Gaps between Jets in the High Energy Limit

TL;DR

The work addresses jet-gap-jet production in the high-energy limit by unifying two QCD resummation frameworks: the BFKL leading-$Y$ approach and a $Q/Q_0$-based gap-cross-section resummation. It introduces the $\pi^2 DLLA$ to capture imaginary parts of loop integrals and derives an all-orders cross section that smoothly interpolates between the LLQ$_0$ and BFKL regimes, including running coupling effects. Three phenomenological all-orders matching schemes (simple, cross-section, and amplitude matching) are developed to combine the gap cross section with fixed-order BFKL results up to $\mathcal{O}(\alpha_s^5)$, while acknowledging potential divergences in certain limits and the need to account for real-emission contributions. Numerical results show that the matched cross sections reproduce the expected limiting behaviors and that BFKL contributions become increasingly important at large rapidity separations $Y$ and scales $L=\ln(Q^2/Q_0^2)$. The findings offer a practical framework for predicting jet-gap-jet observables at high-energy colliders like the Tevatron and LHC, facilitating future refinements toward a fully rigorous all-orders unification.

Abstract

We use perturbative QCD to calculate the parton level cross section for the production of two jets that are far apart in rapidity, subject to a limitation on the total transverse momentum Q0 in the interjet region. We specifically address the question of how to combine the approach which sums all leading logarithms in Q/Q0 (where Q is the jet transverse momentum) with the BFKL approach, in which leading logarithms of the scattering energy are summed. This paper constitutes progress towards the simultaneous summation of all important logarithms. Using an "all orders" matching, we are able to obtain results for the cross section which correctly reproduce the two approaches in the appropriate limits.