Order statistics for multijet events

Abstract

We show that rank-ordered jet rapidity distributions - a direct application of order statistics - provide a simple yet powerful probe of high-energy (small-x) QCD dynamics at the LHC. In inclusive dijet topologies at s^(1/2) = 8 and 13 TeV, with realistic jet selections, we compare a BFKL-based Monte Carlo (BFKLex) to two general-purpose event generators based on collinear factorization and DGLAP parton showers, PYTHIA8 (pT-ordered) and HERWIG7 (angular-ordered). Even when two underlying dynamics happen to give similar inclusive jet rapidity distributions, such observables are too coarse to discriminate their underlying rapidity point processes, whereas the rank-ordered distributions remain sensitive to the differences in how rapidity space is filled. For fixed multiplicity (N=3) and for the second-most-forward/backward jets across multiplicities, BFKLex populates the rapidity interval more democratically, whereas the general-purpose event generators exhibit comparatively stronger edge enhancement for N=3 and narrower, more centrally concentrated distributions for the second-most ranks. These shape differences are stable under variations of jet radius, proton PDFs, and MPI/hadronization settings, and persist when requiring large rapidity separation between the outer jets. Rank-ordered rapidities thus compress genuinely exclusive information about the multi-jet final state into one-dimensional, normalized histograms that are directly measurable with existing dijet and Mueller-Navelet selections and provide a new handle on high-energy radiation patterns.