CMS-PAS-SMP-21-006

CMS-PAS-SMP-21-006
Cross section measurements of jet multiplicity and jet transverse momenta in multijet events at $\sqrt{s}=$ 13 TeV
CMS Collaboration
July 2021

Abstract: Multijet events at large transverse momentum ( $p_{\mathrm{T}}$ ) are measured at $\sqrt{s}=$ 13 TeV with data recorded with the CMS detector at the LHC corresponding to an integrated luminosity of 36.3 fb $^{-1}$ . The multiplicity of jets with $p_{\mathrm{T}} >$ 50 GeV in addition to a high $p_{\mathrm{T}}$ dijet system is measured for different regions of the transverse momentum of the leading $p_{\mathrm{T}}$ jet and as a function of the azimuthal angle $\Delta\phi_{1,2}$ between the two leading jets in the dijet system. The differential cross section of the four jets leading in $p_{\mathrm{T}}$ is measured as a function of their transverse momentum. The measurements are compared to leading order matrix-element calculations supplemented with parton shower, hadronization and multiparton interactions. In addition next-to-leading order matrix-element calculations combined with conventional parton shower as well as with Parton Branching (PB) transverse momentum dependent (TMD) parton densities and PB-TMD initial state parton shower are compared to the measurements.
Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, Submitted to EPJC. The superseded preliminary plots can be found here.

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Probability matrix (condition number: 4.9) for the ${p_{\mathrm {T}}}$ of the four leading jets constructed with the MadGraph+Py8 sample. The global 4 $\times$ 4 sectors corresponds to each one of the first four jets ${p_{\mathrm {T}}}$ distributions, the $x$ -axis corresponds to the hadron(gen) level and $y$ -axis corresponds to the detector(rec) level as labeled in each axis. The $z$ -axis covers a range from 10 $^{-6}$ to 1 indicating the probability of migrations from the hadron level bin to the correspondent detector level bin.
png pdf	Figure 2: Probability matrix (condition number: 3.0) for the jet multiplicity distribution constructed with the MadGraph+Py8 sample. The global 3 $\times$ 3 sectors (delimited by the thick black lines) corresponds to the ${p_{\mathrm{T1}}}$ bins, indicated by the labels in the $x$ (down) and $y$ (left) axis; and inside this ones there are smaller 3 $\times$ 3 structures corresponding to the ${\Delta \phi _{1,2}}$ bins, indicated in the uppermost row and rightmost column, the $x$ ( $y$ )-axis of these ${\Delta \phi _{1,2}}$ cells corresponds to the jet multiplicity at hadron(detector) level. The $z$ -axis covers a range from 10 $^{-6}$ to 1 indicating the probability of migrations from the hadron level bin to the correspondent detector level bin.
png pdf	Figure 3: Correlation matrix for the hadron level ${p_{\mathrm {T}}}$ of the four leading jets. It contains contributions form the data recorded in 2016 and from the limited statistics from the MadGraph+Py8 sample. Here each one of the 4 $\times$ 4 sectors corresponds to one of the ${p_{\mathrm {T}}}$ spectra measured, indicated by the $x$ and $y$ -axis labels. The $z$ -axis covers a range from -1 to 1 indicating the correlations in blue shades and anti-correlations in red shades, the values between -0.1 and 0.1 are represented in white.
png pdf	Figure 4: Correlation matrix at hadron level for the jet multiplicity distribution. It contains contributions form the data recordered in 2016 and from the limited statistics from the MadGraph+Py8 sample. The global 3 $\times$ 3 sectors (delimited by the thick black lines) corresponds to the ${p_{\mathrm{T1}}}$ bins, indicated by the labels in the $x$ (down) and $y$ (left) axis; and inside this ones there are smaller 3 $\times$ 3 structures corresponding to the ${\Delta \phi _{1,2}}$ bins, indicated in the uppermost row and rightmost column, the $x$ and $y$ -axis of these ${\Delta \phi _{1,2}}$ cells corresponds to the jet multiplicity. The $z$ -axis covers a range from $-$ 1 to 1 indicating the correlations in blue shades and anti-correlations in red shades, the values between $-$ 0.1 and 0.1 are represented in white.
png pdf	Figure 5: Relative uncertainties for the jet multiplicity distribution in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . Here Other includes luminosity, pileup, prefiring and unfolding model uncertainties added in quadrature.
png pdf	Figure 6: Relative uncertaities for the ${p_{\mathrm {T}}}$ distributions of the four leading jets. Here Other includes luminosity, pileup, prefiring and unfolding model uncertainties added in quadrature.
png pdf	Figure 7: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to LO predictions normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 7-a: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to LO predictions normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 7-b: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to LO predictions normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 7-c: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to LO predictions normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 8: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 8-a: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 8-b: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 8-c: Differential cross section as function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of ${p_{\mathrm{T1}}}$ and ${\Delta \phi _{1,2}}$ . The data are compared to NLO dijet predictions MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj). The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend.
png pdf	Figure 9: Transverse momenta of the measured four leading jets, here the yellow band represents the total experimental uncertainty. Data is compared to LO (PYTHIA 8) and NLO (MG5_aMC+Py8) predictions. The red band in the NLO prediction represents the scale uncertainty.
png pdf	Figure 10: Transverse momenta of the four leading jets compared to LO predictions normalized to the inclusive dijet data cross section using the scaling factors shown in the legend.
png pdf	Figure 10-a: Transverse momenta of the four leading jets compared to LO predictions normalized to the inclusive dijet data cross section using the scaling factors shown in the legend.
png pdf	Figure 10-b: Transverse momenta of the four leading jets compared to LO predictions normalized to the inclusive dijet data cross section using the scaling factors shown in the legend.
png pdf	Figure 11: Transverse momenta of the four leading jets compared to NLO predictions normalized to the inclusive dijet data cross section by using the scaling factors shown in the legend.
png pdf	Figure 11-a: Transverse momenta of the four leading jets compared to NLO predictions normalized to the inclusive dijet data cross section by using the scaling factors shown in the legend.
png pdf	Figure 11-b: Transverse momenta of the four leading jets compared to NLO predictions normalized to the inclusive dijet data cross section by using the scaling factors shown in the legend.

Tables
png pdf	Table 1: Description of the simulated samples used in the analysis.
png pdf	Table 2: The integrated luminosity for each trigger sample considered in this analysis with the ${p_{\mathrm {T}}}$ thresholds for HLT(PF) reconstruction.

Summary

A study of multi-jet events has been performed in pp collisions at a center-of-mass energy of 13 TeV with data collected with the CMS detector corresponding to an integrated luminosity of 36.3 fb

$^{-1}$ . The measurements are performed by selecting a dijet system containing a jet with

${p_{\mathrm{T}}} >$ 200 GeV and a subleading jet with

${p_{\mathrm{T}}} >$ 100 GeV within

$|y| <$ 2.5.

For the first time, the jet multiplicity in bins of the leading jet

${p_{\mathrm{T}}}$ and the azimuthal angle between the two leading jets

${\Delta\phi_{1,2}}$ is measured. The differential cross section of the four leading

${p_{\mathrm{T}}}$ jets is measured up to the TeV scale. The jet multiplicity distributions show that even in the back-to-back region of the the dijet system, up to seven jets are measurable. The measurement of the differential cross section as a function of the jet

${p_{\mathrm{T}}}$ for the first four leading

${p_{\mathrm{T}}}$ jets is an important benchmark for Standard Model multijet cross section calculations, and especially for the simulations including parton showers for higher jet multiplicity.

The measured multiplicity distribution of jets in addition to the dijet system with

${p_{\mathrm{T}}} >$ 50 GeV and

$|y| <$ 2.5 is reasonably described by the LO multijet MadGraphLO simulation, nonetheless in the back-to-back region HERWIG++ provides a better shape description. The measured differential cross section as a function of the transverse momentum of the four leading

${p_{\mathrm{T}}}$ jets is not well described by any of the predictions, especially cross sections for the third and fourth jets are not described in normalization and shape.

The predictions using dijet NLO matrix elements, MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj) describe the lower multiplicity regions rather well, as well as the transverse momenta of the leading jets. The cross section of the third and fourth jet is described in shape only by MG5_aMC+CA3 (jj). The three jet NLO calculation MG5_aMC+CA3 (jjj) describes very well the cross section of the third and fourth jet.

While the description of the lower jet multiplicity cross section obtained with NLO dijet calculations supplemented with conventional parton shower or with PB -TMDs and TMD parton shower is rather good, the higher jet multiplicities are not described with either parton shower approach. The measurements presented here allow for very stringent tests of theory predictions in the perturbative high

${p_{\mathrm{T}}}$ and high jet multiplicity regions.

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