Measurements of jet multiplicity and jet transverse momentum in multijet events at sqrts13 TeV

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)

CERN-EP-2022-144

2023/08/30

CMS-SMP-21-006

Measurements of jet multiplicity and jet transverse

momentum in multijet events in proton-proton collisions at

√s=13 TeV

The CMS Collaboration*

Abstract

Multijet events at large transverse momentum (pT) are measured at √s=13 TeV

using data recorded with the CMS detector at the LHC, corresponding to an inte-

grated luminosity of 36.3 fb−1. The multiplicity of jets with pT>50 GeV that are

produced in association with a high-pTdijet system is measured in various ranges

of the pTof the jet with the highest transverse momentum and as a function of the

azimuthal angle difference ∆ϕ1,2 between the two highest pTjets in the dijet system.

The differential production cross sections are measured as a function of the transverse

momenta of the four highest pTjets. The measurements are compared with leading

and next-to-leading order matrix element calculations supplemented with simula-

tions of parton shower, hadronization, and multiparton interactions. In addition, the

measurements are compared with next-to-leading order matrix element calculations

combined with transverse-momentum dependent parton densities and transverse-

momentum dependent parton shower.

Published in the European Physical Journal C as doi:10.1140/epjc/s10052-023-11753-y.

*See Appendix A for the list of collaboration members

arXiv:2210.13557v2 [hep-ex] 28 Aug 2023

1 Introduction

The production of jets, which are reconstructed from a stream of hadrons coming from the

fragmentation of energetic partons, is described by the theory of strong interactions, quantum

chromodynamics (QCD). In proton-proton (pp) collisions, at leading order (LO) in the strong

coupling αS, two colliding partons from the incident protons scatter and produce two high

transverse-momentum (pT) partons in the ﬁnal state. The jets that originate from such a pro-

cess are strongly correlated in the transverse plane, and the azimuthal angle difference between

them, ∆ϕ1,2, should be close to π. However, higher-order corrections to the lowest order pro-

cess will result in a decorrelation in the azimuthal plane, and ∆ϕ1,2 will signiﬁcantly deviate

from π. These corrections can be due to either hard parton radiation, calculated at the ma-

trix element (ME) level at next-to-leading order (NLO), or softer multiple parton radiation de-

scribed by parton showers. In a recent approach [1], transverse-momentum dependent (TMD)

parton densities are obtained with the parton-branching method [2, 3] (PB-TMDs). These PB-

TMDs were combined with NLO ME calculations [4] supplemented with PB initial-state parton

showers [5], leading to predictions where the initial-state parton shower is determined by the

PB-TMD densities without tunable parameters. In Drell-Yan production at the LHC this ap-

proach leads to a good description of the measurements [6], whereas other approaches need

speciﬁc tunes. Therefore, it is interesting to study the PB prediction in a jet environment, es-

pecially since the PB-TMD initial-state shower also becomes important. Although ∆ϕ1,2 is an

inclusive observable, it is interesting for the theoretical understanding of the complete event

to measure the multiplicity of jets in different regions of ∆ϕ1,2 and the transverse momenta of

the ﬁrst four jets. The ∆ϕ1,2 measurement is mainly sensitive to initial-state parton showers at

an inclusive level, whereas the measurement of the jet multiplicity in different regions of ∆ϕ1,2

illustrates how many high-pTjets contribute to the ∆ϕ1,2 decorrelation.

The azimuthal correlation in high-pTdijet events was measured previously at: the Fermilab

Tevatron in proton-antiproton collisions by the D0 Collaboration at √s=1.96 TeV [7, 8]; and

at the CERN LHC in pp collisions by both the ATLAS Collaboration at √s=7 TeV [9] and the

CMS Collaboration at √s=7, 8, and 13 TeV [10–13].

In this paper, we describe new measurements of dijet events with rapidity |y|<2.5 and with

transverse momenta of the leading jet pT1 >200 GeV and the subleading jet pT2 >100 GeV. The

multiplicity of jets with pT>50 GeV is measured in bins of pT1 and ∆ϕ1,2. The jet multiplicity

in bins of ∆ϕ1,2 provides information on the ∆ϕ1,2 decorrelation. The cross sections for the four

leading jets are measured as a function of pTof each jet, which can give additional information

on the structure of the higher-order corrections.

This paper is organized as follows; in Section 2, a brief summary of the CMS detector and the

relevant components is given. In Section 3, the theoretical models for comparison at detector

level, as well as with the ﬁnal results are described. Section 4 gives an overview of the analysis,

with the event selection, data correction, and a discussion of the uncertainties. The ﬁnal results

and comparison with theoretical predictions are discussed in Section 5.

2 The CMS detector and event reconstruction

The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal di-

ameter, providing a magnetic ﬁeld of 3.8 T. Within the solenoid volume are silicon pixel and

strip tracker detectors, a lead tungstate crystal electromagnetic calorimeter (ECAL), and a brass

and scintillator hadron calorimeter (HCAL), each composed of a barrel part and two endcap

sections.

Events of interest are selected using a two-tiered trigger system. The ﬁrst level, composed of

custom hardware processors, uses information from the calorimeters and muon detectors to

select events at a rate of around 100 kHz within a ﬁxed latency of about 4 µs [14]. The second

level, known as the high-level trigger (HLT), consists of a farm of processors running a version

of the full event reconstruction software optimized for fast processing, while reduces the event

rate to around 1 kHz for data storage [15].

During the 2016 data-taking period, a gradual shift in the timing of the inputs of the ECAL

ﬁrst level trigger in the pseudorapidity region |η|>2.0, also known as “preﬁring”, caused

some trigger inefﬁciencies [14]. For events containing a jet with pT>100 GeV, in the region

2.5 <|η|<3.0 the efﬁciency loss is 10–20%, depending on pT,η, and the data-taking pe-

riod. Correction factors were computed from data and applied to the acceptance evaluated by

simulation.

The particle-ﬂow (PF) algorithm [16] reconstructs and identiﬁes each individual particle in an

event, with an optimized combination of information from the various elements of the CMS

detector. The energy of charged hadrons is determined from a combination of their momentum

measured in the tracker and the matching ECAL and HCAL energy deposits, corrected for the

response function of the calorimeters to hadronic showers. The energy of neutral hadrons is

obtained from the corresponding corrected ECAL and HCAL energies.

The candidate vertex with the largest value of summed physics-object p2

Tis taken to be the

primary vertex (PV) of pp interactions as described in Section 9.4.1 of Ref. [17]. The physics

objects are the jets, clustered using the jet ﬁnding algorithm [18, 19] with the tracks assigned to

candidate vertices as inputs, and the associated missing transverse momentum.

Jets are reconstructed from PF objects, clustered using the anti-kTalgorithm [18, 19] with a dis-

tance parameter of R=0.4. The jet momentum is determined as the vectorial sum of all particle

momenta in the jet, and is found from simulation to be, typically, within 5 to 10% of the true

momentum over the entire pTspectrum and detector acceptance. Additional pp interactions

within the same or nearby bunch crossings can contribute additional tracks and calorimetric

energy deposits, increasing the apparent jet momentum. To mitigate this effect, tracks iden-

tiﬁed as originating from pileup vertices are discarded and an offset correction based on the

average amount of transverse energy in the event per unit area is applied to correct for the re-

maining contributions [20]. Jet energy corrections are derived from simulation studies so that

the average measured energy of jets becomes identical to that of particle-level jets. However,

the selective ECAL readout leads to a bias in the jet energy scale. In situ measurements of the

momentum balance in dijet, photon+jet, Z+jet, and multijet events are used to determine any

residual differences between the jet energy scale (JES) in data and in simulation, and appro-

priate corrections are made [21]. Additional selection criteria are applied to each jet to remove

jets potentially dominated by instrumental effects or reconstruction failures. The jet energy

resolution (JER) amounts typically to 15–20% at 30 GeV, 10% at 100 GeV, and 5% at 1 TeV [21].

The missing transverse momentum vector ⃗

pmiss

Tis computed as the negative vector sum of

the transverse momenta of all the PF candidates in an event, and its magnitude is denoted as

pmiss

T[22]. The ⃗

pmiss

Tis modiﬁed to include corrections to the energy scale of the reconstructed

jets in the event. Anomalous high-pmiss

Tevents can be due to a variety of reconstruction fail-

ures, detector malfunctions, or noncollision backgrounds. Such events are rejected by event

ﬁlters that are designed to identify more than 85–90% of the spurious high-pmiss

Tevents with a

mistagging rate less than 0.1% [22].

A more detailed description of the CMS detector, together with a deﬁnition of the coordinate

system used and the relevant kinematic variables, can be found in Ref. [23].

3 Theoretical predictions

Theoretical predictions from Monte Carlo (MC) event generators at LO and NLO are used for

comparison with measurements of the jet multiplicities as well as with the pTspectra in multijet

ﬁnal states.

We use the following predictions at LO:

•PYTHIA8 [24] (version 8.219) simulates LO 2 →2 hard processes. The parton shower

is generated in a phase space ordered in transverse momentum and longitudinal

momentum of the emitted partons, and the colored strings are hadronized using the

Lund string fragmentation model. The CUETP8M1 [25] tune (with the parton distri-

bution function (PDF) set NNPDF2.3LO [26]) gives the parameters for multiparton

interactions (MPI).

•HERWIG++ [27] (version 2.7.1) simulates LO 2 →2 hard processes. The emitted

partons in the parton shower follow angular ordering conditions, and the cluster

fragmentation model is used to transform colored partons into observable hadrons.

The CUETHppS1 [25] tune (with the PDF set CTEQ6L1 [28]) is applied.

•MADGRAPH5 aMC@NLO [4] (version 2.3.3) event generator, labeled MADGRAPH+PY8,

is used in the LO mode, with up to four noncollinear high-pTpartons included in the

matrix element (ME), supplemented with parton showering and MPI using PYTHIA

8 with the CUETP8M1 tune and merged according to the kT-MLM matching proce-

dure [29] with a matching scale of 10 GeV.

•MADGRAPH5 aMC@NLO [4] (version 2.6.3) event generator, labeled MADGRAPH+CA3,

is used in the LO mode to generate up to four noncollinear high-pTpartons included

in the ME. The PB-method describes the DGLAP evolution as a process of succes-

sive branching processes. It has been shown [2, 3] that on an inclusive level, the

DGLAP evolution is exactly reproduced, whereas the simulation of each branching

determines the transverse momentum distribution obtained during evolution. The

PB-TMDs are obtained from a ﬁt to inclusive HERA deep-inelastic electron proton

collision data [1]. Since the PB-TMDs come from a (forward) branching evolution,

the initial-state parton shower (in a backward evolution) follows directly from the

PB-TMD distributions, and therefore no free parameters are left for the initial-state

shower. We use the TMD merging [30] procedure for combining the TMD parton

shower with the ME calculations. The NLO PB-TMD set 2 [1] with αS(mZ) = 0.118

is used. The inclusion of the transverse momentum kTand initial-state PB-TMD par-

ton shower is performed with CASCADE3 [5] (version 3.2.3). The initial-state par-

ton shower follows the PB-TMD distribution, and has no free parameters left. The

ﬁnal-state radiation (since not constrained by TMDs) as well as hadronization is per-

formed with PYTHIA6 (version 6.428) [31] with an angular ordering veto imposed. A

merging scale value of 30 GeV is used, since it provides a smooth transition between

ME and PS computations. MPI effects are not simulated.

At NLO, different theoretical predictions are used. The factorization and renormalization scales

are set to half the sum over the scalar transverse momenta of all produced partons, 1/2 ∑HT.

However, we have explicitly checked that the distributions do not change when choosing

1/4 ∑HTor even 1/6 ∑HT. The uncertainty bands of the NLO predictions are determined

from the variation of the factorization and renormalization scales by a factor of two up and

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EUROPEANORGANIZATIONFORNUCLEARRESEARCH(CERN)CERN-EP-2022-1442023/08/30CMS-SMP-21-006Measurementsofjetmultiplicityandjettransversemomentuminmultijeteventsinproton-protoncollisionsat√s=13TeVTheCMSCollaboration*AbstractMultijeteventsatlargetransversemomentum(pT)aremeasuredat√s=13TeVusingdatarecordedwit...

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Measurements of jet multiplicity and jet transverse momentum in multijet events at sqrts13 TeV

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