Glauber Gluons and Multiple Parton Interactions

Abstract

We show that for hadronic transverse energy $E_T$ in hadron-hadron collisions, the classic Collins-Soper-Sterman (CSS) argument for the cancellation of Glauber gluons breaks down at the level of two Glauber gluons exchanged between the spectators. Through an argument that relates the diagrams with these Glauber gluons to events containing additional soft scatterings, we suggest that this failure of the CSS cancellation actually corresponds to a failure of the `standard' factorisation formula with hard, soft and collinear functions to describe $E_T$ at leading power. This is because the observable receives a leading power contribution from multiple parton interaction (or spectator-spectator Glauber) processes. We also suggest that the same argument can be used to show that a whole class of observables, which we refer to as MPI sensitive observables, do not obey the standard factorisation at leading power. MPI sensitive observables are observables whose distributions in hadron-hadron collisions are disrupted strongly by the presence of multiple parton interactions (MPI) in the event. Examples of further MPI sensitive observables include the beam thrust $B^+_{a,b}$ and transverse thrust.