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.