Glauber Phases in Non-Global LHC Observables: Resummation for Quark-Initiated Processes

It has been known for many years that jet cross sections at hadron colliders exhibit double-logarithmic corrections starting at four-loop order, arising from two soft Glauber-gluon interactions between the two colliding partons. The resummation of these "super-leading logarithms" has been achieved only recently by means of a renormalization-group treatment in soft-collinear effective theory. We generalize this result and, within the same framework and for quark-initiated processes, resum the double logarithms arising in the presence of an arbitrary number of Glauber-gluon exchanges. For typical choices of parameters, the higher-order Glauber terms give rise to corrections which are expected to be numerically of the same magnitude as the super-leading logarithms. However, we find that the Glauber series for jet cross sections is dominated by the two-Glauber contribution.Comment: 24 pages, 4 figure

Factorization of Non-Global LHC Observables and Resummation of Super-Leading Logarithms

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy $\sqrt{\hat s}$, and low-energy matrix elements, which are sensitive to the low scale $Q_0\ll\sqrt{\hat s}$ characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary $2\to M$ jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called "super-leading logarithms" discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for $pp\to 2\,\text{jets}$ processes, but suppressed in $H/Z$ and $H/Z$+jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.Comment: 72 pages, 18 figures, 1 appendi

Glauber Phases in Non-Global LHC Observables: Resummation for Gluon-Initiated Processes

The resummation of the ''Glauber series'' in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called ''super-leading logarithms'', together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor $(i\pi)^2$. On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for $gg$ and eleven elements for $qg$ scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for $gg$ scattering at relatively small vetoes $Q_0$, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected.Comment: 38 pages, 5 figure

Glauber phases in non-global LHC observables: resummation for gluon-initiated processes

Abstract The resummation of the “Glauber series” in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called “super-leading logarithms”, together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor (iπ)2. On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for gg and eleven elements for qg scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for gg scattering at relatively small vetoes Q 0, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected