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### Longitudinal Layer Calibration

### Adding Energy constraint

### Cell E/V calibration: Coarse vs Fine granularity

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 methodLongitudinal 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

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

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

ConclusionsBelen 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

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