Abstract
Coherence violation is an interesting and counter-intuitive phenomenon in QCD. We discuss the circumstances under which violation occurs in observables sensitive to soft radiation and arrive at the conclusion that almost all such observables at hadron colliders will violate coherence to some degree. We illustrate our discussion by considering the gaps-between-jets observable, where coherence violation is super-leading, then we generalise to other observables, including precise statements on the logarithmic order of coherence violation.
Highlights
The Sudakov operator VQ0,Q corresponds to no soft-gluon emission directly into the region between the dijets with transverse momentum greater than Q0
Notwithstanding the role of this non-global radiation, our focus here is on the collinear evolution of the incoming partons and for that we will continue to neglect the non-global corrections
This means that all observables at hadron-hadron colliders that have any sensitivity to soft gluon emission will violate coherence to some degree
Summary
We consider more general pure QCD processes in hadron-hadron collisions (we will consider electroweak processes later) and begin with a generalisation of eq (1.3):. Eq (2.4) can be generalized to a statement that there be no coherence violation in σn, i.e. for any number of collinear emissions, thereby allowing all-orders DGLAP evolution up to the hard scale Q. For this to be so, it is necessary that [Re(ln Vα,β), T2s] M(0n) = 0,. We only need to check the commutativity of a Coulomb exchange with any soft interference term between an initial and a final state parton in order to check for coherence violation. This means that all observables at hadron-hadron colliders that have any sensitivity to soft gluon emission will violate coherence to some degree.
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