CMS-SMP-14-012 ; CERN-EP-2016-152 | ||
Measurement of the transverse momentum spectra of weak vector bosons produced in proton-proton collisions at $ \sqrt{s} = $ 8 TeV | ||
CMS Collaboration | ||
19 June 2016 | ||
JHEP 02 (2017) 096 | ||
Abstract: The transverse momentum spectra of weak vector bosons are measured in the CMS experiment at the LHC. The measurement uses a sample of proton-proton collisions at $ \sqrt{s} = $ 8 TeV, collected during a special low-luminosity running that corresponds to an integrated luminosity of 18.4 $\pm$ 0.5 pb$^{-1}$. The production of W bosons is studied in both electron and muon decay modes, while the production of Z bosons is studied using only the dimuon decay channel. The ratios of $\mathrm{ W }^{-}$ to $\mathrm{ W }^{+}$ and Z to W differential cross sections are also measured. The measured differential cross sections and ratios are compared with theoretical predictions up to next-to-next leading order in QCD. | ||
Links: e-print arXiv:1606.05864 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ; |
Figures & Tables | Summary | Additional Figures & Tables | References | CMS Publications |
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Figures | |
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Figure 1:
The ${E_{\mathrm {T}}^{\text {miss}}}$ distributions for the selected ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mathrm{ e } ^+\nu }$ (a,b) and ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mu ^+\nu }$ (c,d) candidates for 17.5 $ < { {p_{\mathrm {T}}} ^{\mathrm {W}}}< $ 24 GeV (a,c) and the corresponding QCD multijet-enriched control sample (b,d). Solid lines represent the results of the fit. The dotted lines represent the signal shape after background subtraction. The bottom panels show the difference between data and fitted results divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 1-a:
The ${E_{\mathrm {T}}^{\text {miss}}}$ distributions for the selected ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mathrm{ e } ^+\nu }$ candidates for 17.5 $ < { {p_{\mathrm {T}}} ^{\mathrm {W}}}< $ 24 GeV. Solid lines represent the results of the fit. The dotted lines represent the signal shape after background subtraction. The bottom panel shows the difference between data and fitted results divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 1-b:
The ${E_{\mathrm {T}}^{\text {miss}}}$ distributions for the selected ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mathrm{ e } ^+\nu }$ candidates for the corresponding QCD multijet-enriched control sample. Solid lines represent the results of the fit. The dotted lines represent the signal shape after background subtraction. The bottom panel shows the difference between data and fitted results divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 1-c:
The ${E_{\mathrm {T}}^{\text {miss}}}$ distributions for the selected ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mu ^+\nu }$ candidates for 17.5 $ < { {p_{\mathrm {T}}} ^{\mathrm {W}}}< $ 24 GeV. Solid lines represent the results of the fit. The dotted lines represent the signal shape after background subtraction. The bottom panel shows the difference between data and fitted results divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 1-d:
The ${E_{\mathrm {T}}^{\text {miss}}}$ distributions for the selected ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mu ^+\nu }$ candidates for the corresponding QCD multijet-enriched control sample. Solid lines represent the results of the fit. The dotted lines represent the signal shape after background subtraction. The bottom panel shows the difference between data and fitted results divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 2:
Signal and background yields after fitting the data for ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mathrm{ e } ^+\nu }$ (a), ${ {{ {\mathrm{ W } }^-}} {\rightarrow }\mathrm{ e } ^-\bar{\nu} }$ (b), ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mu ^+\nu }$ (c), and ${ {{ {\mathrm{ W } }^-}} {\rightarrow }\mu ^-\bar{\nu} }$ (d) as a function of the W boson ${p_{\mathrm {T}}}$. The points are data yields with statistical uncertainties. The stacked histogram shows the signal and background components estimated from a fit to the ${E_{\mathrm {T}}^{\text {miss}}}$ or ${{M}_{\mathrm {T}}}$ distribution at each W boson ${p_{\mathrm {T}}}$ bin. |
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Figure 2-a:
Signal and background yields after fitting the data for ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mathrm{ e } ^+\nu }$ as a function of the W boson ${p_{\mathrm {T}}}$. The points are data yields with statistical uncertainties. The stacked histogram shows the signal and background components estimated from a fit to the ${E_{\mathrm {T}}^{\text {miss}}}$ or ${{M}_{\mathrm {T}}}$ distribution at each W boson ${p_{\mathrm {T}}}$ bin. |
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Figure 2-b:
Signal and background yields after fitting the data for ${ {{ {\mathrm{ W } }^-}} {\rightarrow }\mathrm{ e } ^-\bar{\nu} }$ as a function of the W boson ${p_{\mathrm {T}}}$. The points are data yields with statistical uncertainties. The stacked histogram shows the signal and background components estimated from a fit to the ${E_{\mathrm {T}}^{\text {miss}}}$ or ${{M}_{\mathrm {T}}}$ distribution at each W boson ${p_{\mathrm {T}}}$ bin. |
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Figure 2-c:
Signal and background yields after fitting the data for ${ {{ {\mathrm{ W } }^+}} {\rightarrow }\mu ^+\nu }$ as a function of the W boson ${p_{\mathrm {T}}}$. The points are data yields with statistical uncertainties. The stacked histogram shows the signal and background components estimated from a fit to the ${E_{\mathrm {T}}^{\text {miss}}}$ or ${{M}_{\mathrm {T}}}$ distribution at each W boson ${p_{\mathrm {T}}}$ bin. |
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Figure 2-d:
Signal and background yields after fitting the data for ${ {{ {\mathrm{ W } }^-}} {\rightarrow }\mu ^-\bar{\nu} }$ as a function of the W boson ${p_{\mathrm {T}}}$. The points are data yields with statistical uncertainties. The stacked histogram shows the signal and background components estimated from a fit to the ${E_{\mathrm {T}}^{\text {miss}}}$ or ${{M}_{\mathrm {T}}}$ distribution at each W boson ${p_{\mathrm {T}}}$ bin. |
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Figure 3:
Data and simulated events for both DY processes and various backgrounds after event reconstruction. a (b): events for low (high) $ { {p_{\mathrm {T}}} ^{\mathrm {Z}} }$, $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}} <$ 30 ($\ge$ 30) GeV. The lower panels show the difference between the data and the simulation predictions divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 3-a:
Data and simulated events for both DY processes and various backgrounds after event reconstruction: events for low $ { {p_{\mathrm {T}}} ^{\mathrm {Z}} }$, $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}} <$ 30 GeV. The lower panel shows the difference between the data and the simulation predictions divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 3-b:
Data and simulated events for both DY processes and various backgrounds after event reconstruction: events for high $ { {p_{\mathrm {T}}} ^{\mathrm {Z}} }$, $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}} \ge$ 30 GeV. The lower panel shows the difference between the data and the simulation predictions divided by the statistical uncertainty in data, $\sigma _{\rm Data}$. |
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Figure 4:
Normalized differential cross sections for charge independent W boson production at the lepton pre-FSR level as a function of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ for electron (a,b) and muon (c,d) decay channels. The b,d panels show the ratios of theory predictions to the data. The bands include (i) the statistical uncertainties, uncertainties from scales, and PDF uncertainties for FEWZ; (ii) the statistical uncertainties and PDF uncertainties for POWHEG; (iii) the uncertainty from scales for ResBos-P; and (iv) the sum of the statistical and systematic uncertainties in quadrature for data. |
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Figure 4-a:
Normalized differential cross sections for charge independent W boson production at the lepton pre-FSR level as a function of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ for the electron decay channel. |
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Figure 4-b:
Normalized differential cross sections for charge independent W boson production at the lepton pre-FSR level as a function of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ for the electron decay channel. The panel shows the ratios of theory predictions to the data. The bands include (i) the statistical uncertainties, uncertainties from scales, and PDF uncertainties for FEWZ; (ii) the statistical uncertainties and PDF uncertainties for POWHEG; (iii) the uncertainty from scales for ResBos-P; and (iv) the sum of the statistical and systematic uncertainties in quadrature for data. |
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Figure 4-c:
Normalized differential cross sections for charge independent W boson production at the lepton pre-FSR level as a function of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ for the muon decay channel. |
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Figure 4-d:
Normalized differential cross sections for charge independent W boson production at the lepton pre-FSR level as a function of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ for the muon decay channel. The panel shows the ratios of theory predictions to the data. The bands include (i) the statistical uncertainties, uncertainties from scales, and PDF uncertainties for FEWZ; (ii) the statistical uncertainties and PDF uncertainties for POWHEG; (iii) the uncertainty from scales for ResBos-P; and (iv) the sum of the statistical and systematic uncertainties in quadrature for data. |
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Figure 5:
Comparison of the normalized dimuon differential transverse momentum distribution from data (solid symbols) with different theoretical predictions. The right panels show the ratios of theory predictions to the data. The ResBos-CP version with scale and PDF variation is used for comparison. |
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Figure 5-a:
Comparison of the normalized dimuon differential transverse momentum distribution from data (solid symbols) with different theoretical predictions. The panel shows the ratios of theory predictions to the data. The ResBos-CP version with scale and PDF variation is used for comparison. |
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Figure 5-b:
Comparison of the normalized dimuon differential transverse momentum distribution from data (solid symbols) with different theoretical predictions. The right panels show the ratios of theory predictions to the data. The ResBos-CP version with scale and PDF variation is used for comparison. |
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Figure 6:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ W }^- $ to $\mathrm{ W }^+ $ for muon channel compared with theoretical predictions. Data points include the sum of the statistical and systematic uncertainties in quadrature. More details are given in the Fig. 4 caption. |
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Figure 6-a:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ W }^- $ to $\mathrm{ W }^+ $ for muon channel compared with theoretical predictions. Data points include the sum of the statistical and systematic uncertainties in quadrature. More details are given in the Fig. 4 caption. |
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Figure 6-b:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ W }^- $ to $\mathrm{ W }^+ $ for muon channel compared with theoretical predictions. Data points include the sum of the statistical and systematic uncertainties in quadrature. More details are given in the Fig. 4 caption. |
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Figure 7:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ Z } $ to W for muon channel compared with theoretical predictions. The right panels show the ratios of theory predictions to the data. The larger than expected uncertainties for ResBos arise from the different strategies in terms of the scale and PDF variations between ResBos-P and ResBos-CP version. More details are given in the Fig. 4 and 5 caption. |
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Figure 7-a:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ Z } $ to W for muon channel compared with theoretical predictions. |
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Figure 7-b:
The normalized $ {p_{\mathrm {T}}} $ differential cross section ratio of $\mathrm{ Z } $ to W for muon channel compared with theoretical predictions. The panel shows the ratios of theory predictions to the data. The larger than expected uncertainties for ResBos arise from the different strategies in terms of the scale and PDF variations between ResBos-P and ResBos-CP version. More details are given in the Fig. 4 and 5 caption. |
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Figure 8:
Comparison of the shapes of the differential $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}$ distributions in the muon channel at centre-of-mass energies of 7 and 8 TeV compared with the predictions from POWHEG for $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}< $ 20 GeV and FEWZ for $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}> $ 20 GeV. |
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Figure 8-a:
Comparison of the shapes of the differential $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}$ distributions in the muon channel at centre-of-mass energies of 7 and 8 TeV compared with the predictions from POWHEG for $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}< $ 20 GeV. |
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Figure 8-b:
Comparison of the shapes of the differential $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}$ distributions in the muon channel at centre-of-mass energies of 7 and 8 TeV compared with the predictions from FEWZ for $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}> $ 20 GeV. |
Tables | |
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Table 1:
The fiducial cross sections at pre-FSR level calculated as the sum of differential cross sections. The fiducial volumes are defined in the text. |
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Table 2:
The W boson normalized differential cross sections for the electron channel in bins of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$, (1/$\sigma $)(d$\sigma $/d$ {p_{\mathrm {T}}} $) ($\mathrm{ W } \rightarrow \mathrm{ e } \nu $), and systematic uncertainties from various sources in units of %, where $\sigma $ is the sum of the cross sections for the $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$ bins. (1/$\sigma $)(d$\sigma $/d$ {p_{\mathrm {T}}} $) is shown with total uncertainty, i.e. the sum of statistical and systematic uncertainties in quadrature. |
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Table 3:
The W boson normalized differential cross sections for the muon channel in bins of $ { {p_{\mathrm {T}}} ^{\mathrm {W}}}$, (1/$\sigma $)(d$\sigma $/d$ {p_{\mathrm {T}}} $) ($\mathrm{ W } \rightarrow \mu \nu $), and systematic uncertainties from various sources in units of%. Other details are the same as in Table 1. |
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Table 4:
The $\mathrm{ Z } $ boson normalized differential cross sections for the muon channel in bins of $ { {p_{\mathrm {T}}} ^{\mathrm {Z}}}$, (1/$\sigma $)(d$\sigma $/d$ {p_{\mathrm {T}}} $) ($\mathrm{ Z } \rightarrow \mu ^+ \mu ^-$), and systematic uncertainties from various sources in units of%. Other details are the same as in Table 1. |
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Table 5:
Estimated ratios of pre-FSR level normalized differential cross sections within the muon fiducial volume. The uncertainty is the sum of statistical and systematic uncertainties in quadrature. |
Summary |
The production cross sections of the weak vector bosons, W and Z, as a function of transverse momentum, are measured by the CMS experiment using a sample of proton-proton collisions during a special low luminosity running of the LHC at $ \sqrt{s} = $ 8 TeV that corresponds to an integrated luminosity of 18.4 pb$^{-1}$. The production of W bosons is analyzed in both electron and muon decay modes, while the production of Z bosons is analyzed using only the dimuon decay channel. The measured normalized cross sections are compared to various theoretical predictions. All the predictions provide reasonable descriptions of the data, but POWHEG at NLO overestimates the yield by up to 12% around $p_{\mathrm{T}}^{\mathrm{W}} =$ 25 GeV. POWHEG shows 27% lower expectation in the $p_{\mathrm{T}}^{\mathrm{Z}}$ range 0-2.5 GeV and 18% excess for the $p_{\mathrm{T}}^{\mathrm{Z}}$ interval 7.5-10 GeV. FEWZ at NNLO shows 10% discrepancy around $p_{\mathrm{T}}^{\mathrm{W}} =$ 60 GeV and divergent behavior in the low $p_{\mathrm{T}}^{\mathrm{Z}}$ region where bin widths are finer than those of the W boson study. ResBos-P systematically overestimates the cross section by approximately 20% above $p_{\mathrm{T}}^{\mathrm{W}} =$ 110 GeV, but the CP version demonstrates good agreement with data in the accessible region of $p_{\mathrm{T}}^{\mathrm{Z}}$. The ratios of $\mathrm{ W }^-$ to $\mathrm{ W }^+$, Z to W boson differential cross sections, as well as the ratio of Z boson production cross sections at centre-of-mass energies 7 to 8 TeV are calculated to allow for more precise comparisons with data. Overall, the different theoretical models describe the ratios well. |
Additional Figures | |
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Additional Figure 1:
The unfolding from selected event to post-FSR level distribution for data (circles) and Powheg theory (line) for ${{{\mathrm {W}}} {\rightarrow} {\mu \nu}}$ channel(left), ${{{\mathrm {Z}}} {\rightarrow} {{\mu}^+{\mu}^-}}$ channel (right). SVD technique is used to unfold the measured events to post-FSR level to compensate the detector effect. The lepton from bosons is dressed with DR=0 (bare lepton) in this level. The POWHEG baseline MC describes the response matrix which formulates the relation between selected event and post-FSR event. |
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Additional Figure 1-a:
The unfolding from selected event to post-FSR level distribution for data (circles) and Powheg theory (line) for the ${{{\mathrm {W}}} {\rightarrow} {\mu \nu}}$ channel. SVD technique is used to unfold the measured events to post-FSR level to compensate the detector effect. The lepton from bosons is dressed with DR=0 (bare lepton) in this level. The POWHEG baseline MC describes the response matrix which formulates the relation between selected event and post-FSR event. |
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Additional Figure 1-b:
The unfolding from selected event to post-FSR level distribution for data (circles) and Powheg theory (line) for the ${{{\mathrm {Z}}} {\rightarrow} {{\mu}^+{\mu}^-}}$ channel. SVD technique is used to unfold the measured events to post-FSR level to compensate the detector effect. The lepton from bosons is dressed with DR=0 (bare lepton) in this level. The POWHEG baseline MC describes the response matrix which formulates the relation between selected event and post-FSR event. |
Additional Tables | |
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Additional Table 1:
The post-FSR level W boson normalized differential cross sections for the muon channel in bins of $ {p_{\mathrm {T}}} ^{\mathrm{W}}$, $(1/\sigma )(\mathrm{d}\sigma /\mathrm{d} {p_{\mathrm {T}}}) ({\mathrm{W} \rightarrow \mu \nu })$, and systematic uncertainties from various sources in units of %. where $\sigma $ is the sum of the cross sections for the $ {p_{\mathrm {T}}} ^{\mathrm{W}}$ bins. $(1/\sigma )(\mathrm{d}\sigma /\mathrm{d} {p_{\mathrm {T}}})$ is shown with total uncertainty, i.e. the sum of statistical and systematic uncertainties in quadrature. SVD technique is used to unfold the measured events to post-FSR level to compensate the detector effect. The lepton from bosons is dressed with DR=0 (bare lepton) in this level. |
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Additional Table 2:
The post-FSR level Z boson normalized differential cross sections for the $\mathrm{Z} \rightarrow \mu ^+ \mu ^-$ channel in bins of $ {p_{\mathrm {T}}} ^{\mathrm{Z}}$, $(1/\sigma )(\mathrm{d}\sigma /\mathrm{d} {p_{\mathrm {T}}}) ({\mathrm{Z} \rightarrow \mu ^+ \mu ^-})$, and systematic uncertainties from various sources in units of %. Other details are the same as in Additional Table 1. |
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Compact Muon Solenoid LHC, CERN |