CMS-LUM-20-002

CMS-LUM-20-002 ; CERN-EP-2025-018
Luminosity measurement for lead-lead collisions at $\sqrt{\smash[b]{s_{_{\mathrm{NN}}}}}=$ 5.02 TeV in 2015 and 2018 at CMS
CMS Collaboration
5 March 2025
Submitted to Eur. Phys. J. C
Abstract: Measurements of the luminosity delivered to the CMS experiment during the lead-lead data-taking periods in 2015 and 2018 are presented for the first time. The collisions were recorded at a nucleon-nucleon center-of-mass energy of 5.02 TeV; the 2018 data sample is three times larger than the 2015 data sample. Three subdetectors are used: the pixel luminosity telescope, the forward hadron calorimeters, and the fast beam conditions monitor. The absolute luminosity calibration is determined using the van der Meer technique that relies on transverse beam separation scans. The dominant sources of uncertainty are the transverse factorizability of the bunch density profiles and, in 2015, the difference between the results obtained using various detectors. The total uncertainty in the integrated luminosity, including the stability of the calibrated subdetector response over time, amounts to 3.0% for 2015, 1.7% for 2018, and 1.6% for the combined data sample.
Links: e-print arXiv:2503.03946 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: Schematic cross section through the CMS detector in the $r$ -- $z$ plane. The luminometers used during PbPb collisions in 2015 and 2018 are highlighted. The approximate locations of PLT, BCM1F, and HF with respect to the IP are indicated with purple, orange, and red rectangles, respectively. The center of the detector, corresponding to the approximate position of the PbPb collision point, is located at the origin. The parts of the muon detectors at radii larger than 4 m are omitted in this schema.
png pdf	Figure 2: Horizontal and vertical beam displacements derived from the LHC corrector magnet currents during the vdM scan program in fill 4689 (upper), fill 7442 (middle), and fill 7443 (lower). The first $x$ offset scan in fill 7442 was performed with smaller then planned maximal separation and was retaken. The last vdM scan in fill 7442 was interrupted by a premature beam dump and is thus not used in the analysis.
png pdf	Figure 2-a: Horizontal and vertical beam displacements derived from the LHC corrector magnet currents during the vdM scan program in fill 4689 (upper), fill 7442 (middle), and fill 7443 (lower). The first $x$ offset scan in fill 7442 was performed with smaller then planned maximal separation and was retaken. The last vdM scan in fill 7442 was interrupted by a premature beam dump and is thus not used in the analysis.
png pdf	Figure 2-b: Horizontal and vertical beam displacements derived from the LHC corrector magnet currents during the vdM scan program in fill 4689 (upper), fill 7442 (middle), and fill 7443 (lower). The first $x$ offset scan in fill 7442 was performed with smaller then planned maximal separation and was retaken. The last vdM scan in fill 7442 was interrupted by a premature beam dump and is thus not used in the analysis.
png pdf	Figure 2-c: Horizontal and vertical beam displacements derived from the LHC corrector magnet currents during the vdM scan program in fill 4689 (upper), fill 7442 (middle), and fill 7443 (lower). The first $x$ offset scan in fill 7442 was performed with smaller then planned maximal separation and was retaken. The last vdM scan in fill 7442 was interrupted by a premature beam dump and is thus not used in the analysis.
png pdf	Figure 3: Examples of 2015 scan distributions, i.e.,, the normalized rate recorded by PLT in BCID 955 as a function of the beam separation in $x$ (left) and $y$ (right), respectively. The error bars represent the statistical uncertainty in the measured rate. The purple curve corresponds to the single-Gaussian fit, and the obtained $\chi^2/\text{dof}$ is given on the plots. The lower panels show the residuals, defined as the difference between the measured and fitted values divided by the statistical uncertainty in the rate.
png pdf	Figure 3-a: Examples of 2015 scan distributions, i.e.,, the normalized rate recorded by PLT in BCID 955 as a function of the beam separation in $x$ (left) and $y$ (right), respectively. The error bars represent the statistical uncertainty in the measured rate. The purple curve corresponds to the single-Gaussian fit, and the obtained $\chi^2/\text{dof}$ is given on the plots. The lower panels show the residuals, defined as the difference between the measured and fitted values divided by the statistical uncertainty in the rate.
png pdf	Figure 3-b: Examples of 2015 scan distributions, i.e.,, the normalized rate recorded by PLT in BCID 955 as a function of the beam separation in $x$ (left) and $y$ (right), respectively. The error bars represent the statistical uncertainty in the measured rate. The purple curve corresponds to the single-Gaussian fit, and the obtained $\chi^2/\text{dof}$ is given on the plots. The lower panels show the residuals, defined as the difference between the measured and fitted values divided by the statistical uncertainty in the rate.
png pdf	Figure 4: The absolute difference in the displacement of the two beams at IP as measured by the DOROS and arc BPMs during the 2018 vdM1--5 scans as a function of the nominal beam separation in $x$ (left) and $y$ (right). The error bars indicate the statistical uncertainty in the measured beam positions.
png pdf	Figure 4-a: The absolute difference in the displacement of the two beams at IP as measured by the DOROS and arc BPMs during the 2018 vdM1--5 scans as a function of the nominal beam separation in $x$ (left) and $y$ (right). The error bars indicate the statistical uncertainty in the measured beam positions.
png pdf	Figure 4-b: The absolute difference in the displacement of the two beams at IP as measured by the DOROS and arc BPMs during the 2018 vdM1--5 scans as a function of the nominal beam separation in $x$ (left) and $y$ (right). The error bars indicate the statistical uncertainty in the measured beam positions.
png pdf	Figure 5: Difference between the reconstructed beamspot and the nominal positions as a function of the latter during the 2015 length scale calibration scans. The results are shown for the $x$ (left) and $y$ (right) scans, separately for the forward (purple) and backward (green) directions. The error bars represent the statistical uncertainty in the reconstructed beamspot position. The lines denote linear fits with slope and $\chi^2/\text{dof}$ values shown in the legend.
png pdf	Figure 5-a: Difference between the reconstructed beamspot and the nominal positions as a function of the latter during the 2015 length scale calibration scans. The results are shown for the $x$ (left) and $y$ (right) scans, separately for the forward (purple) and backward (green) directions. The error bars represent the statistical uncertainty in the reconstructed beamspot position. The lines denote linear fits with slope and $\chi^2/\text{dof}$ values shown in the legend.
png pdf	Figure 5-b: Difference between the reconstructed beamspot and the nominal positions as a function of the latter during the 2015 length scale calibration scans. The results are shown for the $x$ (left) and $y$ (right) scans, separately for the forward (purple) and backward (green) directions. The error bars represent the statistical uncertainty in the reconstructed beamspot position. The lines denote linear fits with slope and $\chi^2/\text{dof}$ values shown in the legend.
png pdf	Figure 6: Model dependence of the factorizability correction in 2015 for DG, DG2, and supG fit models without and with an extra constant (the latter are labeled as ``+C''). The points represent the mean values, with the error bars defined by the RMS over residual OD variations and luminometers of the BCID-averaged corrections. The dashed line indicates the average and the shaded band shows the RMS range around the average for the six models.
png pdf	Figure 7: Time dependence of the factorizability correction in 2018 for fill 7443, based on the scan combinations vdM3+offset2, vdM3+diag2, offset2+vdM4, diag2+vdM4, and vdM5+diag3 using the supG model as baseline. The error bars show the combined uncertainty. The dashed blue line shows the trend line over the scan combinations, with the solid gray area denoting the total uncertainty. The hatched areas denote contributions to the uncertainty due to the model choice including supG, DG, SG+supG, and supG+supG (orange) and due to the fit (blue) uncertainty of the trend line.
png pdf	Figure 8: Cross-detector comparison of the fitted $\Sigma_x$ as a function of BCID for the 2015 vdM3 (left) and 2018 vdM5 (right) scans. The error bars represent the statistical uncertainty. The horizontal dashed lines indicate the averaged values of the corresponding set of points.
png pdf	Figure 8-a: Cross-detector comparison of the fitted $\Sigma_x$ as a function of BCID for the 2015 vdM3 (left) and 2018 vdM5 (right) scans. The error bars represent the statistical uncertainty. The horizontal dashed lines indicate the averaged values of the corresponding set of points.
png pdf	Figure 8-b: Cross-detector comparison of the fitted $\Sigma_x$ as a function of BCID for the 2015 vdM3 (left) and 2018 vdM5 (right) scans. The error bars represent the statistical uncertainty. The horizontal dashed lines indicate the averaged values of the corresponding set of points.
png pdf	Figure 9: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 9-a: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 9-b: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 9-c: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 9-d: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 9-e: The measured $\sigma_{\text{vis}}$ in 2015 (upper row) and 2018 (lower row) calculated by averaging over all BCIDs for each vdM scan pair after all corrections are applied. From left to right the results are given for PLT, HFOC, and in 2018 also for BCM1F. The error bars represent the standard deviation of the measurements per BCID, accounting for statistical fluctuations. To calculate the central value of $\sigma_{\text{vis}}$ , the uncertainty-weighted average of the individual measurements for the various vdM scans are calculated along with its uncertainty.
png pdf	Figure 10: Cross-detector comparison of the measured luminosities using the PLT over HFOC luminosity ratio, cumulatively (upper) and as a function of integrated luminosity (middle and lower), for 2015 (upper left and middle) and 2018 (upper right and lower). The luminosity is integrated per 20 LS.
png pdf	Figure 10-a: Cross-detector comparison of the measured luminosities using the PLT over HFOC luminosity ratio, cumulatively (upper) and as a function of integrated luminosity (middle and lower), for 2015 (upper left and middle) and 2018 (upper right and lower). The luminosity is integrated per 20 LS.
png pdf	Figure 10-b: Cross-detector comparison of the measured luminosities using the PLT over HFOC luminosity ratio, cumulatively (upper) and as a function of integrated luminosity (middle and lower), for 2015 (upper left and middle) and 2018 (upper right and lower). The luminosity is integrated per 20 LS.
png pdf	Figure 10-c: Cross-detector comparison of the measured luminosities using the PLT over HFOC luminosity ratio, cumulatively (upper) and as a function of integrated luminosity (middle and lower), for 2015 (upper left and middle) and 2018 (upper right and lower). The luminosity is integrated per 20 LS.
png pdf	Figure 10-d: Cross-detector comparison of the measured luminosities using the PLT over HFOC luminosity ratio, cumulatively (upper) and as a function of integrated luminosity (middle and lower), for 2015 (upper left and middle) and 2018 (upper right and lower). The luminosity is integrated per 20 LS.
png pdf	Figure 11: The ratio of $\sigma_{\text{vis}}$ -normalized PLT to HFOC cross sections from emittance scans recorded during fills 7442--7443 and routine data-taking conditions in 2018 as indicated with corresponding fill numbers. The error bars indicate the statistical uncertainty.

Tables
png pdf	Table 1: Summary of the LHC conditions at IP5 for the 2015 and 2018 PbPb luminosity scan programs. The table shows the number $n_{\text{b}}$ of colliding bunch pairs, $\phi$ , $\beta^\ast$ , the targeted proton-equivalent transverse emittance $\varepsilon$ at injection, the beam intensities $N_1$ , $N_2$ , and the initial instantaneous luminosity $\mathcal{L}_{\text{init}}$ .
png pdf	Table 2: Summary of the beam separation scans performed during the 2015 and 2018 PbPb luminosity scan programs. The table shows the total number of vdM, length scale calibration (``lsc''), off-axis (offset or diagonal), and emittance (``em'') scan pairs that were performed, as well as the number of super-separation periods (``sep''). Only the scans used for the measurements reported here are included.
png pdf	Table 3: Ghost fractions ( $f_{\text{g}}$ ) and satellite fractions ( $f_{\text{s}}$ ) per beam, and total impact on $\sigma_{\text{vis}}$ ( $\Delta\sigma_{\text{vis}}$ ).
png pdf	Table 4: Scan combinations used in the transverse factorizability evaluation. The components of the scan combinations are listed in time order.
png pdf	Table 5: Summary of the BCID-averaged corrections to $\sigma_{\text{vis}}$ . Where applicable, the average correction applied to $\sigma_{\text{vis}}$ of PLT is shown.
png pdf	Table 6: Summary of contributions to the relative systematic uncertainty in the integrated luminosity. The systematic uncertainty is divided into groups affecting the description of the vdM profile and the bunch population product measurement (normalization), and the measurement of the rate in physics running conditions (integration). The last column specifies the correlation of the systematic source among years.
png pdf	Table 7: Summary of the measured recorded luminosity integrated over time periods when the CMS subsystems necessary for physics studies with muons in the final state were in good operational state. Also shown are the correlated and uncorrelated sources of uncertainties, which do not depend on the choice of the integration periods. The actual amount of recorded data can depend significantly on the data quality requirements imposed on the various subsystems.

Summary

The measurement of the luminosity delivered to the CMS experiment during the lead-lead (PbPb) data-taking periods in 2015 and 2018 at a nucleon-nucleon center-of-mass energy of 5.02 TeV is presented for the first time. Three subdetectors are used, listed in the order of their priority to provide the luminosity measurement: the pixel luminosity telescope, the forward hadron calorimeter, and the fast beam conditions monitor. Two groups of uncertainties are considered for effects related to ``normalization'' and ``integration''. The former concerns the visible cross section as determined from the van der Meer (vdM) scan procedure, and the latter the stability and quality of the measurements by the luminosity subdetectors under the PbPb data-taking conditions. The dominant sources of uncertainty contributing to the normalization and integration, as estimated in 2018, are associated to the transverse factorizability of the colliding bunch densities and cross-detector stability, respectively. In 2015, transverse factorizability, cross-detector consistency, and stability represent the main sources of the uncertainty. The estimated stability in 2018 is consistent with the analysis of short vdM-like scans performed regularly during the PbPb data-taking period. The uncertainty in the normalization is 2.9% in 2015 and 1.5% in 2018, and it is about 0.7--0.8% in the integration in both years. These are treated as uncorrelated and are summed in quadrature. When applying the vdM calibration to the entire periods and requiring that the detectors essential for studying final states with muons took high quality data, the total recorded luminosity is 0.433

$\pm$ 0.013 nb

$^{-1}$ in 2015, and 1.700

$\pm$ 0.029 nb

$^{-1}$ in 2018. The relative precision of the integrated luminosity measurement is 3.0% in 2015 and 1.7% in 2018, and holds also for other choices of the integration period. Taking into account the correlations among various systematic sources specified in the last column of Table 6, one can evaluate the combined 2015+2018 luminosity measurement. The results are summarized in Table 7. The combined uncorrelated contribution is mainly determined by the 2018 uncorrelated precision since it is the significantly larger data set. The combined data set has an integrated luminosity uncertainty of 1.6%.

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