Order statistics for multijet events

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.

💡 Research Summary

This paper introduces a novel class of observables for probing high-energy QCD dynamics at the LHC by applying the mathematical framework of order statistics to multijet final states in inclusive dijet topologies. The core idea is to treat the rapidities of all jets in an event as a sample drawn from an underlying “parent” distribution and to analyze the distributions of the ordered rapidities (e.g., the most backward, the second-most backward, …, the most forward jet).

The study performs a comparative Monte Carlo analysis at √s = 8 and 13 TeV, contrasting a BFKL-based event generator (BFKLex) with two general-purpose generators employing DGLAP-based parton showers: PYTHIA8 (pT-ordered) and HERWIG7 (angular-ordered). Jets are reconstructed with standard anti-kT algorithm cuts (pT > 20 GeV, |y| < 4.7). Two families of normalized, shape-sensitive histograms are examined: 1) distributions for the three ordered jets in events with exactly N=3 jets, and 2) distributions for the most backward/forward (MB/MF) and second-most backward/forward (SMB/SMF) jets, aggregated across all event multiplicities (N≥2).

The key finding is that while the inclusive jet rapidity density (dN/dy) can be similar for different dynamics, the rank-ordered distributions reveal fundamental differences in how rapidity space is populated. For fixed N=3, BFKLex populates the rapidity interval more uniformly, whereas the DGLAP showers show stronger enhancement at the edges for the outer jets (Jet1, Jet3) and a narrower, more centrally peaked distribution for the middle jet (Jet2). Across multiplicities, the most striking discrimination power is found in the SMB and SMF distributions: BFKLex produces broader, skewed distributions, while PYTHIA8 and HERWIG7 yield distributions that are more concentrated towards the central region.

These shape differences are demonstrated to be robust under variations of the jet radius, proton PDF sets, and the inclusion/exclusion of non-perturbative effects (MPI, hadronization). They also persist when imposing a large rapidity separation between the outermost jets, a typical Mueller-Navelet selection. The stability of these observables suggests they are sensitive to the core characteristics of the emission pattern—BFKL’s diffusive, rapidity-ordered evolution versus DGLAP’s coherent, angular-ordered showers—rather than peripheral details.

The paper argues that rank-ordered rapidity distributions act as a powerful compression tool, transforming genuinely exclusive information about the multi-jet final state into simple, normalized one-dimensional histograms that are directly measurable with existing LHC datasets. This provides a new, theoretically interpretable handle to distinguish high-energy QCD dynamics, complementing traditional observables like azimuthal angular correlations. The authors suggest extending the analysis to NLL BFKL accuracy and encourage experimental measurement.