CMS logoCMS event Hgg
Compact Muon Solenoid
LHC, CERN

CMS-EGM-18-001 ; CERN-EP-2020-105
Reconstruction of signal amplitudes in the CMS electromagnetic calorimeter in the presence of overlapping proton-proton interactions
JINST 15 (2020) P10002
Abstract: A template fitting technique for reconstructing the amplitude of signals produced by the lead tungstate crystals of the CMS electromagnetic calorimeter is described. This novel approach is designed to suppress the increased out-of-time pileup contribution to the signal following the reduction of the accelerator bunch spacing from 50 to 25 ns at the start of Run 2 of the LHC. Execution of the algorithm is sufficiently fast for it to be employed in the CMS high-level trigger. It is also used in the offline event reconstruction. Results obtained from simulations and from collision data demonstrate a substantial improvement in the energy resolution of the calorimeter over a range of energies extending from a few GeV to several tens of GeV.
Figures Summary References CMS Publications
Figures

png pdf
Figure 1:
Two examples of fitted pulses for simulated events with 20 average pileup interactions and 25 ns bunch spacing. Signals from individual crystals are shown. They arise from a $ {p_{\mathrm {T}}} = $ 10 GeV photon shower in the barrel (left) and in an endcap (right). Filled circles with error bars represent the 10 digitized samples, the red dashed distributions (dotted multicolored distributions) represent the fitted in-time (out-of time) pulses with positive amplitudes. The solid dark blue histograms represent the sum of all the fitted contributions. Within the dotted distributions, the color distinguishes the fitted out-of-time pulses with different BX, while the legend represent them as a generic gray dotted line.

png pdf
Figure 1-a:
Two examples of fitted pulses for simulated events with 20 average pileup interactions and 25 ns bunch spacing. Signals from individual crystals are shown. They arise from a $ {p_{\mathrm {T}}} = $ 10 GeV photon shower in the barrel. Filled circles with error bars represent the 10 digitized samples, the red dashed distributions (dotted multicolored distributions) represent the fitted in-time (out-of time) pulses with positive amplitudes. The solid dark blue histograms represent the sum of all the fitted contributions. Within the dotted distributions, the color distinguishes the fitted out-of-time pulses with different BX, while the legend represent them as a generic gray dotted line.

png pdf
Figure 1-b:
Two examples of fitted pulses for simulated events with 20 average pileup interactions and 25 ns bunch spacing. Signals from individual crystals are shown. They arise from a $ {p_{\mathrm {T}}} = $ 10 GeV photon shower in an endcap. Filled circles with error bars represent the 10 digitized samples, the red dashed distributions (dotted multicolored distributions) represent the fitted in-time (out-of time) pulses with positive amplitudes. The solid dark blue histograms represent the sum of all the fitted contributions. Within the dotted distributions, the color distinguishes the fitted out-of-time pulses with different BX, while the legend represent them as a generic gray dotted line.

png pdf
Figure 2:
Pulse shape binned templates, measured in collision data recorded during June 2017 in a typical LHC fill, for a channel in the barrel (left) and in an endcap (right). The horizontal error bars represent the bin size. The first 3 bins are the pedestal samples, and their values equal zero by construction. The following 7 bins are estimated from the average of the digitized samples on many hits, while the rightmost 5 bins are estimated by extrapolating the distribution using the function of Eq. (5) (blue solid line).

png pdf
Figure 2-a:
Pulse shape binned templates, measured in collision data recorded during June 2017 in a typical LHC fill, for a channel in the barrel. The horizontal error bars represent the bin size. The first 3 bins are the pedestal samples, and their values equal zero by construction. The following 7 bins are estimated from the average of the digitized samples on many hits, while the rightmost 5 bins are estimated by extrapolating the distribution using the function of Eq. (5) (blue solid line).

png pdf
Figure 2-b:
Pulse shape binned templates, measured in collision data recorded during June 2017 in a typical LHC fill, for a channel in an endcap. The horizontal error bars represent the bin size. The first 3 bins are the pedestal samples, and their values equal zero by construction. The following 7 bins are estimated from the average of the digitized samples on many hits, while the rightmost 5 bins are estimated by extrapolating the distribution using the function of Eq. (5) (blue solid line).

png pdf
Figure 3:
Correlation matrix of the pulse shape binned templates, $ {\rho}_\text {pulse}$, measured in collision data recorded during June 2017 in a typical LHC fill, for one channel in the barrel (left) and in an endcap (right). The elements with $i=$ 5 or $k=$ 5 have zero variance by definition, since $S_5 = 1$ for all the hits. The elements $\rho _\text {pulse}^{i,k}$ with $i < $ 3 or $k < $ 3 are the presamples, where no signal is expected, and are set to zero. Those with $i > $ 9 or $k > $ 9 are estimated from simulations with a shifted BX. The others are measured in collision data, as described in the text. All the values in the figure represent 100$\rho _\text {pulse}^{i,k}$ for readability.

png pdf
Figure 3-a:
Correlation matrix of the pulse shape binned templates, $ {\rho}_\text {pulse}$, measured in collision data recorded during June 2017 in a typical LHC fill, for one channel in the barrel. The elements with $i=$ 5 or $k=$ 5 have zero variance by definition, since $S_5 = 1$ for all the hits. The elements $\rho _\text {pulse}^{i,k}$ with $i < $ 3 or $k < $ 3 are the presamples, where no signal is expected, and are set to zero. Those with $i > $ 9 or $k > $ 9 are estimated from simulations with a shifted BX. The others are measured in collision data, as described in the text. All the values in the figure represent 100$\rho _\text {pulse}^{i,k}$ for readability.

png pdf
Figure 3-b:
Correlation matrix of the pulse shape binned templates, $ {\rho}_\text {pulse}$, measured in collision data recorded during June 2017 in a typical LHC fill, for one channel in an endcap. The elements with $i=$ 5 or $k=$ 5 have zero variance by definition, since $S_5 = 1$ for all the hits. The elements $\rho _\text {pulse}^{i,k}$ with $i < $ 3 or $k < $ 3 are the presamples, where no signal is expected, and are set to zero. Those with $i > $ 9 or $k > $ 9 are estimated from simulations with a shifted BX. The others are measured in collision data, as described in the text. All the values in the figure represent 100$\rho _\text {pulse}^{i,k}$ for readability.

png pdf
Figure 4:
History of the pedestal mean value for the ECAL barrel (left) and its noise (right), measured for the highest MGPA gain in collision or noncollision runs taken during the 2016-2018 data taking period. The inset in the left panel shows an enlargement of two days in August 2018, to show in more detail the variation of the pedestal mean during LHC fills.

png pdf
Figure 4-a:
History of the pedestal mean value for the ECAL barrel, measured for the highest MGPA gain in collision or noncollision runs taken during the 2016-2018 data taking period. The inset shows an enlargement of two days in August 2018, to show in more detail the variation of the pedestal mean during LHC fills.

png pdf
Figure 4-b:
History of the noise for the ECAL barrel, measured for the highest MGPA gain in collision or noncollision runs taken during the 2016-2018 data taking period.

png pdf
Figure 5:
Correlation matrix of the electronics noise, $ {\rho}_\text {noise}$, measured in dedicated pedestal runs in Run 2, averaged over all the channels of the barrel (left) or endcaps (right). All the values in the figure represent 100$ {\rho}_\text {noise}$ for readability.

png pdf
Figure 5-a:
Correlation matrix of the electronics noise, $ {\rho}_\text {noise}$, measured in dedicated pedestal runs in Run 2, averaged over all the channels of the barrel (left) or endcaps (right). All the values in the figure represent 100$ {\rho}_\text {noise}$ for readability.

png pdf
Figure 5-b:
Correlation matrix of the electronics noise, $ {\rho}_\text {noise}$, measured in dedicated pedestal runs in Run 2, averaged over all the channels of the barrel (left) or endcaps (right). All the values in the figure represent 100$ {\rho}_\text {noise}$ for readability.

png pdf
Figure 6:
Reconstructed amplitude bias for the IT amplitude, $< A > -A_\text {true}$, as a function of pedestal shifts $\Delta P$, for a single-crystal pulse of $E = $ 50 GeV the EB.

png pdf
Figure 7:
Reconstructed amplitude over true amplitude, $< A > /A_\text {true}$, as a function of the timing shift of the pulse template, $\Delta T_\text {max}$, for a single-crystal pulse of $E = $ 50 GeV in the EB (left) and EE (right). The insets show an enlargement in the $ \pm $1 ns range with a finer $\Delta T_\text {max}$ granularity.

png pdf
Figure 7-a:
Reconstructed amplitude over true amplitude, $< A > /A_\text {true}$, as a function of the timing shift of the pulse template, $\Delta T_\text {max}$, for a single-crystal pulse of $E = $ 50 GeV in the EB (left) and EE (right). The insets show an enlargement in the $ \pm $1 ns range with a finer $\Delta T_\text {max}$ granularity.

png pdf
Figure 7-b:
Reconstructed amplitude over true amplitude, $< A > /A_\text {true}$, as a function of the timing shift of the pulse template, $\Delta T_\text {max}$, for a single-crystal pulse of $E = $ 50 GeV in the EB (left) and EE (right). The insets show an enlargement in the $ \pm $1 ns range with a finer $\Delta T_\text {max}$ granularity.

png pdf
Figure 8:
Average timing of ECAL pulses in proton-proton collisions collected in 2017, as measured in Ref. [21]. For each point, the average of the hits reconstructed in all barrel and endcaps channels is used. The sharp changes in $T_\text {max}$ correspond to restarts of data taking following LHC technical stops, as discussed in the text. At the beginning of the yearly data taking, the timing is calibrated so that the average $T_\text {max}=$ 0.

png pdf
Figure 9:
Measured amplitude resolution for two generated energy deposits ($E = $ 2 GeV or $E = $ 50 GeV) in a single ECAL barrel crystal, at $\eta =$ 0, reconstructed with either the multifit or the weights algorithm. Filled points show the effective resolution expressed as the difference between the reconstructed energy and the true energy, divided by the true energy. Open points show the percentage resolution estimated when the true energy is replaced with the sum of the true energy and the in-time pileup energy.

png pdf
Figure 9-a:
Measured amplitude resolution for two generated energy deposits ($E = $ 2 GeV or $E = $ 50 GeV) in a single ECAL barrel crystal, at $\eta =$ 0, reconstructed with either the multifit or the weights algorithm. Filled points show the effective resolution expressed as the difference between the reconstructed energy and the true energy, divided by the true energy. Open points show the percentage resolution estimated when the true energy is replaced with the sum of the true energy and the in-time pileup energy.

png pdf
Figure 9-b:
Measured amplitude resolution for two generated energy deposits ($E = $ 2 GeV or $E = $ 50 GeV) in a single ECAL barrel crystal, at $\eta =$ 0, reconstructed with either the multifit or the weights algorithm. Filled points show the effective resolution expressed as the difference between the reconstructed energy and the true energy, divided by the true energy. Open points show the percentage resolution estimated when the true energy is replaced with the sum of the true energy and the in-time pileup energy.

png pdf
Figure 10:
Left: bias in the out-of-time amplitude estimated by the multifit algorithm as a function of BX, for the bunch crossings $-5\le \mathrm {BX}\le +4$. The in-time interaction corresponds to BX $=$ 0 in the figure. The bias is estimated as the mode of the distribution of the ratio between the measured and the true energy. Only statistical uncertainties are shown. Right: energy spectrum in an ECAL barrel crystal, at $\eta \approx $ 0.

png pdf
Figure 10-a:
Left: bias in the out-of-time amplitude estimated by the multifit algorithm as a function of BX, for the bunch crossings $-5\le \mathrm {BX}\le +4$. The in-time interaction corresponds to BX $=$ 0 in the figure. The bias is estimated as the mode of the distribution of the ratio between the measured and the true energy. Only statistical uncertainties are shown. Right: energy spectrum in an ECAL barrel crystal, at $\eta \approx $ 0.

png pdf
Figure 10-b:
Left: bias in the out-of-time amplitude estimated by the multifit algorithm as a function of BX, for the bunch crossings $-5\le \mathrm {BX}\le +4$. The in-time interaction corresponds to BX $=$ 0 in the figure. The bias is estimated as the mode of the distribution of the ratio between the measured and the true energy. Only statistical uncertainties are shown. Right: energy spectrum in an ECAL barrel crystal, at $\eta \approx $ 0.

png pdf
Figure 11:
Effective energy resolutions for nonconverted photons in barrel (left) and endcaps (right) as a function of the generated ${p_{\mathrm {T}}}$ of the photon. The photons are generated with a uniform ${p_{\mathrm {T}}}$ distribution and their interaction is obtained with the full detector simulation. The average number of PU interactions is 40. The horizontal error bars represent the bin width. The statistical uncertainties are too small to be displayed.

png pdf
Figure 11-a:
Effective energy resolutions for nonconverted photons in barrel (left) and endcaps (right) as a function of the generated ${p_{\mathrm {T}}}$ of the photon. The photons are generated with a uniform ${p_{\mathrm {T}}}$ distribution and their interaction is obtained with the full detector simulation. The average number of PU interactions is 40. The horizontal error bars represent the bin width. The statistical uncertainties are too small to be displayed.

png pdf
Figure 11-b:
Effective energy resolutions for nonconverted photons in barrel (left) and endcaps (right) as a function of the generated ${p_{\mathrm {T}}}$ of the photon. The photons are generated with a uniform ${p_{\mathrm {T}}}$ distribution and their interaction is obtained with the full detector simulation. The average number of PU interactions is 40. The horizontal error bars represent the bin width. The statistical uncertainties are too small to be displayed.

png pdf
Figure 12:
Examples of the $\pi ^0$-meson peak reconstructed from the invariant mass of photon pairs in the barrel (left) and endcaps (right), for the single-crystal amplitudes measured with either the weights or the multifit reconstruction. A portion of collision data with typical Run 2 conditions, recorded during July 2018, is used. Error bars represent the statistical uncertainty. The result of the fit with a Gaussian distribution (green dotted line) plus a polynomial function (red dashed line) is superimposed on the measured distributions for the multifit case (dark blue solid line). For the weights case the same model is used, but only the total likelihood is shown superimposed (light orange solid line).

png pdf
Figure 12-a:
Examples of the $\pi ^0$-meson peak reconstructed from the invariant mass of photon pairs in the barrel (left) and endcaps (right), for the single-crystal amplitudes measured with either the weights or the multifit reconstruction. A portion of collision data with typical Run 2 conditions, recorded during July 2018, is used. Error bars represent the statistical uncertainty. The result of the fit with a Gaussian distribution (green dotted line) plus a polynomial function (red dashed line) is superimposed on the measured distributions for the multifit case (dark blue solid line). For the weights case the same model is used, but only the total likelihood is shown superimposed (light orange solid line).

png pdf
Figure 12-b:
Examples of the $\pi ^0$-meson peak reconstructed from the invariant mass of photon pairs in the barrel (left) and endcaps (right), for the single-crystal amplitudes measured with either the weights or the multifit reconstruction. A portion of collision data with typical Run 2 conditions, recorded during July 2018, is used. Error bars represent the statistical uncertainty. The result of the fit with a Gaussian distribution (green dotted line) plus a polynomial function (red dashed line) is superimposed on the measured distributions for the multifit case (dark blue solid line). For the weights case the same model is used, but only the total likelihood is shown superimposed (light orange solid line).

png pdf
Figure 13:
Peak position, normalized to the mass measured in the first BX of the train, (left) and Gaussian resolution $\sigma _{m({\gamma \gamma})}$ (right) of the invariant mass distribution of $\pi ^0\to \gamma \gamma $ decays with both photons in the EB, within a bunch train of 8 colliding bunches from an LHC fill in October 2017. Error bars represent the statistical uncertainty. The single-crystal energy is reconstructed either with the weights method (open circles) or with the multifit method (filled circles). Each point is obtained by fitting the diphoton invariant mass distribution in collisions selected from a single BX of the train.

png pdf
Figure 13-a:
Peak position, normalized to the mass measured in the first BX of the train, (left) and Gaussian resolution $\sigma _{m({\gamma \gamma})}$ (right) of the invariant mass distribution of $\pi ^0\to \gamma \gamma $ decays with both photons in the EB, within a bunch train of 8 colliding bunches from an LHC fill in October 2017. Error bars represent the statistical uncertainty. The single-crystal energy is reconstructed either with the weights method (open circles) or with the multifit method (filled circles). Each point is obtained by fitting the diphoton invariant mass distribution in collisions selected from a single BX of the train.

png pdf
Figure 13-b:
Peak position, normalized to the mass measured in the first BX of the train, (left) and Gaussian resolution $\sigma _{m({\gamma \gamma})}$ (right) of the invariant mass distribution of $\pi ^0\to \gamma \gamma $ decays with both photons in the EB, within a bunch train of 8 colliding bunches from an LHC fill in October 2017. Error bars represent the statistical uncertainty. The single-crystal energy is reconstructed either with the weights method (open circles) or with the multifit method (filled circles). Each point is obtained by fitting the diphoton invariant mass distribution in collisions selected from a single BX of the train.

png pdf
Figure 14:
Example of the $\mathrm{Z} \to \mathrm{e^{+}} \mathrm{e^{-}} $ invariant mass distribution in a central region of the barrel (0.200 $ < \text {max}({| \eta _1 |}, {| \eta _2 |}) < $ 0.435) with the single-crystal amplitude estimated using either the weights or the multifit method. A portion of collision data with typical Run 2 conditions, recorded during October 2016, is used. Error bars represent the statistical uncertainty. The energy is summed over a 5${\times}$5 crystal matrix. The reported values of $\sigma _\text {eff}$ include the natural width of the Z boson, and are expressed as a percentage of the position of the peak, $m$, of the corresponding invariant mass distribution.

png pdf
Figure 15:
History of the median of the $R_9$ cluster shape for electrons from $\mathrm{Z} \to \mathrm{e^{+}} \mathrm{e^{-}} $ decays during one typical LHC fill in 2016. Hits are reconstructed with either the multifit (filled circles) or the weights algorithm (open circles). Each point represents the median of the distribution for a 5 hour period during the considered LHC fill. Error bars represent the statistical uncertainty on the median. The bottom panel shows the instantaneous luminosity delivered by the LHC as a function of time.
Summary
A multifit algorithm that uses a template fitting technique to reconstruct the energy of single hits in the CMS electromagnetic calorimeter has been presented. This algorithm was implemented before the start of the Run 2 data taking period of the LHC, replacing the weights method used in Run 1. The change was motivated by the reduction of the LHC bunch spacing from 50 to 25 ns, and by the higher instantaneous luminosity delivered in Run 2, which led to a substantial increase in both the in-time and out-of-time pileup. Procedures have been developed to provide regular updates of input parameters to ensure the stability of energy reconstruction over time.

Studies based on control samples in data show that the energy resolution for deposits ranging from a few to several tens of GeV is improved, using $\pi^0\to\gamma\gamma$ and $\mathrm{Z}\to\mathrm{e^{+}}\mathrm{e^{-}}$ decays. The gain is more significant for lower energy electromagnetic deposits, for which the relative contribution of pileup is larger. This enhances the reconstruction of jets and missing transverse energy with the particle-flow algorithm used in CMS. These results have been reproduced with simulation studies, which show that an improvement relative to the weights method is obtained at all energies, including those relevant for photons from Higgs boson decays.

Simulation studies show that the new algorithm will perform successfully at the high-luminosity LHC, where a peak pileup of about 200 interactions per bunch crossing, with 25 ns bunch spacing, is expected.
References
1 CMS Collaboration The CMS experiment at the CERN LHC JINST 3 (2008) S08004 CMS-00-001
2 CMS Collaboration The CMS electromagnetic calorimeter project: technical design report CDS
3 P. Adzic et al. Reconstruction of the signal amplitude of the CMS electromagnetic calorimeter EPJC 46 (2006) 23
4 CMS Collaboration The CMS trigger system JINST 12 (2017) P01020 CMS-TRG-12-001
1609.02366
5 S. Gadomski et al. The deconvolution method of fast pulse shaping at hadron colliders NIMA 320 (1992) 217
6 CMS Collaboration CMS tracking performance results from early LHC operation EPJC 70 (2010) 1165
7 F. James and M. Roos MINUIT: a system for function minimization and analysis of the parameter errors and correlations CPC 10 (1975) 343
8 D. Chen and R. J. Plemmons Nonnegativity constraints in numerical analysis in The Birth of Numerical Analysis, p. 109 2009
9 C. L. Lawson and R. J. Hanson Solving least squares problems Society for Industrial and Applied Mathematics, 1995
10 GEANT4 Collaboration GEANT4 --- a simulation toolkit NIMA 506 (2003) 250
11 G. Guennebaud and B. Jacob Eigen v3 2010 \url http://eigen.tuxfamily.org
12 C. Richardson CMS high level trigger timing measurements J. Phys. Conf. Ser. 664 (2015) 082045
13 CMS Collaboration Energy calibration and resolution of the CMS electromagnetic calorimeter in pp collisions at $ \sqrt{s} = $ 7 TeV JINST 8 (2013) P09009 CMS-EGM-11-001
1306.2016
14 CMS Collaboration Anomalous APD signals in the CMS electromagnetic calorimeter NIMA 695 (2012) 293
15 CMS Collaboration Performance and operation of the CMS electromagnetic calorimeter JINST 5 (2010) T03010 CMS-CFT-09-004
0910.3423
16 CMS Collaboration CMS luminosity based on pixel cluster counting --- Summer 2013 update CMS-PAS-LUM-13-001 CMS-PAS-LUM-13-001
17 M. Anfreville et al. Laser monitoring system for the CMS lead tungstate crystal calorimeter NIMA 594 (2008) 292
18 L.-Y. Zhang et al. Performance of the monitoring light source for the CMS lead tungstate crystal calorimeter IEEE Trans. Nucl. Sci. 52 (2005) 1123
19 S. D. Guida et al. The CMS condition database system in Proceedings, 21st International Conference on Computing in High Energy and Nuclear Physics (CHEP 2015)
20 Z. Antunovic et al. Radiation hard avalanche photodiodes for the CMS detector NIMA 537 (2005) 379
21 CMS Collaboration Time reconstruction and performance of the CMS electromagnetic calorimeter JINST 5 (2010) T03011 CMS-CFT-09-006
0911.4044
22 G. Apollinari et al. High-Luminosity Large Hadron Collider (HL-LHC) CERN Yellow Rep. Monogr. 4 (2017) 1
23 CMS Collaboration The Phase-2 upgrade of the CMS barrel calorimeters CMS-PAS-TDR-17-002 CMS-PAS-TDR-17-002
24 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
25 CMS Collaboration Performance of electron reconstruction and selection with the CMS detector in proton-proton collisions at $ \sqrt{s} = $ 8 TeV JINST 10 (2015) P06005 CMS-EGM-13-001
1502.02701
26 CMS Collaboration Particle-flow reconstruction and global event description with the CMS detector JINST 12 (2017) P10003 CMS-PRF-14-001
1706.04965
27 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
28 CMS Collaboration Jet energy scale and resolution performance with 13 TeV data collected by CMS in 2016 CDS
29 CMS Collaboration Performance of missing transverse momentum reconstruction in proton-proton collisions at $ \sqrt{s} = $ 13 TeV using the CMS detector JINST 14 (2019) P07004 CMS-JME-17-001
1903.06078
Compact Muon Solenoid
LHC, CERN