CMS logoCMS event Hgg
Compact Muon Solenoid
LHC, CERN

CMS-FSQ-15-006 ; CERN-EP-2018-308
Measurement of the energy density as a function of pseudorapidity in proton-proton collisions at $\sqrt{s} = $ 13 TeV
Eur. Phys. J. C 79 (2019) 391
Abstract: A measurement of the energy density in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}= $ 13 TeV is presented. The data have been recorded with the CMS experiment at the LHC during low luminosity operations in 2015. The energy density is studied as a function of pseudorapidity in the ranges $-6.6 < \eta < -5.2$ and $ 3.15 < | {\eta} | < 5.20 $. The results are compared with the predictions of several models. All the models considered suggest a different shape of the pseudorapidity dependence compared to that observed in the data. A comparison with LHC proton-proton collision data at $\sqrt{s}=$ 0.9 and 7 TeV confirms the compatibility of the data with the hypothesis of limiting fragmentation.
Figures & Tables Summary References CMS Publications
Figures

png pdf
Figure 1:
Distribution of the absolute number of events as a function of the highest energy tower, $E_\mathrm {HF+}$ and $E_\mathrm {HF-}$, in the HF$+$ and HF$-$ calorimeters. The left panel shows the smaller of the two HF calorimeter energies, min($E_\mathrm {HF-},E_\mathrm {HF+}$), whereas the right panel shows the higher of the two energies, max($E_\mathrm {HF-},E_\mathrm {HF+}$). The lines represent the simulations, while the markers represent the data. The measured detector noise distributions are shown as shaded areas.

png pdf
Figure 1-a:
Distribution of the absolute number of events as a function of the highest energy tower, $E_\mathrm {HF+}$ and $E_\mathrm {HF-}$, in the HF$+$ and HF$-$ calorimeters. The panel shows the smaller of the two HF calorimeter energies, min($E_\mathrm {HF-},E_\mathrm {HF+}$). The lines represent the simulations, while the markers represent the data. The measured detector noise distributions are shown as shaded areas.

png pdf
Figure 1-b:
Distribution of the absolute number of events as a function of the highest energy tower, $E_\mathrm {HF+}$ and $E_\mathrm {HF-}$, in the HF$+$ and HF$-$ calorimeters. The panel shows the higher of the two energies, max($E_\mathrm {HF-},E_\mathrm {HF+}$). The lines represent the simulations, while the markers represent the data. The measured detector noise distributions are shown as shaded areas.

png pdf
Figure 2:
Energy density at the stable-particle level for the INEL (upper row), NSD-enhanced (middle row), and SD-enhanced (lower row) event selections categories compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty. The right panels show the ratio of model predictions to measured data.

png pdf
Figure 2-a:
Energy density at the stable-particle level for the INEL event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty.

png pdf
Figure 2-b:
Energy density at the stable-particle level for the INEL event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 2-c:
Energy density at the stable-particle level for the NSD-enhanced event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty.

png pdf
Figure 2-d:
Energy density at the stable-particle level for the NSD-enhanced event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 2-e:
Energy density at the stable-particle level for the SD-enhanced event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty.

png pdf
Figure 2-f:
Energy density at the stable-particle level for the SD-enhanced event selection category compared to predictions from PYTHIA 8 MONASH, EPOS-LHC, and QGSJETLL.04. The gray band shows the total systematic uncertainty. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 3:
Energy density at the stable-particle level for the INEL (upper row), NSD-enhanced (middle row), and SD-enhanced (lower row) event selections categories compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters. The right panels show the ratio of model predictions to measured data.

png pdf
Figure 3-a:
Energy density at the stable-particle level for the INEL event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters.

png pdf
Figure 3-b:
Energy density at the stable-particle level for the INEL event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 3-c:
Energy density at the stable-particle level for the NSD-enhanced event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters.

png pdf
Figure 3-d:
Energy density at the stable-particle level for the NSD-enhanced event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 3-e:
Energy density at the stable-particle level for the SD-enhanced event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters.

png pdf
Figure 3-f:
Energy density at the stable-particle level for the SD-enhanced event selection category compared to predictions from PYTHIA 8 with the tunes CUETP8M1, CUETP8M1+MBR, and CUETP8S1. The gray band shows the total systematic uncertainty. The band around PYTHIA 8 CUETP8S1 corresponds to the uncertainties of the tune parameters. The panel shows the ratio of model predictions to measured data.

png pdf
Figure 4:
A comparison of the measurements of the transverse energy density, $ {{\mathrm {d}} E_{\mathrm {T}}}/ {{\mathrm {d}}\eta '}$, at $\sqrt {s} = $ 13 TeV, as a function of shifted pseudorapidity, $\eta '=\eta - y_{\mathrm {beam}}$, to the predictions and to earlier proton-proton data [6] for NSD-enhanced events at several different centre-of-mass energies. The error bars indicate the total systematic uncertainties. The beam rapidities $ y_{\mathrm {beam}}$ are about 9.5, 8.9, and 6.8 at $\sqrt {s} $ of 13, 7 and 0.9 TeV, respectively.
Tables

png pdf
Table 1:
Summary of the event selections used for the different event categories in data at the detector level and in simulations at the stable-particle level.

png pdf
Table 2:
Selection factors and purities for various event categories. The last two rows are derived using the formulae in the text. The event selection probability $\epsilon $ is determined from simulations, and the value quoted here is the average value from all event generators, with a maximal model dependence of 2%. The rightmost column quantifies the combined correction due to noise and pileup. All statistical uncertainties are negligible.

png pdf
Table 3:
The uncertainties in the energy density measurement for the three event categories. The results depend slightly on the pseudorapidity.
Summary
The energy density, $\mathrm{d} E / \mathrm{d} \eta$, is measured in the pseudorapidity range $-6.6 < \eta < -5.2$ and 3.15 $ < | {\eta} | < $ 5.20. Special low-luminosity data recorded by the CMS experiment during proton-proton collisions at the centre-of-mass energy $\sqrt{s} = $ 13 TeV are analysed for this purpose. The data are presented at the stable-particle level to allow a straightforward comparison to any theory prediction or model simulation. The measurements are compared to models tuned to describe high-energy hadronic interactions (PYTHIA{8}) and to the predictions of models used in cosmic ray physics (EPOS, QGSJET) for inclusive inelastic (INEL), NSD (NSD-enhanced), and SD (SD-enhanced) event selections.

It is shown that the INEL and NSD-enhanced data are extremely sensitive to multi-parton interactions, while the SD-enhanced are essentially unaffected. The shape of the measured $\eta$ dependencies suggest a difference in the models compared to the data. However, the predictions of PYTHIA{8} tune cuetp8s1 are in satisfactory agreement with all measurements when the experimental and tune uncertainties are combined. The EPOS and QGSJET models exhibit the largest differences when compared to the SD results.

At high energies, the hypothesis of limiting fragmentation [9,10] assumes a longitudinal scaling behaviour in terms of shifted pseudorapidity $\eta'=\eta-y_{\text{beam}}$ (where $y_{\text{beam}}$ is the beam rapidity) and thus soft-particle production in the projectile fragmentation region, $\eta' \approx 0$, is predicted to be independent of the centre-of-mass energy. This is studied by measuring the transverse energy density $\mathrm{d} E_{\mathrm{T}} / \mathrm{d} \eta$, with $E_{\mathrm{T}}=E \cosh(\eta)$, and comparing it to measurements performed in proton-proton collisions at different centre-of-mass energies. The predictions of the EPOS and QGSJET models nicely describe the combined data in the forward pseudorapidity range close to the projectile fragmentation region. The result supports the mechanism of limiting fragmentation. Since this predicts the independence of very forward particle production on the energy of the projectile particle, these data are very important for the modelling of ultra-high energy interactions that typically occur in cosmic ray collisions.
References
1 T. Sjostrand and M. van Zijl Multiple parton-parton interactions in an impact parameter picture PLB 188 (1987) 149
2 T. Sjostrand and M. van Zijl A multiple-interaction model for the event structure in hadron collisions PRD 36 (1987) 2019
3 I. Borozan and M. H. Seymour An eikonal model for multiparticle production in hadron-hadron interactions JHEP 09 (2002) 015 hep-ph/0207283
4 T. Sjostrand and P. Z. Skands Multiple interactions and the structure of beam remnants JHEP 03 (2004) 053 hep-ph/0402078
5 CMS Collaboration First measurement of the underlying event activity at the LHC with $ \sqrt{s} = $ 0.9 TeV EPJC 70 (2010) 555 CMS-QCD-10-001
1006.2083
6 CMS Collaboration Measurement of energy flow at large pseudorapidities in pp collisions at $ \sqrt{s} = $ 0.9 and 7 TeV JHEP 11 (2011) 148 CMS-FWD-10-011
1110.0211
7 ATLAS Collaboration Measurements of the pseudorapidity dependence of the total transverse energy in proton-proton collisions at $ \sqrt{s}= $ 7 TeV with ATLAS JHEP 11 (2012) 033 1208.6256
8 LHCb Collaboration Measurement of the forward energy flow in pp collisions at $ \sqrt{s}= $ 7 TeV EPJC 73 (2013) 2421 1212.4755
9 J. Benecke, T. T. Chou, C.-N. Yang, and E. Yen Hypothesis of limiting fragmentation in high-energy collisions PR188 (1969) 2159
10 J. Ruan and W. Zhu Particle multiplicities at energies available at the CERN Large Hadron Collider (LHC) and deviations from limiting fragmentation PRC 81 (2010) 055210 1005.2790
11 R. Ulrich, R. Engel, and M. Unger Hadronic multiparticle production at ultra-high energies and extensive air showers PRD 83 (2011) 054026 1010.4310
12 D. d'Enterria et al. Constraints from the first LHC data on hadronic event generators for ultra-high energy cosmic-ray physics Astropart. Phys. 35 (2011) 98 1101.5596
13 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004 CMS-00-001
14 T. Sjostrand et al. An Introduction to PYTHIA 8.2 CPC 191 (2015) 159 1410.3012
15 V. N. Gribov and L. N. Lipatov Deep inelastic ep scattering in perturbation theory Sov. J. NP 15 (1972) 438.[Yad.\ Fiz.\ 15 (1972) 781]
16 V. N. Gribov and L. N. Lipatov e$ ^+ $e$ ^- $ pair annihilation and deep inelastic ep scattering in perturbation theory Sov. J. NP 15 (1972) 675.[Yad. Fiz. 15 (1972) 1218]
17 L. N. Lipatov The parton model and perturbation theory Sov. J. NP 20 (1975) 94, .[Yad. Fiz. 20 (1974) 181]
18 G. Altarelli and G. Parisi Asymptotic freedom in parton language NPB 126 (1977) 298
19 Y. L. Dokshitzer Calculation of the structure functions for deep inelastic scattering and e$ ^+ $e$ ^- $ annihilation by perturbation theory in quantum chromodynamics. Sov. Phys. JETP 46 (1977) 641.[Zh. Eksp. Teor. Fiz. 73 (1977) 1216]
20 B. Andersson, G. Gustafson, G. Ingelman, and T. Sjostrand Parton fragmentation and string dynamics PR 97 (1983) 31
21 CMS Collaboration Event generator tunes obtained from underlying event and multiparton scattering measurements EPJC 76 (2016) 155 CMS-GEN-14-001
1512.00815
22 P. Skands, S. Carrazza, and J. Rojo Tuning PYTHIA 8.1: the Monash 2013 Tune EPJC 74 (2014) 3024 1404.5630
23 R. Ciesielski and K. Goulianos MBR Monte Carlo Simulation in PYTHIA8 PoS ICHEP2012 (2013) 301 1205.1446
24 R. Corke and T. Sjostrand Interleaved parton showers and tuning prospects JHEP 03 (2011) 032 1011.1759
25 NNPDF Collaboration Parton distributions with LHC data NPB 867 (2013) 244 1207.1303
26 J. Pumplin et al. New generation of parton distributions with uncertainties from global QCD analysis JHEP 07 (2002) 012 hep-ph/0201195
27 T. Pierog et al. EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider PRC 92 (2015) 034906 1306.0121
28 S. Ostapchenko Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. QGSJET-II model PRD 83 (2011) 014018 1010.1869
29 H. J. Drescher et al. Parton-Based Gribov-Regge Theory PR 350 (2001) 93 hep-ph/0007198
30 GEANT4 Collaboration GEANT4--a simulation toolkit NIMA 506 (2003) 250
31 CMS Collaboration The CMS trigger system JINST 12 (2017) P01020 CMS-TRG-12-001
1609.02366
32 CMS Collaboration Measurement of the inelastic proton-proton cross section at $ \sqrt{s}= $ 13 TeV JHEP 07 (2018) 161 CMS-FSQ-15-005
1802.02613
33 V. Andreev et al. Performance studies of a full-length prototype for the CASTOR forward calorimeter at the CMS experiment EPJC 67 (2010) 601
34 CMS Collaboration Studies of the nuclear stopping power in PbPb collisions at 2.76 TeV with CMS NP A 904-905 (2013) 787c
Compact Muon Solenoid
LHC, CERN