We introduce a method to compute one-loop soft functions for exclusive N - jet processes at hadron colliders, allowing for different definitions of the algorithm that determines the jet regions and of the measurements in those regions. In particular, we generalize the N -jettiness hemisphere decomposition of ref. [1] in a manner that separates the dependence on the jet boundary from the observables measured inside the jet and beam regions. Results are given for several factorizable jet definitions, including anti- k T , XCone, and other geometric partitionings. We calculate explicitly the soft functions for angularity measurements, including jet mass and jet broadening, in pp → L + 1 jet and explore the differences for various jet vetoes and algorithms. This includes a consistent treatment of rapidity divergences when applicable. We also compute analytic results for these soft functions in an expansion for a small jet radius R . We find that the small- R results, including corrections up to O R 2 $$ \mathcal{O}\left({R}^2\right) $$ , accurately capture the full behavior over a large range of R .

United States

Daniele Bertolini

Daniel Kolodrubetz

Duff Neill

Germany

Piotr Pietrulewicz

Iain Stewart

Frank Tackmann

Netherlands

Wouter Waalewijn

Soft functions for generic jet algorithms and observables at hadron colliders

In collider physics, jet algorithms are a ubiquitous tool for clustering particles into discrete jet objects. Event shapes offer an alternative way to characterize jets, and one can define a jet multiplicity event shape, which can take on fractional values, using the framework of “jets without jets”. In this paper, we perform the first analytic studies of fractional jet multiplicity Ñ jet in the context of e + e − collisions. We use fixed-order QCD to understand the Ñ jet cross section at order α s 2 , and we introduce a candidate factorization theorem to capture certain higher-order effects. The resulting distributions have a hybrid jet algorithm/event shape behavior which agrees with parton shower Monte Carlo generators. The Ñ jet observable does not satisfy ordinary soft-collinear factorization, and the Ñ jet cross section exhibits a number of unique features, including the absence of collinear logarithms and the presence of soft logarithms that are purely non-global. Additionally, we find novel divergences connected to the energy sharing between emissions, which are reminiscent of rapidity divergences encountered in other applications. Given these interesting properties of fractional jet multiplicity, we advocate for future measurements and calculations of Ñ jet at hadron colliders like the LHC.

Jesse Thaler

Jonathan Walsh

The first calculation of fractional jets

We propose a new method for pileup mitigation by implementing “pileup per particle identification” (PUPPI). For each particle we first define a local shape α which probes the collinear versus soft diffuse structure in the neighborhood of the particle. The former is indicative of particles originating from the hard scatter and the latter of particles originating from pileup interactions. The distribution of α for charged pileup, assumed as a proxy for all pileup, is used on an event-by-event basis to calculate a weight for each particle. The weights describe the degree to which particles are pileup-like and are used to rescale their four-momenta, superseding the need for jet-based corrections. Furthermore, the algorithm flexibly allows combination with other, possibly experimental, probabilistic information associated with particles such as vertexing and timing performance. We demonstrate the algorithm improves over existing methods by looking at jet p T and jet mass. We also find an improvement on non-jet quantities like missing transverse energy.

United Kingdom

CERN

Philip Harris

Matthew Low

Nhan Tran

Pileup per particle identification

We introduce a new class of event shapes to characterize the jet-like structure of an event. Like traditional event shapes, our observables are infrared/collinear safe and involve a sum over all hadrons in an event, but like a jet clustering algorithm, they incorporate a jet radius parameter and a transverse momentum cut. Three of the ubiquitous jet-based observables — jet multiplicity, summed scalar transverse momentum, and missing transverse momentum — have event shape counterparts that are closely correlated with their jet-based cousins. Due to their “local” computational structure, these jet-like event shapes could potentially be used for trigger-level event selection at the LHC. Intriguingly, the jet multiplicity event shape typically takes on non-integer values, highlighting the inherent ambiguity in defining jets. By inverting jet multiplicity, we show how to characterize the transverse momentum of the n -th hardest jet without actually finding the constituents of that jet. Since many physics applications do require knowledge about the jet constituents, we also build a hybrid event shape that incorporates (local) jet clustering information. As a straightforward application of our general technique, we derive an event-shape version of jet trimming, allowing event-wide jet grooming without explicit jet identification. Finally, we briefly mention possible applications of our method for jet substructure studies.

Tucker Chan

Jet observables without jet algorithms