CMS-PAS-LUM-21-001

CMS-PAS-LUM-21-001
Luminosity determination using Z boson production at the CMS experiment
CMS Collaboration
20 March 2023

Abstract: The measurement of Z boson production is presented as a means to determine the integrated luminosity. The analysis makes use of 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. An in situ "tag-and-probe" measurement is used to determine the trigger and identification efficiency for Z bosons in small intervals, 20 pb$^{-1} $, of integrated luminosity, thus facilitating the efficiency measurement as a function of instantaneous luminosity and time. The correlations between the efficiencies for the different muon track components and between the two muons are also studied. Using the ratio of the efficiency-corrected numbers of measured 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 luminosity measurement is performed. It is shown that the Z boson rate measurement constitutes a precise and complementary method to monitor and transfer the luminosity calibration between data sets, and that it can improve the measurement of the integrated luminosity.
Links: CDS record (PDF) ; CADI line (restricted) ; These preliminary results are superseded in this paper, EPJC 84 (2024) 26. The superseded preliminary plots can be found here.

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The upper panels show the reconstructed invariant mass distributions of Z boson candidates for 20 pb$^{-1}$ 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, while the red curve illustrates the modeled signal plus background contribution. The numbers of signal and background candidates are given by $ N_i^{\mathrm{sig}}=N_i - N_i^{\mathrm{bkg}} $ and $ N_i^{\mathrm{bkg}} $ respectively. The error bars indicate the statistical uncertainties. 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 panels show the reconstructed invariant mass distributions of Z boson candidates for 20 pb$^{-1}$ 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, while the red curve illustrates the modeled signal plus background contribution. The numbers of signal and background candidates are given by $ N_i^{\mathrm{sig}}=N_i - N_i^{\mathrm{bkg}} $ and $ N_i^{\mathrm{bkg}} $ respectively. The error bars indicate the statistical uncertainties. 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-b: The upper panels show the reconstructed invariant mass distributions of Z boson candidates for 20 pb$^{-1}$ 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, while the red curve illustrates the modeled signal plus background contribution. The numbers of signal and background candidates are given by $ N_i^{\mathrm{sig}}=N_i - N_i^{\mathrm{bkg}} $ and $ N_i^{\mathrm{bkg}} $ respectively. The error bars indicate the statistical uncertainties. 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 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 (line) 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 50% of the correction.
png pdf	Figure 3: Left: the Z boson rate, corrected for efficiency, compared to the reference luminosity measurement, in LHC Fill 6255, recorded on 29 September 2017. Each bin corresponds to about 20 pb$^{-1}$, as determined by the reference measurement. For shape comparison, the Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. Right: the measured single-muon efficiencies as a function of time, in the same LHC Fill 6255.
png pdf	Figure 3-a: Left: the Z boson rate, corrected for efficiency, compared to the reference luminosity measurement, in LHC Fill 6255, recorded on 29 September 2017. Each bin corresponds to about 20 pb$^{-1}$, as determined by the reference measurement. For shape comparison, the Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. Right: the measured single-muon efficiencies as a function of time, in the same LHC Fill 6255.
png pdf	Figure 3-b: Left: the Z boson rate, corrected for efficiency, compared to the reference luminosity measurement, in LHC Fill 6255, recorded on 29 September 2017. Each bin corresponds to about 20 pb$^{-1}$, as determined by the reference measurement. For shape comparison, the Z boson rate is normalized to the reference integrated luminosity. The panel at the bottom shows the ratio of the two measurements. Right: the measured single-muon efficiencies as a function of time, in the same LHC Fill 6255.
png pdf	Figure 4: Fiducial Z 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 rates are combined, the error bars correspond to the statistical uncertainties of the Z rates. The leftmost point, highlighted in red, corresponds to the $ \mathrm{lowPU} $ data. The result of a fit to a linear function is shown as a red line and the uncertainties are covered by the gray band.
png pdf	Figure 5: Each entry of the histogram represents the measurement of the luminosity from Z bosons in one interval of 20 pb$^{-1}$ of the $ \mathrm{highPU} $ data, divided by the integrated luminosity of the reference luminometer in the same interval. The first and last bins include the underflow and overflow contributions. For comparison, a Gaussian distribution with mean and standard deviation of the histogram is shown in red.
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 $ \mathrm{highPU} $ data. Each green point represents the luminosity values measured in one luminosity slice for the measurement of the Z reconstruction efficiency. The size of the point reflects the reference luminosity contained in each measurement. 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 reference luminosities [31].

Tables
png pdf	Table 1: Summary of the uncertainties in the number of delivered Z bosons in the 2017 $ \mathrm{highPU} $ and $ \mathrm{lowPU} $ data, and their ratio. The symbol $ \delta $ denotes the relative uncertainty, i.e.,, $ \delta x = \Delta x / x $.
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 $ \mathrm{highPU} $ and $ \mathrm{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 an alternative and complementary method to transfer integrated luminosity measurements between data sets. This study makes use of events with Z boson candidates decaying into a pair of muons. The data were recorded with the CMS experiment at the CERN LHC in 2017, at a $ {\mathrm{p}\mathrm{p}} $ center-of-mass energy of 13 TeV. The integrated luminosity of the largest data sample recorded in 2017 is obtained from that of a data set recorded at low 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 factors for the triggering, reconstruction, and selection is determined in intervals of 20 pb$^{-1}$, in situ, from the data. Monte Carlo simulations are only used to describe the shape of the resonant Z boson signal and for the study of possible biases of the method. A full quantitative study of the systematic uncertainties and their dependencies on pileup is performed for the first time. In the luminosity ratio, the systematic uncertainties cancel almost completely, with the exception of the pileup-dependent effects. The resulting uncertainty on the ratio is 0.4%. With its high precision, and providing in situ calibration options, Z boson counting is competitive with, and independent from, conventional methods for the extrapolation and integration of luminosity determined in van-der-Meer scan data. In the future, it can also be used to improve the systematic uncertainty in analysis that combine the integrated luminosities measured in different years.

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