validation of scattering models in geant4 - cern summer student

Outline Introduction Validation Summary

Validation of scattering models in Geant4 -CERN Summer student project

Ørjan Dale

Supervisor: Vladimir IvantchenkoUniversity of Bergen & CERN PH-SFT

04.10.2010

Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 1 / 29


1 IntroductionAim of projectScatteringScattering in Geant4

2 ValidationSingle scattering of high energy muonsScattering of high energy hadronsScattering of high energy muons

3 SummaryConclusionBack-up



Aim of project

Aim of project

• Validation of Geant4 simulation of scattering of high energy muonsand hadrons through thin targets

• Compare different Geant4 models of scattering with published data

• Find potential differences between the accuracies of the models indifferent energy and angular regions

• Implement results as test in Geant4 testing suite



Scattering

Why look at scattering?

• Geant4 used as main simulation engine for applications rangingfrom HEP to medicine

• Limits spatial resolution of detectors

• Limits response and resolution of EM calorimeters



Scattering

Multiple scattering (MSC)

• Deflection of charged particle traversing matter due to manysmall-angle Coulomb scatters from nuclei

• For hadronic projectiles the strong interaction also contributes

• Scattering distribution at small angles is described by Moliere theory

• Gaussian distribution for small deflection angles plus non-gaussiantail due to inelastic Rutherford scattering

• To account for tail Moliere theory must be modified to includecenter of mass corrections and form factors of nuclei



Scattering in Geant4


• Two categories of scattering simulations:• Single - Computes each scattering seperately ⇒ Accurate but slow

• Multiple - Effective scattering angle after given step ⇒ Less accurate but faster

• Geant4 MSC models does not use Moliere theory, but morecomplete Lewis theory

• Moliere theory only valid for small scattering angles (⇒ small stepsimposed in simulations)

• Lewis theory is valid for all angles (perturbative expansion)




Scattering models in Geant4

• emstandard opt0 - UrbanMsc90• Default MSC model for muons and hadrons

• Based on Lewis theory (first two terms of Lewis expansion and parameterised tail)

• emstandard msc93 - UrbanMsc93• Modified version of UrbanMsc90

• Default MSC model for electrons and positrons

• standardSS - Single Scattering• Coulomb scattering - Precise but slow

• Based on Wentzel scattering function

• emstandard opt2 - WVI+SS• New approach - combines single and multiple scattering models

• Uses multiple scattering for small angles and Coulomb scattering for larger



Definitions

• Scattering angle, θ, anglebetween incident andscattered momentumdirection

• θz is projection of θ on z-axis

Figure: MSC geometry to definescattering angles



Single scattering of high energy muons

High energy muons - emulsion

• Data taken from: Single scattering of 5 GeV/c muons on nuclearemulsion, P.J. McNulty et al.

• Nuclear emulsion - stack of photographic plates recording particletrack scanned with microscope

• Single plane scattering angles larger than 1.4 mrad recorded

• However, not 100% measurement efficiency below 2 mrad




Simulation

• Step at each coulomb interaction and record scattering angle foreach scattering

• Only single scattering model included in test

• Could approximate scattering angle for effective MSC models bystepping on geometric boundary of very thin target (see back upslides)

• Probabilities are found relative to total number of scatterings above1.4 mrad




(mrad)zθ2 3 4 5 6 7 8 9 10

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zθComparison of GEANT4 and data

GEANT4 - SS

Data

Figure: Probability of muon scattering > θplane - SS at 5 GeV/c




(mrad)zθ2 3 4 5 6 7 8 9 10

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Figure: Comparison Geant4 with data - SS at 5 GeV/c




• SS appears to underestimate single scattering angles larger than 1.4mrad

• However, measurement efficiency below 2 mrad is not 100%.Observe also that the deviation between simulation and data isroughly constant above this angle

⇒ Use only the measurements above 2 mrad to avoid systematicdeviation due to normalization to potential wrong value of totalnumber of observed events




(mrad)zθ2 3 4 5 6 7 8 9 10

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GEANT4 - SS

Data

Figure: Probability of muon scattering > θplane for data above 2 mrad -SS at 5 GeV/c




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Figure: Comparison Geant4 using data above 2 mrad - SS at 5 GeV/c




Results

• Omitting the two first measured points, a good agreement isobserved for angles up to 7 mrad

• Above 7 mrad statistics are limited, but a clear underestimation bythe SS model is observed

• Should note that we corrected for an deficiency in the listing of theresults in the original paper



Scattering of high energy hadrons

High energy hadrons

• Data taken from: Measurement of multiple scattering at 50 to 200GeV/c,G. Shen et al.

• Hadron projectiles through various targets (∼ 0.1 r.l.)

• Found θe - angle at which distributions fall by 1/e

• Moliere theory well approximated by the three paramater functionfor angles up to 2θe :

dσ

dΩ= exp[A− (1 + C )( θ2

θe 2 ) + C ( θ4

θe 4 )] (1)

• Make a fit to 1 with C fixed at predicted value to determine θe




(mrad)zθ0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Nu

mb

er o

f ev

ents

0

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hh2Entries 100000

Mean 0.03041

RMS 0.02784

/ ndf 2χ 387.1 / 70

p0 0.0± 12.2

p1 0.00006± 0.02742

(a) Fit to (1) for 175 GeV/c K+ inPb - emstandard opt0

(mrad)zθ0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

0

100

200

300

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hh2Entries 99996

Mean 0.08934

RMS 0.05494

/ ndf 2χ 282.7 / 177

p0 0.01± 9.84

p1 0.0003± 0.0908

(b) Fit for 70 GeV/c K+ in Sn -WVI+SS



Scattering of high energy hadrons (

mra

d)eθ

0

0.01

0.02

0.03

0.04

0.05

: Pb & 175 GeVeθComparison of GEANT4 and data

+π -π +K-K p p

ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScatData

(c) Data and MC - 175 GeV/c in Pb

(m

rad)

eθ

0.07

0.08

0.09

0.1

0.11

0.12

: Sn & 70 GeVeθComparison of GEANT4 and data

+π -π +K-K p p

ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScatData

(d) Data and MC - 70 GeV/c in Sn

(GE

AN

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Mol

iere

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ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScat

+π -π +K-K p p

(e) MC over “bare“ Moliere theory - 175 GeV/c in Pb

(GE

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iere

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%

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+π -π +K-K p p

(f) MC over “bare“ Moliere theory - 70 GeV/c in Sn




(GE

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+π -π +K-K p p

Figure: Comparison of MC and Data - 175 GeV/c in Pb




(GE

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+π -π +K-K p p

Figure: Comparison of MC and Data - 70 GeV/c in Sn




Results

• WVI+SS are within 3-5% while the other theories are within 6-8%of ”bare” Moliere theory

• WVI+SS seems to give systematically larger θe than the othermodels

• The two UrbanMSC models yield similar results - UrbanMSC90yields slightly higher θe

• Generally smaller difference between the different models at highprojectile momentum

• The χ2/ndof for the fits of the different models are ranging from1.2 - 1.7 for 70 GeV/c Sn, to 3-5 for 175 GeV/c Pb

• Similar results are obtained for Al, Be, C, Cu and Sn targets at 50,70, 125, 175 and 200 GeV/c



Scattering of high energy muons

High energy muons

• Data taken from: Multiple coulomb scattering of 7.3 and 11.7GeV/c muons on a Cu target, S.A. Akimenko et al.

• Background dominated by

• Error of track reconstruction for primary muons• Scattering of primary muons in scintillation counter

⇒ Smear final scattering angle with gaussian distributiondetermined from background




bEntries 22

Mean -0.5264

RMS 1.014

/ ndf 2χ 4 / 1

Prob 0.0455

Constant 71.5± 6514

Mean 0.00775± -0.01115

Sigma 0.0067± 0.8615

(mrad)planeθ-20 -15 -10 -5 0 5 10 15

Num

ber

of e

vent

s

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bEntries 22

Mean -0.5264

RMS 1.014

/ ndf 2χ 4 / 1

Prob 0.0455

Constant 71.5± 6514

Mean 0.00775± -0.01115

Sigma 0.0067± 0.8615

background

Figure: Gaussian fit to background




Figure: Probability of scattering θe for 7.3 GeV/c muonsValidation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 25 / 29



Figure: Comparison of Data and Geant4 for 7.3 GeV/c muonsValidation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 26 / 29



Results

• Small deviations in modeling of the central part of the distributionfor the different models.

• WVI+SS and SS gives the closest agreement with the tail of thedata

• The two Urban models yields quite similar results. Deviations attails might be due to modeling of form factors of nuclei in themodels

• There is an asymmetry in the data which is not properly accountedfor by smearing

• Modeling of the background is harder at 11.7 GeV/c, which leads tolarger deviations between data and simulations

• However, the different models still show the same characteristics for11.7 GeV/c as for 7.3 GeV/c



Conclusion

Conclusion

• For all models there is good agreement with data at small angles,but deviations are observed at larger angles

• WVI+SS and SS give the best agreement with data for the tail forHE muons

• SS underestimates large angle scatterings of HE muons in emulsion,but otherwise good agreement

• WVI+SS systematically higher than other models for HE hadrons

• No major differences between UrbanMsc90 & UrbanMsc93 observed

• Would expect closer agreement between SS and data comparedwith MSC models for HE hadron projectiles (?)



Back-up

Emulsion test for MSC models

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GEANT4 - SS

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(a) Probability - UrbanMSC

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(b) Comparison - UrbanMSC

(mrad)zθ2 3 4 5 6 7 8 9 10

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GEANT4 - SS

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(c) Probabilty - WVI+SS

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(d) Comparison - WVI+SS


validation of scattering models in geant4 - cern summer student

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