CMS-LUM-21-001

CMS-LUM-21-001 ; CERN-EP-2023-163
Luminosity determination using Z boson production at the CMS experiment
CMS Collaboration
2 September 2023
Eur. Phys. J. C 84 (2024) 26
Abstract: The measurement of Z boson production is presented as a method to determine the integrated luminosity of CMS data sets. The analysis uses proton-proton collision data, recorded by the CMS experiment at the CERN LHC in 2017 at a center-of-mass energy of 13 TeV. Events with Z bosons decaying into a pair of muons are selected. The total number of Z bosons produced in a fiducial volume is determined, together with the identification efficiencies and correlations from the same dataset, in small intervals of 20 pb$^{-1}$ of integrated luminosity, thus facilitating the efficiency and rate measurement as a function of time and instantaneous luminosity. Using the ratio of the efficiency-corrected numbers of Z bosons, the precisely measured integrated luminosity of one data set is used to determine the luminosity of another. For the first time, a full quantitative uncertainty analysis of the use of Z bosons for the integrated luminosity measurement is performed. The uncertainty in the extrapolation between two data sets, recorded in 2017 at low and high instantaneous luminosity, is less than 0.5%. We show that the Z boson rate measurement constitutes a precise method, complementary to traditional methods, with the potential to improve the measurement of the integrated luminosity.
Links: e-print arXiv:2309.01008 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; Physics Briefing ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The upper panels show the reconstructed invariant mass distributions of Z boson candidates in a 20 pb$^{-1}$ sample of data for events where one (left ) or two (right ) muons pass the single-muon trigger selection. The blue curve shows the fitted background contribution and the red curve illustrates the modeled signal-plus-background contribution. The error bars indicate the statistical uncertainties. The numbers of signal and background candidates are given by $ N_i^{\text{sig}}=N_i - N_i^{\text{bkg}} $ and $ N_i^{\text{bkg}} $, respectively. Also indicated are the $ \chi^2 $ values per degree of freedom (dof). The lower panels contain the pulls of the distributions, defined as the difference between the data and the fit model in each bin, divided by the statistical uncertainty estimated from the expected number of entries given by the model.
png pdf	Figure 1-a: The upper panel shows the reconstructed invariant mass distributions of Z boson candidates in a 20 pb$^{-1}$ sample of data for events where one muon passes the single-muon trigger selection. The blue curve shows the fitted background contribution and the red curve illustrates the modeled signal-plus-background contribution. The error bars indicate the statistical uncertainties. The numbers of signal and background candidates are given by $ N_i^{\text{sig}}=N_i - N_i^{\text{bkg}} $ and $ N_i^{\text{bkg}} $, respectively. Also indicated are the $ \chi^2 $ values per degree of freedom (dof). The lower panel contains the pull of the distribution, defined as the difference between the data and the fit model in each bin, divided by the statistical uncertainty estimated from the expected number of entries given by the model.
png pdf	Figure 1-b: The upper panel shows the reconstructed invariant mass distributions of Z boson candidates in a 20 pb$^{-1}$ sample of data for events where two muons pass the single-muon trigger selection. The blue curve shows the fitted background contribution and the red curve illustrates the modeled signal-plus-background contribution. The error bars indicate the statistical uncertainties. The numbers of signal and background candidates are given by $ N_i^{\text{sig}}=N_i - N_i^{\text{bkg}} $ and $ N_i^{\text{bkg}} $, respectively. Also indicated are the $ \chi^2 $ values per degree of freedom (dof). The lower panel contains the pull of the distribution, defined as the difference between the data and the fit model in each bin, divided by the statistical uncertainty estimated from the expected number of entries given by the model.
png pdf	Figure 2: Correction factor $ C_{\mathrm{HLT}} $ for the correlation between the measured muon trigger efficiencies of the two muons as a function of the number of reconstructed primary vertices, $ N_{\mathrm{PV}} $, in the simulation (lines) and the data (points). The data points are drawn at the mean value of $ N_{\mathrm{PV}} $ in each bin of the measurement. The horizontal error bars on the points show the bin width, and the vertical error bars show the statistical uncertainty. The gray band indicates the $ \pm$100% uncertainty in the correction factor.
png pdf	Figure 3: left: the efficiency-corrected Z boson rate, compared to the reference luminosity measurement, in the LHC fill 6255, recorded on September 29, 2017. Each bin corresponds to about 20 pb$^{-1}$, as determined by the reference measurement. For shape comparison, the integrated Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. The vertical error bars show the statistical uncertainty in the Z boson rate. right: the measured single-muon efficiencies as functions of time for the same LHC fill. The vertical error bars show the statistical uncertainty in the efficiency.
png pdf	Figure 3-a: The efficiency-corrected Z boson rate, compared to the reference luminosity measurement, in the LHC fill 6255, recorded on September 29, 2017. Each bin corresponds to about 20 pb$^{-1}$, as determined by the reference measurement. For shape comparison, the integrated Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. The vertical error bars show the statistical uncertainty in the Z boson rate.
png pdf	Figure 3-b: The measured single-muon efficiencies as functions of time for the same LHC fill. The vertical error bars show the statistical uncertainty in the efficiency.
png pdf	Figure 4: Fiducial Z boson production cross section as a function of the instantaneous recorded luminosity, normalized to the average measured cross section. In each point, multiple measurements of the delivered Z boson rates are combined, the error bars correspond to the statistical uncertainties of the Z boson rate measurement. The leftmost point, highlighted in red, corresponds to the lowPU data. The result of a fit to a linear function is shown as a red line and the statistical uncertainties are covered by the gray band.
png pdf	Figure 5: Distribution of the ratio of integrated luminosities between Z boson counting and the reference luminometer. The entries, each corresponding to one interval of 20 pb$^{-1}$ of highPU data, are weighted with the respective measured luminosity.
png pdf	Figure 6: The luminosity as measured from Z bosons divided by the reference luminosity as a function of the integrated luminosity for the 2017 highPU data. Each green point represents the ratio from one measurement of the number of Z bosons. The blue lines show the averages of 50 consecutive measurements, each containing about 1 fb$ ^{-1} $ of data. The gray band has a width of 1.5%, corresponding to the uncertainty in the ratio of the integrated reference luminosities from the lowPU to the one of highPU [32].

Tables
png pdf	Table 1: Summary of the uncertainties in the number of delivered Z bosons in the 2017 highPU and lowPU data, and their ratio. The symbol $ \delta $ denotes the relative uncertainty, i.e., $ \delta x = \Delta x / x $. The systematic and statistical uncertainties are added in quadrature to obtain the total uncertainty.
png pdf	Table 2: Summary of cross checks performed by varying the length of the luminosity interval, the bin width of the $ m_{\mu\mu} $ histograms, and the range of the fit. As in Table 1, the resulting variations of the number of Z bosons in the 2017 highPU and lowPU data, and their ratio, are shown. The $ \delta $ denotes the relative variations, i.e., $ \delta x = \Delta x / x $.

Summary

The precision measurement of the Z boson production rate provides a complementary method to transfer integrated luminosity measurements between data sets. This study makes use of events with Z bosons decaying into a pair of muons. The data were recorded with the CMS experiment at the CERN LHC in 2017, at a proton-proton center-of-mass energy of 13 TeV. The integrated luminosity of a larger data sample recorded in 2017 is obtained from that of a smaller data set recorded at lower pileup using the ratio of the efficiency-corrected numbers of Z bosons counted in the two data sets. The full set of efficiencies and correlation correction factors for triggering, reconstruction, and selection are determined in intervals of 20 pb$^{-1}$ from the same Z boson data samples. Monte Carlo simulations are used only to describe the shape of the resonant Z boson signal and for the study of possible biases of the method. A detailed quantitative study of the systematic uncertainties and their dependencies on pileup is performed for the first time. In the integrated luminosity ratio, the systematic uncertainties cancel almost completely, with the exception of the pileup-dependent effects. The resulting uncertainty in the ratio is 0.5%. With its high precision, the Z boson counting is competitive with and independent of conventional methods for the extrapolation and integration of luminosity.

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