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| 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 | ||
| CMS Collaboration | ||
| 25 June 2020 | ||
| 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. | ||
| Links: e-print arXiv:2006.14359 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| Figures | |
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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. |
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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. |
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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. |
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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). |
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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). |
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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). |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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. |
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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). |
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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). |
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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). |
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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. |
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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. |
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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. |
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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. |
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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. |
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