CMS logoCMS event Hgg
Compact Muon Solenoid
LHC, CERN

CMS-SMP-19-010 ; CERN-EP-2020-250
Measurements of the differential cross sections of the production of Z$+$jets and $\gamma +$jets and of Z boson emission collinear with a jet in pp collisions at $\sqrt{s} = $ 13 TeV
JHEP 05 (2021) 285
Abstract: Measurements of the differential cross sections of Z$+$jets and $\gamma +$jets production, and their ratio, are presented as a function of the boson transverse momentum. Measurements are also presented of the angular distribution between the Z boson and the closest jet. The analysis is based on pp collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 35.9 fb$^{-1}$ recorded by the CMS experiment at the LHC. The results, corrected for detector effects, are compared with various theoretical predictions. In general, the predictions at higher orders in perturbation theory show better agreement with the measurements. This work provides the first measurement of the ratio of the differential cross sections of Z$+$jets and $\gamma +$jets production at 13 TeV, as well as the first direct measurement of Z bosons emitted collinearly with a jet.
Figures & Tables Summary References CMS Publications
Figures

png pdf
Figure 1:
A fit to the ${\sigma _{\eta \eta}}$ distribution using signal and background templates to extract a value for the purity in the photon ${p_{\mathrm {T}}}$ bin of 300-350 GeV. The signal region is to the left of the vertical dashed line (left). Purity as a function of photon ${p_{\mathrm {T}}}$, as extracted from a fit to the ${\sigma _{\eta \eta}}$ distribution in each ${p_{\mathrm {T}}}$ bin. The error bars show the total statistical and systematic uncertainty and the solid line is the fit to the data points (right).

png pdf
Figure 1-a:
A fit to the ${\sigma _{\eta \eta}}$ distribution using signal and background templates to extract a value for the purity in the photon ${p_{\mathrm {T}}}$ bin of 300-350 GeV. The signal region is to the left of the vertical dashed line.

png pdf
Figure 1-b:
Purity as a function of photon ${p_{\mathrm {T}}}$, as extracted from a fit to the ${\sigma _{\eta \eta}}$ distribution in each ${p_{\mathrm {T}}}$ bin. The error bars show the total statistical and systematic uncertainty and the solid line is the fit to the data points.

png pdf
Figure 2:
Measured differential cross sections as a function of the boson ${p_{\mathrm {T}}}$ for Z$+$jets (left) and $\gamma +$jets (right) and their comparisons with several theoretical predictions. The LO MadGraph 5_aMC@NLO prediction for Z$+$jets has been normalized to the NNLO cross section (denoted by k$_{\textrm {NNLO}}$). The vertical bars in the upper panels represent the statistical uncertainty in the measurement and the hatched band in the lower and upper panels is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The lower panels show the ratios of the theoretical predictions to the unfolded data. The shaded band in the LO MadGraph 5_aMC@NLO and SHERPA + OpenLoops calculations shows the statistical uncertainty. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO and the JetPhox prediction represents the PDF (scale) uncertainties, whereas the statistical uncertainties are barely visible.

png pdf
Figure 2-a:
Measured differential cross section as a function of the boson ${p_{\mathrm {T}}}$ for Z$+$jets and comparisons with several theoretical predictions. The LO MadGraph 5_aMC@NLO prediction for Z$+$jets has been normalized to the NNLO cross section (denoted by k$_{\textrm {NNLO}}$). The vertical bars represent the statistical uncertainty in the measurement and the hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 2-b:
Measured differential cross section as a function of the boson ${p_{\mathrm {T}}}$ for $\gamma +$jets

png pdf
Figure 2-c:
Measured differential cross section as a function of the boson ${p_{\mathrm {T}}}$ for Z$+$jets and comparisons with several theoretical predictions. The panel shows the ratios of the theoretical predictions to the unfolded data. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO and the JetPhox prediction represents the PDF (scale) uncertainties, whereas the statistical uncertainties are barely visible. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 2-d:
Measured differential cross section as a function of the boson ${p_{\mathrm {T}}}$ for $\gamma +$jets and comparisons with several theoretical predictions. The panel shows the ratios of the theoretical predictions to the unfolded data. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO and the JetPhox prediction represents the PDF (scale) uncertainties, whereas the statistical uncertainties are barely visible. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 3:
Differential cross section ratio of Z$+$jets to $\gamma +$jets as a function of the vector boson (V) transverse momentum compared with the theoretical prediction from MadGraph 5_aMC@NLO and SHERPA + OpenLoops. Only vector bosons produced centrally, with $ {| y |} < $ 1.4, in association with one or more jets are considered. The lower panel shows the ratio of the theoretical prediction to the unfolded data. The vertical bars in the upper panel represent the statistical uncertainty in the measurement and the hatched band in the lower and upper panels is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO represents the PDF (scale) uncertainties, which are treated as uncorrelated between Z$+$jets and $\gamma +$jets, whereas the statistical uncertainties are barely visible. The shaded band on the SHERPA + OpenLoops calculation is the statistical uncertainty.

png pdf
Figure 3-a:
Differential cross section ratio of Z$+$jets to $\gamma +$jets as a function of the vector boson (V) transverse momentum compared with the theoretical prediction from MadGraph 5_aMC@NLO and SHERPA + OpenLoops. Only vector bosons produced centrally, with $ {| y |} < $ 1.4, in association with one or more jets are considered. The vertical bars represent the statistical uncertainty in the measurement. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 3-b:
Differential cross section ratio of Z$+$jets to $\gamma +$jets as a function of the vector boson (V) transverse momentum compared with the theoretical prediction from MadGraph 5_aMC@NLO and SHERPA + OpenLoops. Only vector bosons produced centrally, with $ {| y |} < $ 1.4, in association with one or more jets are considered. The panel shows the ratio of the theoretical prediction to the unfolded data. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO represents the PDF (scale) uncertainties, which are treated as uncorrelated between Z$+$jets and $\gamma +$jets, whereas the statistical uncertainties are barely visible. The shaded band on the SHERPA + OpenLoops calculation is the statistical uncertainty.

png pdf
Figure 4:
Measured differential cross section of Z$+$jets as a function of the angular separation between the Z boson and the closest jet, compared with theoretical predictions from MadGraph 5_aMC@NLO and SHERPA + OpenLoops, where the leading jet ${p_{\mathrm {T}}}$ is above 300 (left) and 500 (right) GeV. The vertical bars in the upper panel represent the statistical uncertainty in the measurement and the hatched band in the lower and upper panels is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The lower panels show the ratio of the theoretical predictions to the unfolded data. The shaded band on the LO MadGraph 5_aMC@NLO and SHERPA + OpenLoops calculations is the statistical uncertainty. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO represents the PDF (scale) uncertainties.

png pdf
Figure 4-a:
Measured differential cross section of Z$+$jets as a function of the angular separation between the Z boson and the closest jet, compared with theoretical predictions from MadGraph 5_aMC@NLO and SHERPA + OpenLoops, where the leading jet ${p_{\mathrm {T}}}$ is above 300 GeV. The vertical bars represent the statistical uncertainty in the measurement. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 4-b:
Measured differential cross section of Z$+$jets as a function of the angular separation between the Z boson and the closest jet, compared with theoretical predictions from MadGraph 5_aMC@NLO and SHERPA + OpenLoops, where the leading jet ${p_{\mathrm {T}}}$ is above 300 GeV. The vertical bars represent the statistical uncertainty in the measurement. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement.

png pdf
Figure 4-c:
Measured differential cross section of Z$+$jets as a function of the angular separation between the Z boson and the closest jet, compared with theoretical predictions from MadGraph 5_aMC@NLO and SHERPA + OpenLoops, where the leading jet ${p_{\mathrm {T}}}$ is above 300 GeV. The panel shows the ratio of the theoretical predictions to the unfolded data. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The shaded band on the LO MadGraph 5_aMC@NLO and SHERPA + OpenLoops calculations is the statistical uncertainty. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO represents the PDF (scale) uncertainties.

png pdf
Figure 4-d:
Measured differential cross section of Z$+$jets as a function of the angular separation between the Z boson and the closest jet, compared with theoretical predictions from MadGraph 5_aMC@NLO and SHERPA + OpenLoops, where the leading jet ${p_{\mathrm {T}}}$ is above 300 GeV. The panel shows the ratio of the theoretical predictions to the unfolded data. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The shaded band on the LO MadGraph 5_aMC@NLO and SHERPA + OpenLoops calculations is the statistical uncertainty. The dark (light) shaded band on the NLO prediction from MadGraph 5_aMC@NLO represents the PDF (scale) uncertainties.
Tables

png pdf
Table 1:
The contributions to the uncertainty in the differential cross section measurements for the Z$+$jets and $\gamma +$jets processes, the Z/$\gamma$ ratio, and the ${{{\Delta R}}_{\mathrm{Z},\text {j}}}$ region. The uncertainties are expressed in percent, and a range represents the minimum and maximum effect observed.
Summary
This paper presents measurements of standard model processes that probe regions of phase space characterized by the production of Z$+$jets and $\gamma +$jets at large boson transverse momentum (${p_{\mathrm{T}}}$), and of a Z boson in association with at least one very high ${p_{\mathrm{T}}}$ jet.

The measurements utilize data recorded with the CMS detector in pp collisions at $\sqrt{s}$ = 13 TeV at the LHC that correspond to an integrated luminosity of 35.9 fb$^{-1}$. Comparisons are made between the unfolded data and several theory predictions.

The Z$+$jets and $\gamma +$jets cross sections as a function of boson ${p_{\mathrm{T}}}$ are presented for ${p_{\mathrm{T}}}$ above 200 GeV and compared with predictions from (i) the leading-order (LO) and next-to-leading-order (NLO) calculations from MadGraph5+MCatNLO, and (ii) the NLO quantum chromodynamics and electroweak (QCD+EW) calculation from SHERPA + OpenLoops . In addition, the $\gamma +$jets measurement is compared with NLO JetPhox predictions. The data are consistent with theory for both the $\gamma$ and Z boson final states, although in some regions of phase space a few tens of percent deviations are observed. In general, the perturbative NLO corrections exhibit a better agreement with the measurements.

This is the first measurement at 13 TeV of the ratio of cross sections for Z$+$jets to $\gamma +$jets as a function of boson ${p_{\mathrm{T}}}$. This ratio is compared with the NLO calculation from MadGraph5+MCatNLO and the NLO QCD+EW prediction from SHERPA + OpenLoops ; and it probes the region up to 1.5 TeV in boson ${p_{\mathrm{T}}}$. The data are generally in agreement with theory within the uncertainties over the full range of boson ${p_{\mathrm{T}}}$. This ratio provides an important theoretical input for the estimation, based on the $\gamma +$jets process, of the ${\mathrm{Z}\to\mathrm{\nu\bar{nu}}} $ background relevant in searches for new physics.

The measurement of the emission of a Z boson collinear to a jet represents the first explicit study of this topology at the LHC. It is accessed through the production of a Z boson in association with at least one high-${p_{\mathrm{T}}}$ jet ($ > $300 or $ > $500 GeV), and the differential cross section is measured as a function of the angular separation between the Z boson and the closest jet (${{{\Delta R} }_{\mathrm{Z},\text{j}}} $). The unfolded data are compared with the LO and NLO calculations from MadGraph5+MCatNLO, and the NLO QCD+EW prediction from SHERPA + OpenLoops . The NLO {MadGraph} shows agreement over most of the measured distribution, but underpredicts it for the ${{{\Delta R} }_{\mathrm{Z},\text{j}}} $ region below 0.8, which is dominated by events with the emission of a Z boson in close proximity to a jet. The prediction from SHERPA is also generally consistent with the measurement.

The measurements presented in this paper will become increasingly important in current and future runs of the LHC, where the higher $\sqrt{s}$ and larger integrated luminosity will push the LHC program into new territory, necessitating an understanding of standard model processes in regions of previously unexplored phase space.
References
1 A. Gehrmann-De Ridder et al. Precise QCD predictions for the production of a Z boson in association with a hadronic jet PRL 117 (2016) 022001 1507.02850
2 R. Boughezal et al. Z-boson production in association with a jet at next-to-next-to-leading order in perturbative QCD PRL 116 (2016) 152001 1512.01291
3 L. Carminati et al. Sensitivity of the LHC isolated-gamma+jet data to the parton distribution functions of the proton EPL 101 (2013) 61002 1212.5511
4 R. Boughezal, A. Guffanti, F. Petriello, and M. Ubiali The impact of the LHC Z-boson transverse momentum data on PDF determinations JHEP 07 (2017) 130 1705.00343
5 CMS Collaboration Search for new physics in final states with an energetic jet or a hadronically decaying $ W $ or $ Z $ boson and transverse momentum imbalance at $ \sqrt{s}=$ 13 TeV PRD 97 (2018) 092005 CMS-EXO-16-048
1712.02345
6 W. J. Stirling and E. Vryonidou Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC JHEP 04 (2013) 155 1212.6537
7 A. Denner, S. Dittmaier, T. Kasprzik, and A. M$\ddot\rm u$ck Electroweak corrections to W + jet hadroproduction including leptonic W-boson decays JHEP 08 (2009) 075 0906.1656
8 A. Denner, S. Dittmaier, T. Kasprzik, and A. M$\ddot\rm u$ck Electroweak corrections to dilepton + jet production at hadron colliders JHEP 06 (2011) 069 1103.0914
9 A. Denner, S. Dittmaier, T. Kasprzik, and A. M$\ddot\rm u$ck Electroweak corrections to monojet production at the LHC EPJC 73 (2013) 2297 1211.5078
10 A. Denner, L. Hofer, A. Scharf, and S. Uccirati Electroweak corrections to lepton pair production in association with two hard jets at the LHC JHEP 01 (2015) 094 1411.0916
11 S. Kallweit et al. NLO QCD+EW predictions for V+jets including off-shell vector-boson decays and multijet merging JHEP 04 (2016) 021 1511.08692
12 J. M. Lindert et al. Precise predictions for V+jets dark matter backgrounds EPJC 77 (2017) 829 1705.04664
13 M. Schönherr et al. NLO QCD+EW for V+jets in Proceedings of the 4th Large Hadron Collider Physics Conference (LHCP 2016), p. 58 2016 1609.01445
14 R. Frederix et al. The automation of next-to-leading order electroweak calculations JHEP 07 (2018) 185 1804.10017
15 CMS Collaboration Comparison of the Z/$ \gamma^{*} $ + jets to $ \gamma $ + jets cross sections in pp collisions at $ \sqrt{s}= $ 8 TeV JHEP 10 (2015) 128 CMS-SMP-14-005
1505.06520
16 U. Baur Weak boson emission in hadron collider processes PRD 75 (2007) 013005 hep-ph/0611241
17 J. R. Christiansen and T. Sjöstrand Weak gauge boson radiation in parton showers JHEP 04 (2014) 115 1401.5238
18 F. Krauss, P. Petrov, M. Schönherr, and M. Spannowsky Measuring collinear W emissions inside jets PRD 89 (2014) 114006 1403.4788
19 ATLAS Collaboration Measurement of W boson angular distributions in events with high transverse momentum jets at $ \sqrt{s}= $ 8 TeV using the ATLAS detector PLB 765 (2017) 132 1609.07045
20 CMS Collaboration Measurement of the differential cross sections for the associated production of a W boson and jets in proton-proton collisions at $ \sqrt{s}= $ 13 TeV PRD 96 (2017) 072005 CMS-SMP-16-005
1707.05979
21 CMS Collaboration The CMS trigger system JINST 12 (2017) P01020 CMS-TRG-12-001
1609.02366
22 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004 CMS-00-001
23 J. Alwall et al. The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations JHEP 07 (2014) 079 1405.0301
24 T. Sjöstrand et al. An introduction to PYTHIA 8.2 CPC 191 (2015) 159 1410.3012
25 R. Frederix and S. Frixione Merging meets matching in MC@NLO JHEP 12 (2012) 061 1209.6215
26 K. Melnikov and F. Petriello Electroweak gauge boson production at hadron colliders through O($ \alpha(s)^{2} $) PRD 74 (2006) 114017 hep-ph/0609070
27 J. Alwall et al. Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions EPJC 53 (2008) 473 0706.2569
28 S. Catani, M. Fontannaz, J. P. Guillet, and E. Pilon Cross-section of isolated prompt photons in hadron-hadron collisions JHEP 05 (2002) 028 hep-ph/0204023
29 P. Aurenche et al. A new critical study of photon production in hadronic collisions PRD 73 (2006) 094007 hep-ph/0602133
30 Z. Belghobsi et al. Photon-jet correlations and constraints on fragmentation functions PRD 79 (2009) 114024 0903.4834
31 L. Bourhis, M. Fontannaz, and J. P. Guillet Quark and gluon fragmentation functions into photons EPJC 2 (1998) 529 hep-ph/9704447
32 E. Bothmann et al. Event generation with Sherpa 2.2 SciPost Phys. 7 (2019) 034 1905.09127
33 T. Gleisberg and S. Hoeche Comix, a new matrix element generator JHEP 12 (2008) 039 0808.3674
34 F. Buccioni et al. Openloops 2 EPJC 79 (2019) 866 1907.13071
35 S. Schumann and F. Krauss A parton shower algorithm based on Catani-Seymour dipole factorisation JHEP 03 (2008) 038 0709.1027
36 S. Hoeche, F. Krauss, M. Schönherr, and F. Siegert A critical appraisal of NLO+PS matching methods JHEP 09 (2012) 049 1111.1220
37 S. Frixione and B. R. Webber Matching NLO QCD computations and parton shower simulations JHEP 06 (2002) 029 hep-ph/0204244
38 N. Kidonakis Differential and total cross sections for top pair and single top production in 20th International Workshop on Deep-Inelastic Scattering and Related Subjects, p. 40 2012 1205.3453
39 M. Czakon, P. Fiedler, and A. Mitov Total top-quark pair-production cross section at hadron colliders through O($ \alpha_{s}^{4} $) PRL 110 (2013) 252004 1303.6254
40 P. Nason A new method for combining NLO QCD with shower Monte Carlo algorithms JHEP 11 (2004) 040 hep-ph/0409146
41 S. Frixione, P. Nason, and C. Oleari Matching NLO QCD computations with parton shower simulations: the POWHEG method JHEP 11 (2007) 070 0709.2092
42 S. Alioli, P. Nason, C. Oleari, and E. Re A general framework for implementing NLO calculations in shower Monte Carlo programs: the POWHEG BOX JHEP 06 (2010) 043 1002.2581
43 E. Re Single-top Wt-channel production matched with parton showers using the POWHEG method EPJC 71 (2011) 1547 1009.2450
44 NNPDF Collaboration Parton distributions for the LHC Run 2 JHEP 04 (2015) 040 1410.8849
45 CMS Collaboration Event generator tunes obtained from underlying event and multiparton scattering measurements EPJC 76 (2016) 155 CMS-GEN-14-001
1512.00815
46 GEANT4 Collaboration GEANT4: A simulation toolkit NIMA 506 (2003) 250
47 R. D. Ball et al. Parton distributions with LHC data NPB 867 (2013) 244 1207.1303
48 CMS Collaboration Particle-flow reconstruction and global event description with the CMS detector JINST 12 (2017) P10003 CMS-PRF-14-001
1706.04965
49 CMS Collaboration Performance of photon reconstruction and identification with the CMS detector in proton-proton collisions at $ \sqrt{s} = $ 8 TeV JINST 10 (2015) P08010 CMS-EGM-14-001
1502.02702
50 CMS Collaboration Electron and photon reconstruction and identification with the CMS experiment at the CERN LHC (12, 2020) CMS-EGM-17-001
2012.06888
51 M. Cacciari, G. P. Salam, and G. Soyez The anti-$ {k_{\mathrm{T}}} $ jet clustering algorithm JHEP 04 (2008) 063 0802.1189
52 M. Cacciari, G. P. Salam, and G. Soyez FastJet user manual EPJC 72 (2012) 1896 1111.6097
53 M. Cacciari and G. P. Salam Pileup subtraction using jet areas PLB 659 (2008) 119 0707.1378
54 CMS Collaboration Determination of jet energy calibration and transverse momentum resolution in CMS JINST 6 (2011) P11002 CMS-JME-10-011
1107.4277
55 CMS Collaboration Jet energy scale and resolution in the CMS experiment in pp collisions at 8 TeV JINST 12 (2017) P02014 CMS-JME-13-004
1607.03663
56 CMS Collaboration Performance of the CMS muon detector and muon reconstruction with proton-proton collisions at $ \sqrt{s} = $ 13 TeV JINST 13 (2018) P06015 CMS-MUO-16-001
1804.04528
57 R. J. Barlow and C. Beeston Fitting using finite Monte Carlo samples CPC 77 (1993) 90005
58 S. Schmitt TUnfold: an algorithm for correcting migration effects in high energy physics JINST 7 (2012) T10003 1205.6201
59 A. N. Tikhonov Solution of incorrectly formulated problems and the regularization method Soviet Math. Dokl. 4 (1963) 1035
60 P. C. Hansen The L-curve and its use in the numerical treatment of inverse problems in Computational Inverse Problems in Electrocardiology, ed. P. Johnston, Advances in Computational Bioengineering, p. 119 WIT Press
61 CMS Collaboration Measurement of the inclusive W and Z production cross sections in pp collisions at $ \sqrt{s}= $ 7 TeV JHEP 10 (2011) 132 CMS-EWK-10-005
1107.4789
62 CMS Collaboration CMS luminosity measurements for the 2016 data taking period CMS-PAS-LUM-17-001 CMS-PAS-LUM-17-001
Compact Muon Solenoid
LHC, CERN