feynman graphs in light cone (time-ordered) perturbation theory, we show that the corrections enhanced by double logarithms (either energy-collinear, or double collinear) are associated with soft gluon emissions which are strictly ordered in lifetime. These corrections can be resummed to all orders by solving an evolution equation which is non-local in rapidity. This equation can be equivalently rewritten in local form, but with modified kernel and initial conditions, which resum double collinear logs to all orders. We extend this resummation to the next-to-leading order BFKL and BK equations. The first numerical studies of the collinearly-improved BK equation demonstrate the essential role of the resummation in both stabilizing and slowing down the evolution.Comment: 16 pages, 5 figure

Monte Carlo study of double logarithms in the smallxregion

“…In this case it was shown in [1] that this resums to a Bessel function of the first kind (this approach, in γ-space, has already been successfully applied in many phenomenological applications [23,24,25,26,27,28,29,30,31]). A similar conclusion has recently been reached in coordinate space in [32].…”

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

“…As it was shown in [2] this expression resums to a Bessel function of the first kind (similar results have recently been obtained in coordinate representation in [26]). 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].…”

Rapidity evolution of gluon TMD from low to moderate x

“…The NLO corrections to the BFKL [44,45] and BK [17][18][19][20][46][47][48][49] equation are available but they suffer from the well-known problem that they lead to negative cross sections. This difficulty can be overcome by the "collinear resummation" of double-logarithmic contributions for the BFKL [50][51][52][53] and BK [54][55][56] equations and we hope that our eq. (5.5) and especially its future NLO version will help to solve the problem of negative cross sections of NLO amplitudes at high energies.…”