Performance of electron energy calibration in the CMS ECAL using graph neural networks

Link to CDS: CMS DP-2022/009 (public link pending)

Introduction

• The energy deposited by electrons in the CMS ECAL is subject to a number of losses, including
  • Energy loss upstream of the ECAL
  • Leakage into the HCAL
  • Energy loss in gaps and dead crystals
• To mitigate this effect, a multivariate regression is used to derive per-particle energy corrections
• During the Run-2 data-taking period, this regression was based on a Boosted Decision Tree (BDT) machine learning architecture which operates on high-level reconstructed features describing the electromagnetic shower
• We have developed a new machine learning architecture called the Dynamic Reduction Network (DRN) which uses graph neural network techniques to regress directly on the detector hits associated with a given incident particle

Outline

• In this note we show the performance of our DRN architecture on the electrons used for detector calibration, compared to the Run 2 BDT algorithm
• Performance metrics are obtained by fitting histograms of the predicted energy (E_Pred ) divided by the generated energy (E_True) with a Cruijff function to extract mean response and resolution
• Figures presented in this note include:
  • Performance in particle gun simulation with ideal detector calibrations:
    • In bins of generated particle energy
    • In bins of generated particle energy for electrons with low bremsstrahlung (at least 96% of shower energy contained in 3x3 crystals around the highest-energy deposit)
    • In bins of pileup, measured as the median transverse energy density of the event
  • Performance in Z->ee decays, in both 2018 Legacy simulation and data
    • In barrel-barrel category, both inclusive and low bremsstrahlung
    • In endcaps-endcaps category, both inclusive and low bremsstrahlung

Performance in particle gun simulation with ideal detector calibrations (ECAL barrel)

Performance as a function of energy (inclusive)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the barrel region of the ECAL detector as a function of energy. Performance evaluated on electron gun simulation. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 0.4% as a function of energy. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of 10% at all energies.

Performance as a function of energy (low brem.)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the barrel region of the ECAL detector as a function of energy. Performance evaluated on electron gun simulation, selecting events in which ≥96% of the energy is deposited in 3x3 crystals around the most energetic hit. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 0.4% as a function of energy. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of ≈ 10% at all energies.

Performance as a function of pileup (inclusive)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the barrel region of the ECAL detector as a function of pileup, measured as the median transverse energy density of the event. The x-axis range considered here corresponds to 0-70 pileup interactions. Performance evaluated on electron gun simulation. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 0.4% as a function of pileup. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of ≈10% at all values of pileup.

Performance in particle gun simulation with ideal detector calibrations (ECAL endcaps)

Performance as a function of energy (inclusive)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the ECAL detector endcaps as a function of energy. Performance evaluated on electron gun simulation. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 4% as a function of energy. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of ≈ 10% at all energies.

Performance as a function of energy (low brem.)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the ECAL detector endcaps as a function of energy. Performance evaluated on electron gun simulation, selecting events in which ≥96% of the energy is deposited in 3x3 crystals around the most energetic hit. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 4% as a function of energy. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of ≈ 10% at all energies.

Performance as a function of pileup (inclusive)

Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) performance in the ECAL detector endcaps as a function of pileup, measured as the median transverse energy density of the event. The x-axis range considered here corresponds to 0-70 pileup interactions. Performance evaluated on electron gun simulation. Error bars represent RMS fitting uncertainties. Left: Mean response E_Pred/E_True. Regression response is stable to within better than 4% as a function of pileup. Right: Relative resolution. The DRN obtains a better resolution than the BDT by a factor of ≈10% at all values of pileup.

Performance in Z->ee events (data and simulation)

Barrel-barrel category (inclusive)

Di-electron invariant mass distributions of Z→ee events in 2018 Legacy data (left) and simulation (right) for both the Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) architectures. Events are selected in which both electrons are detected in the barrel region of the ECAL detector. The Z peak is fit with a relativistic Breit-Wigner distribution convolved with a crystal ball function where the Breit-Wigner parameters are fixed to their known values and the crystal ball parameters are allowed to float in order to parameterize the detector response and resolution. The DRN obtains an improved resolution by a factor of ≈ 5% with respect to the BDT in both data and simulation.

Barrel-barrel category (low brem.)

Di-electron invariant mass distributions of Z→ee events in 2018 Legacy data (left) and simulation (right) for both the Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) architectures. Events are selected in which both electrons are in the ECAL barrel and have ≥96% of their energy contained in 3x3 crystals around their most energetic hits. The Z peak is fit with a relativistic Breit-Wigner distribution convolved with a crystal ball function where the Breit-Wigner parameters are fixed to their known values and the crystal ball parameters are allowed to float in order to parameterize the detector response and resolution.

Endcaps-endcaps category (inclusive)

Di-electron invariant mass distributions of Z->ee events in 2018 Legacy data (left) and simulation (right) for both the Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) architectures. Events are selected in which both electrons are detected in the endcaps of the ECAL detector. The Z peak is fit with a relativistic Breit-Wigner distribution convolved with a crystal ball function where the Breit-Wigner parameters are fixed to their known values and the crystal ball parameters are allowed to float in order to parameterize the detector response and resolution. The DRN obtains a comparable resolution to the BDT. The lessened improvement in the endcaps is likely due to lower training statistics and greater differences between the ideal calibration simulation simulation used for training.

Endcaps-endcaps category (low brem.)

Di-electron invariant mass distributions of Z->ee events in 2018 Legacy data (left) and simulation (right) for both the Dynamic Reduction Network (DRN) and Boosted Decision Tree (BDT) architectures. Events are selected in which both electrons are in the ECAL endcaps and have ≥96% of their energy contained in 3x3 crystals around their most energetic hits. The Z peak is fit with a relativistic Breit-Wigner distribution convolved with a crystal ball function where the Breit-Wigner parameters are fixed to their known values and the crystal ball parameters are allowed to float in order to parameterize the detector response and resolution. The DRN obtains a comparable resolution to the BDT. The lessened improvement in the endcaps is likely due to lower training statistics and greater differences between the ideal calibration simulation simulation used for training.