Longitudinal Layer Calibration

1. Longitudinal Layer Calibration Belen Salvachua High Energy Physics DivisionArgonne National Laboratory

2. 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

3. 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

4. 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

5. 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

6. Longitudinal Layer calibration and Num. Inversion • Linearity within 1-3% • Resolution: • Slightly improvement at low energies

7. Adding Energy constraint Belen Salvachua and Esteban Fullana High Energy Physics DivisionArgonne National Laboratory

8. 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

9. 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

10. 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

11. 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

12. 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?

13. 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

14. 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

15. 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)

16. 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):

17. 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

18. Cone7TowerJets Resolution summary table

19. 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

20. Cell E/V calibration: Coarse vs Fine granularity Belen Salvachua High Energy Physics DivisionArgonne National Laboratory

21. 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

22. 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

23. Scheme of ATLAS calorimeters • Shapes and ratios are approximate TileBar TileExt EMB EME HEC PreSamplerB FCAL PreSamplerE

24. 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

25. 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

26. 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

27. 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