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| CMS-PAS-SMP-23-008 | ||
| Measurement of event shapes in minimum bias events from pp collisions at 13 TeV | ||
| CMS Collaboration | ||
| 4 June 2024 | ||
| Abstract: This note presents a measurement of event-shape variables using a data sample of low-pileup inelastic proton-proton collisions collected by the CMS detector at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 64 $ \mu$b$^{-1} $. A number of observables related to the overall distribution of charged particles in the collisions is corrected for detector effects and compared to simulations. Inclusive event-shape distributions, as well as event shapes as a function of charged-particle multiplicity, are studied. None of the models investigated, including EPOS, one HERWIG7 tune, and several PYTHIA8 tunes, are able to satisfactorily describe the data. Moreover, there are significant trends in this misdescription that are common amongst all generator setups studied, particularly showing data being more isotropic than any of the simulations. Multidimensional unfolded distributions are provided, along with their correlations. | ||
| Links: CDS record (PDF) ; CADI line (restricted) ; | ||
| Figures | |
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Figure 1:
The unfolded results for (left) the particle multiplcity, and (right) invariant mass, compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 1-a:
The unfolded results for (left) the particle multiplcity, and (right) invariant mass, compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 1-b:
The unfolded results for (left) the particle multiplcity, and (right) invariant mass, compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 2:
The unfolded results for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) isotropy compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 2-a:
The unfolded results for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) isotropy compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 2-b:
The unfolded results for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) isotropy compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 2-c:
The unfolded results for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) isotropy compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 2-d:
The unfolded results for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) isotropy compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 3:
The unfolded results for (left) transverse thrust, and (right) transverse sphericity compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 3-a:
The unfolded results for (left) transverse thrust, and (right) transverse sphericity compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 3-b:
The unfolded results for (left) transverse thrust, and (right) transverse sphericity compared to the nominal MC from PYTHIA CP1 tune and predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 4:
The unfolded distributions of sphericity (upper) and transverse sphericity (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 4-a:
The unfolded distributions of sphericity (upper) and transverse sphericity (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 4-b:
The unfolded distributions of sphericity (upper) and transverse sphericity (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 5:
The unfolded distributions of even Isotropy (upper) and Broadening (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 5-a:
The unfolded distributions of even Isotropy (upper) and Broadening (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 5-b:
The unfolded distributions of even Isotropy (upper) and Broadening (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 6:
The unfolded distributions of thrust (upper) and transverse thrust (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 6-a:
The unfolded distributions of thrust (upper) and transverse thrust (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 6-b:
The unfolded distributions of thrust (upper) and transverse thrust (lower) in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 7:
The unfolded invariant charged particle masses in slices of charged-particle multiplicity compared to the nominal MC from PYTHIA CP1 tune and MC predictions from the PYTHIA A14, CP5, A3 tunes, the EPOS generator, and the HERWIG CH3 tune. |
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Figure 8:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) transverse sphericity. |
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Figure 8-a:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) transverse sphericity. |
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Figure 8-b:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) transverse sphericity. |
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Figure 8-c:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) transverse sphericity. |
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Figure 8-d:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) sphericity, (upper right) thrust, (lower left) broadening, and (lower right) transverse sphericity. |
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Figure 9:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) transverse thrust, (upper right) isotropy, (lower left) particle multiplicity, (lower right) invariant mass. |
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Figure 9-a:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) transverse thrust, (upper right) isotropy, (lower left) particle multiplicity, (lower right) invariant mass. |
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Figure 9-b:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) transverse thrust, (upper right) isotropy, (lower left) particle multiplicity, (lower right) invariant mass. |
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Figure 9-c:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) transverse thrust, (upper right) isotropy, (lower left) particle multiplicity, (lower right) invariant mass. |
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Figure 9-d:
The correlations of the unfolding systematic uncertainty between bins of the event shape observables shown for (upper left) transverse thrust, (upper right) isotropy, (lower left) particle multiplicity, (lower right) invariant mass. |
| Tables | |
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Table 1:
Samples of simulated minimum-bias events used for the unfolding. The pileup in the table represents the number of interactions in addition to the generated hardest interaction, i.e., the total number of interactions minus one for each event. The value of the strong coupling constant, $ \alpha_S $, corresponds to that used in the parton density function (PDF) set. |
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Table 2:
Samples of simulated minimum-bias events used for validation. The pileup in the table represents the number of interactions in addition to the generated hardest interaction, i.e., the pileup is equal to the total number of interactions minus one for each event. The value of $ \alpha_S $ corresponds to that used in the PDF set. |
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Table 3:
Relative uncertainties of unfolding from different sources, averaged over bins of transverse sphericity. The uncertainty from regularization and that from the mismodelling of the migration are estimated from the square root of the quadrature sum of the differences between the unfolding result using the nominal MC and those using reweighted MC samples to systematic variations. The MC statistical uncertainty is estimated from the statiscal uncertainty of the histogram of weighted MC samples after the unfolding. The data statistical uncertainty is estimated from the standard deviations of the unfolding results to alternative data samples with weight following a Poisson(1) distribution. The average relative uncertainties for the distributions of other observables are similar in size. |
| Summary |
| A measurement of event shapes in minimum-bias proton-proton collisions at a centre-of-mass energy of 13 TeV has been presented. Low pileup data collected with the CMS detector in 2018 were used, and the kinematics of reconstructed tracks were used to unfold the distributions to the level of stable charged particles. The results show a consistent trend of mismodelling event shapes common across all simulation configurations considered. The simulations under study include several different underlying physics models, from the PYTHIA, EPOS, and HERWIG generators, as well as a number of tunes of the PYTHIA generator. For each of these simulations, the relative isotropy of the event shapes is underpredicted across a range of six different event-shape observables. Some mismodelling of the charged-particle multiplicity and the invariant mass of the charged particles is also observed. The interplay between these two trends was investigated by considering the event-shape observables in slices of charged-particle multiplicity. These investigations show that the data continue to prefer more isotropic distributions even within slices of charged-particle multiplicity and when considering only the plane transverse to the beam direction. An unbinned multi-dimensional unfolding algorithm was used to provide these results. All one- and two-dimensional distributions as well as their covariances are provided. These event-shape observables are important in probing soft and nonperturbative effects in quantum chromodynamics at the LHC. The unfolded data should be used by the community to improve and develop existing proton-proton collision models, as will be critical for understanding phenomena such as quark-gluon plasma and topological effects in non-Abelian gauge theories. |
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Compact Muon Solenoid LHC, CERN |
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