Longitudinal Layer Calibration Belen Salvachua High Energy Physics
Longitudinal Layer Calibration Belen Salvachua High Energy Physics Division Argonne National Laboratory
Longitudinal Layer method Alternative or Complementary to H 1 calibration n Based on longitudinal development of the EM and HAD shower =0 4 longitudinal layers Tile. Ext Tile. Bar EMB 1 Pre. Sampler. B EME HEC < 1. 5 2 longitudinal layers = 3. 2 FCAL Pre. Sampler. E 1 layers 2
Longitudinal Layer method n Described ATLAS-PHYS-2006 -062 n | | < 1. 5 – Layer 0 : Pre. Sampler. B + Pre. Sampler. E + EMB 1 + EME 1 – Layer 1: EMB 2 + EME 2 – Layer 2: EMB 3+EME 3+Tile. Bar 0+Tile. Ext 0+Tile. Gap 1+HEC 0+ FCAL 0 – Layer 3: Everything else n 1. 5 < | | < 3. 2 – Layer 0: electro-magnetic calorimeters – Layer 1: hadronic calorimeters n 3. 2 < | | < 4. 4 – Layer 0: Total Jet energy 3
Longitudinal Layer method n Jet classified in terms of : – Jet : 44 bins from 0 to 4. 4 – Jet energy, 2 bins: – Ejet < Ecut – Ejet > Ecut < 1. 2 < < 3. 2 > 3. 2 300 Ge. V 450 Ge. V 35 cosh( ) Ge. V – Fractional energy (fem), 3 bins: • fem < fem 1 • fem 1 < fem 2 < 1. 5 • fem > fem 2 Ejet < E Ejet > E cut 1. 5 < < 2. 5 cut 2. 5 < < 3. 2 Ejet < Ecut Ejet > Ecut fem 1 0. 65 0. 75 0. 65 0. 55 fem 2 0. 75 0. 85 0. 72 0. 75 0. 65 0. 7 n Weights are parameterized as function of the energy: 4
Longitudinal Layer calibration n Linearity within 2 -3% at high energies and degrades up to 10% at low energies n Resolution: – Sampling term does not change significantly compared to cell E/V – The constant term is reduced Big impact at high energies 5
Longitudinal Layer calibration and Num. Inversion n Linearity within 1 -3% n Resolution: – Slightly improvement at low energies 6
Adding Energy constraint Belen Salvachua and Esteban Fullana High Energy Physics Division Argonne National Laboratory
Outline n The motivation: – H 1 -style calibration has a bias at low energies n The idea/solution: – Add an energy constraint to the minimization of the resolution – Calculate new weights with this method: • Cell energy density dependency like H 1 -style – But we have tried with a simpler E/V dependency • Longitudinal shower development like Layer calibration – Longitudinal energy fraction 8
Mathematical bias at low energies n n Known mathematical bias due to minimization function NIM A 345: 449, 452, 1994 Cell E/V calibration, no JES applied Full jet pseudo-rapidity range Linearity for E > 200 Gev within 2% Apparent non-linearity at E < 200 Ge. V 200 Ge. V H 1 coarse layer segmentation | | ≤ 4. 4 9
Hidden Bias in a Common Calorimeter Calibration Scheme Nucl. Instrum. Meth. A 345: 449, 452, 1994 n When using a 2 of the form: n A bias on the calibrated energy appears because NO constraint on energy n Mathematical bias is more important at low energies | | < 0. 7 n The correction is analytically known: Preliminary 10
Correction of the mathematical bias on the minimization Physically more appropriated n Possible solutions: – Evaluate possibility of including jet energy constraint in minimization function: Benefit: correction contained inside H 1 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 11
Solution n Introduce energy constraint to avoid the mathematical bias using Lagrange multiplier method: n The question now is: – Which parameterization of the Ecalibrated should we use? 12
Comparing improvement at low energies n Clear improvement of the mathematical bias after calibration with energy constrain Traditionally H 1 -style uses a polynomial of 3 rd and 4 th degree on Ln(e/v) New Calibration: pol 4 Ln(e/v) 200 Ge. V H 1 coarse layer segmentation | | ≤ 4. 4 13
Comparing improvement at low energies n Clear improvement of the mathematical bias after calibration with energy constrain 1 term on Ln. E/V 1 term EM/Ejet New Calibration: Lineal Ln(e/v) EM fraction 200 Ge. V H 1 coarse layer segmentation | | ≤ 4. 4 14
H 1 coarse granularity calibration n Traditional H 1 -style needs more statistics to converge using Minuit n H 1 -style results done with 2 Mevt (100 times more statistics done current analysis) 15
E/V dependency n Cell energy density has shown good performance on jet calibration n We try a polynomial of order 4 th dependency on Ln(e/v): Traditionally H 1 -style uses a polynomial of 3 rd and 4 th degree on Ln(e/v) 16
Longitudinal showering No Pre. B Pre. E n Longitudinal energy distribution has also shown good performance on jet calibration n We add a linear term proportional to the fraction of energy in the EM calorimeters: 1 term on Ln. E/V 1 term EM/Ejet 17
Resolution summary table Cone 7 Tower. Jets a b c Standard H 1 0. 49 0. 028 5. 76 Lineal in Ln(E/V) 0. 52 0. 024 5. 15 Pol 4 in Ln(E/V) 0. 48 0. 025 4. 90 Lineal in Ln(E/V) and fem 0. 60 0. 021 4. 26 18
Conclusions n Adding constraint in energy solves bias at low energies n Simple linear dependency on ln(e/v) and on the EM fraction of energy: – Similar resolution than H 1 -style – Better linearity than H 1 -style before the JES n Other combinations can be easily including like: – Merging layers – Adding extra terms n TO DO: – Re-run calibration on Anti-Kt – Use more statistics (20 kevts now) – Test calibration in other MC physics 19
Cell E/V calibration: Coarse vs Fine granularity Belen Salvachua High Energy Physics Division Argonne National Laboratory
Cell energy density calibration: H 1 style n Basis: – Electro-magnetic showers are more dense, energy concentrated in smaller region – Hadronic showers are broader, energy is spread in a larger volume n Mechanism: – Apply a different weight depending on the energy density of the cell H 1 weights INDEPENDENT of jet , E Integrate over all , E Not use jets with: 1. 3 > | | > 1. 5 3. 0 > | | > 3. 5 ETEM < 5 Ge. V ETNTJ < 20 Ge. V | | > 4. 4 DEPENDENT on detector Technology/composition Subdetector and layer segmentation 21
H 1 style calibration Cells classified according to: Cell energy density Layer/detector segmentation E/V space segmented in up to 16 bins 1. Coarse layer granularity 2. Fine layer granularity n H 1 coarse and fine layer granularity contain additional correction for: – Gap correction – Scintillator correction – Cryostat correction: energy estimated as 22
Scheme of ATLAS calorimeters n Shapes and ratios are approximate Tile. Bar Tile. Ext EMB Pre. Sampler. B EME HEC FCAL Pre. Sampler. E 23
H 1 coarse layer granularity Layers can be segmented in up to 16 bins of cell energy density n Shapes and ratios are approximate Tile. Bar EMB 2 + EMB 3 < 0. 8 Tile. Ext EMB 2 + EMB 3 0. 8 EMB 1 Pre. Sampler. E Pre. Sampler. B EME 2 + EME 3 <2. 5 EME 2 + EME 3 >2. 5 HEC < 2. 5 HEC 2. 5 FCAL 1 FCAL 2 + FCAL 3 EME 1 24
H 1 fine layer granularity Layers can be segmented in up to 16 bins of cell energy density n Shapes and ratios are approximate Tile. Bar 2 Tile. Ext 2 Tile. Bar 1 Tile. Ext 1 Tile. Bar 0 Tile. Ext 0 EMB 1 Pre. Sampler. E Pre. Sampler. B EMB 3 <2. 5 EMB 3 0. 8 EMB 2 <2. 5 EMB 2 2. 5 EMB 3 < 0. 8 EMB 2 < 0. 8 HEC 0 + HEC 1 <2. 5 HEC 0+ HEC 1 2. 5 HEC 2 + HEC 3 <2. 5 HEC 2+ HEC 3 2. 5 FCAL 1 FCAL 2 FCAL + FCAL 3 EME 1 25
Linearity and Resolution using H 1 coarse layer granularity n Full jet pseudo-rapidity range n Looks like non-linearity at E < 200 Ge. V – Bias on the minimization (FERMILAB-Pub-93/394) – Corrected after jet energy scale | | ≤ 4. 4 200 Ge. V 26
Linearity and Resolution using H 1 fine layer granularity n Full jet pseudo-rapidity range n Looks like non-linearity at E < 200 Ge. V – Bias on the minimization (FERMILAB-Pub-93/394) – Corrected after jet energy scale | | ≤ 4. 4 200 Ge. V 27
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