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The resummation of the ''Glauber series'' in non-global LHC observables isextended to processes with gluons in the initial state. This seriessimultaneously incorporates large double-logarithmic corrections, the so-called''super-leading logarithms'', together with higher-order exchanges of pairs ofGlauber gluons associated with the large numerical factor $(i\pi)^2$. On atechnical level, the main part of this work is devoted to the systematicreduction 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 sectionsat the parton level show that, in particular for $gg$ scattering at relativelysmall vetoes $Q_0$, the contribution involving four Glauber exchanges gives asizeable correction and should not be neglected.

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