Longitudinal Layer Calibration
This work presents an improved method for longitudinal layer calibration in high energy physics, aiming to address biases observed in traditional H1-style calibration at low energies. By incorporating an energy constraint into the minimization process, we achieve enhanced linearity and resolution of jet energy measurements. Our method engages a new parameterization for energy density dependencies, yielding better performance across various energy regimes. Results demonstrate significant improvements in calibration accuracy, particularly at low energy levels, providing a more reliable framework for calorimetric energy reconstruction.
Longitudinal Layer Calibration
E N D
Presentation Transcript
Longitudinal Layer Calibration Belen Salvachua High Energy Physics DivisionArgonne National Laboratory
Alternative or Complementary to H1 calibration Longitudinal Layer method • Based on longitudinal development of the EM and HAD shower = 0 TileExt TileBar 4 longitudinal layers < 1.5 2 longitudinal layers EMB EME HEC EMB1 PreSamplerB = 3.2 FCAL 1 layers PreSamplerE
Longitudinal Layer method • Described ATLAS-PHYS-2006-062 • || < 1.5 • Layer 0 : PreSamplerB + PreSamplerE + EMB1 + EME1 • Layer 1: EMB2 + EME2 • Layer 2: EMB3+EME3+TileBar0+TileExt0+TileGap1+HEC0+ FCAL0 • Layer 3: Everything else • 1.5 < || < 3.2 • Layer 0: electro-magnetic calorimeters • Layer 1: hadronic calorimeters • 3.2 < || < 4.4 • Layer 0: Total Jet energy
Jet classified in terms of : Jet : 44 bins from 0 to 4.4 Jet energy, 2 bins: Ejet < Ecut Ejet > Ecut Fractional energy (fem), 3 bins: fem < fem1 fem1 < fem < fem2 fem > fem2 Weights are parameterized as function of the energy: Longitudinal Layer method
Longitudinal Layer calibration • Linearity within 2-3% at high energies and degrades up to 10% at low energies • Resolution: • Sampling term does not change significantly compared to cell E/V • The constant term is reduced Big impact at high energies
Longitudinal Layer calibration and Num. Inversion • Linearity within 1-3% • Resolution: • Slightly improvement at low energies
Adding Energy constraint Belen Salvachua and Esteban Fullana High Energy Physics DivisionArgonne National Laboratory
Outline • The motivation: • H1-style calibration has a bias at low energies • The idea/solution: • Add an energy constraint to the minimization of the resolution • Calculate new weights with this method: • Cell energy density dependency like H1-style • But we have tried with a simpler E/V dependency • Longitudinal shower development like Layer calibration • Longitudinal energy fraction
Known mathematical bias due to minimization function NIM A345:449,452,1994 Mathematical bias at low energies • Cell E/V calibration, no JES applied • Full jet pseudo-rapidity range • Linearity for E > 200Gev within 2% • Apparent non-linearity at E < 200GeV 200 GeV H1 coarse layer segmentation || ≤ 4.4
Hidden Bias in a Common Calorimeter Calibration Scheme Nucl.Instrum.Meth.A345:449,452,1994 • When using a 2 of the form: • A bias on the calibrated energy appears because NO constraint on energy • Mathematical bias is more important at low energies • The correction is analytically known: || < 0.7 Preliminary
Correction of the mathematical bias on the minimization Physically more appropriated • Possible solutions: • Evaluate possibility of including jet energy constraint in minimization function: Benefit: correction contained inside H1 weights • Apply the mathematical bias correction described in the NIM: • Jet energy scale can include this correction. Problem: We are mixing two things: * fake non-linearity from mathematical bias * Real non-linearity
Solution • Introduce energy constraint to avoid the mathematical bias using Lagrange multiplier method: • The question now is: • Which parameterization of the Ecalibrated should we use?
Comparing improvement at low energies Traditionally H1-style uses a polynomial of 3rd and 4th degree on Ln(e/v) • Clear improvement of the mathematical bias after calibration with energy constrain 200 GeV H1 coarse layer segmentation New Calibration: pol4 Ln(e/v) || ≤ 4.4
Comparing improvement at low energies • Clear improvement of the mathematical bias after calibration with energy constrain 1 term on LnE/V 1 term EM/Ejet 200 GeV H1 coarse layer segmentation New Calibration: Lineal Ln(e/v) EM fraction || ≤ 4.4
H1 coarse granularity calibration • Traditional H1-style needs more statistics to converge using Minuit • H1-style results done with 2Mevt (100 times more statistics done current analysis)
E/V dependency Traditionally H1-style uses a polynomial of 3rd and 4th degree on Ln(e/v) • Cell energy density has shown good performance on jet calibration • We try a polynomial of order 4th dependency on Ln(e/v):
Longitudinal showering No PreB PreE • Longitudinal energy distribution has also shown good performance on jet calibration • We add a linear term proportional to the fraction of energy in the EM calorimeters: 1 term on LnE/V 1 term EM/Ejet
Cone7TowerJets Resolution summary table
Adding constraint in energy solves bias at low energies Simple linear dependency on ln(e/v) and on the EM fraction of energy: Similar resolution than H1-style Better linearity than H1-style before the JES Other combinations can be easily including like: Merging layers Adding extra terms TO DO: Re-run calibration on Anti-Kt Use more statistics (20kevts now) Test calibration in other MC physics Conclusions
Cell E/V calibration: Coarse vs Fine granularity Belen Salvachua High Energy Physics DivisionArgonne National Laboratory
Cell energy density calibration: H1 style • Basis: • Electro-magnetic showers are more dense, energy concentrated in smaller region • Hadronic showers are broader, energy is spread in a larger volume • Mechanism: • Apply a different weight depending on the energy density of the cell H1 weights Integrate over all , E Not use jets with: INDEPENDENT of jet , E 1.3 > || > 1.5 3.0 > || > 3.5 || > 4.4 ETEM < 5 GeV ETNTJ < 20 GeV DEPENDENT on detector Subdetector and layer Technology/composition segmentation
H1 style calibration Cells classified according to: • H1 coarse and fine layer granularity contain additional correction for: • Gap correction • Scintillator correction • Cryostat correction: energy estimated as Layer/detector segmentation Cell energy density E/V space segmented in up to 16 bins • Coarse layer granularity • Fine layer granularity
Scheme of ATLAS calorimeters • Shapes and ratios are approximate TileBar TileExt EMB EME HEC PreSamplerB FCAL PreSamplerE
H1 coarse layer granularity Layers can be segmented in up to 16 bins of cell energy density • Shapes and ratios are approximate TileBar TileExt EMB2 + EMB3 < 0.8 EMB2 + EMB3 0.8 EME2 + EME3 <2.5 HEC < 2.5 EMB1 HEC 2.5 PreSamplerB EME2 + EME3 >2.5 PreSamplerE FCAL1 FCAL2 + FCAL3 EME1
H1 fine layer granularity Layers can be segmented in up to 16 bins of cell energy density • Shapes and ratios are approximate TileBar2 TileExt2 TileBar1 TileExt1 TileBar0 TileExt0 EMB3 < 0.8 EMB3 0.8 EMB2 <2.5 EMB3 <2.5 HEC HEC0 + HEC1 <2.5 HEC2 + HEC3 <2.5 EMB2 < 0.8 EMB2 0.8 EMB1 HEC0+ HEC1 2.5 HEC2+ HEC3 2.5 PreSamplerB EMB2 2.5 EMB3 2.5 PreSamplerE FCAL FCAL1 FCAL2 + FCAL3 EME1
Linearity and Resolution using H1 coarse layer granularity || ≤ 4.4 • Full jet pseudo-rapidity range • Looks like non-linearity at E < 200 GeV • Bias on the minimization (FERMILAB-Pub-93/394) • Corrected after jet energy scale 200 GeV
Linearity and Resolution using H1 fine layer granularity || ≤ 4.4 • Full jet pseudo-rapidity range • Looks like non-linearity at E < 200 GeV • Bias on the minimization (FERMILAB-Pub-93/394) • Corrected after jet energy scale 200 GeV
