Exact colour evolution for jet observables

Abstract

We perform a systematic and comprehensive analysis of sub-leading colour corrections in perturbative QCD processes involving multiple soft gluon emissions. This necessitates going beyond the standard parton shower paradigm in order to incorporate interference effects and is accomplished using the CVolver program, which simulates parton showers at the amplitude level. We can compute cross-sections with full-colour precision and also broken down explicitly in terms of their $N_c$ dependence. In this paper, we focus on the jet cross-section with a veto of additional jets in some fixed region of phase-space, since this is sensitive to wide-angle, soft gluon radiation. We consider $Z \to q \bar{q}$, $H \to gg$, $q\bar{q} \to q\bar{q}$, $qg \to qg$, $gg \to gg$ and $ZZ \to q\bar{q}q\bar{q}$. We find that non-trivial sub-leading colour effects are generally important at the 5 -- 30\% level and much more than this for certain interference contributions. Remarkably, for this observable, we find that for all of the $t$-channel gluon exchange processes that we consider, the strictly leading colour approximation, which includes the replacement $C_F \to C_A/2$, is an excellent approximation to the full colour result (up to an overall colour factor).