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Longitudinal Layer Calibration. Belen Salvachua High Energy Physics Division Argonne 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.

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longitudinal layer calibration

Longitudinal Layer Calibration

Belen Salvachua

High Energy Physics DivisionArgonne National Laboratory

longitudinal layer method

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 method1
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
longitudinal layer method2
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 calibration1
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
Longitudinal Layer calibration and Num. Inversion
  • Linearity within 1-3%
  • Resolution:
    • Slightly improvement at low energies
adding energy constraint

Adding Energy constraint

Belen Salvachua and Esteban Fullana

High Energy Physics DivisionArgonne National Laboratory

outline
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
mathematical bias at low energies

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
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
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
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
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 energies1
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
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
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
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

conclusions
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

Cell E/V calibration: Coarse vs Fine granularity

Belen Salvachua

High Energy Physics DivisionArgonne National Laboratory

cell energy density calibration h1 style
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
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
Scheme of ATLAS calorimeters
  • Shapes and ratios are approximate

TileBar

TileExt

EMB

EME

HEC

PreSamplerB

FCAL

PreSamplerE

h1 coarse layer granularity
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
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
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
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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