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
Outline Introduction Validation Summary
1 IntroductionAim of projectScatteringScattering in Geant4
2 ValidationSingle scattering of high energy muonsScattering of high energy hadronsScattering of high energy muons
3 SummaryConclusionBack-up
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 2 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 3 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 4 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 5 / 29
Outline Introduction Validation Summary
Scattering in Geant4
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)
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 6 / 29
Outline Introduction Validation Summary
Scattering in Geant4
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 7 / 29
Outline Introduction Validation Summary
Definitions
• Scattering angle, θ, anglebetween incident andscattered momentumdirection
• θz is projection of θ on z-axis
Figure: MSC geometry to definescattering angles
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 8 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 9 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 10 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
(mrad)zθ2 3 4 5 6 7 8 9 10
(%
)zθ
prob
abili
ty p
lane
sca
tterin
g an
gle
>
-110
1
10
210
zθComparison of GEANT4 and data
GEANT4 - SS
Data
Figure: Probability of muon scattering > θplane - SS at 5 GeV/c
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 11 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
(mrad)zθ2 3 4 5 6 7 8 9 10
(Dat
a -
GE
AN
T4)
/Dat
a (%
)
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0
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zθComparison of GEANT4 and data
Figure: Comparison Geant4 with data - SS at 5 GeV/c
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 12 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
• 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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 13 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
(mrad)zθ2 3 4 5 6 7 8 9 10
(%
)zθ
prob
abili
ty p
lane
sca
tterin
g an
gle
>
-110
1
10
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zθComparison of GEANT4 and data
GEANT4 - SS
Data
Figure: Probability of muon scattering > θplane for data above 2 mrad -SS at 5 GeV/c
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 14 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
(mrad)zθ2 3 4 5 6 7 8 9 10
(Dat
a -
GE
AN
T4)
/Dat
a (%
)
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-20
0
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zθComparison of GEANT4 and data
Figure: Comparison Geant4 using data above 2 mrad - SS at 5 GeV/c
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 15 / 29
Outline Introduction Validation Summary
Single scattering of high energy muons
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 16 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 17 / 29
Outline Introduction Validation Summary
Scattering of high energy hadrons
(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
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
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
400
500
600
700
800
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 18 / 29
Outline Introduction Validation Summary
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
T4/
Mol
iere
- 1
) %
-25
-20
-15
-10
-5
0
5
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: Pb & 175 GeVeθComparison of GEANT4 and data
ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScat
+π -π +K-K p p
(e) MC over “bare“ Moliere theory - 175 GeV/c in Pb
(GE
AN
T4/
Mol
iere
-1)
%
-25
-20
-15
-10
-5
0
5
10
15
20
25
: Sn & 70 GeVeθComparison of GEANT4 and data
ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScat
+π -π +K-K p p
(f) MC over “bare“ Moliere theory - 70 GeV/c in Sn
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 19 / 29
Outline Introduction Validation Summary
Scattering of high energy hadrons
(GE
AN
T4/
Dat
a -
1) %
-25
-20
-15
-10
-5
0
5
10
15
20
25
: Pb & 175 GeVeθComparison of GEANT4 and data
ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScat
+π -π +K-K p p
Figure: Comparison of MC and Data - 175 GeV/c in Pb
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 20 / 29
Outline Introduction Validation Summary
Scattering of high energy hadrons
(GE
AN
T4/
Dat
a -
1) %
-25
-20
-15
-10
-5
0
5
10
15
20
25
: Sn & 70 GeVeθComparison of GEANT4 and data
ModelsUrbanMsc90WVI+SSUrbanMsc93SingleScat
+π -π +K-K p p
Figure: Comparison of MC and Data - 70 GeV/c in Sn
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 21 / 29
Outline Introduction Validation Summary
Scattering of high energy hadrons
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 22 / 29
Outline Introduction Validation Summary
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 23 / 29
Outline Introduction Validation Summary
Scattering of high energy muons
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
0
1000
2000
3000
4000
5000
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 24 / 29
Outline Introduction Validation Summary
Scattering of high energy muons
Figure: Probability of scattering θe for 7.3 GeV/c muonsValidation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 25 / 29
Outline Introduction Validation Summary
Scattering of high energy muons
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
Outline Introduction Validation Summary
Scattering of high energy muons
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
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 27 / 29
Outline Introduction Validation Summary
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 (?)
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 28 / 29
Outline Introduction Validation Summary
Back-up
Emulsion test for MSC models
(mrad)zθ2 3 4 5 6 7 8 9 10
(%
)zθ
prob
abili
ty p
lane
sca
tterin
g an
gle
>
-110
1
10
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zθComparison of GEANT4 and data
GEANT4 - SS
Data
(a) Probability - UrbanMSC
(mrad)zθ2 3 4 5 6 7 8 9 10
(Dat
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AN
T4)
/Dat
a (%
)
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zθComparison of GEANT4 and data
(b) Comparison - UrbanMSC
(mrad)zθ2 3 4 5 6 7 8 9 10
(%
)zθ
prob
abili
ty p
lane
sca
tterin
g an
gle
>
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1
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zθComparison of GEANT4 and data
GEANT4 - SS
Data
(c) Probabilty - WVI+SS
(mrad)zθ2 3 4 5 6 7 8 9 10
(Dat
a -
GE
AN
T4)
/Dat
a (%
)
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zθComparison of GEANT4 and data
(d) Comparison - WVI+SS
Validation of scattering models in Geant4 - CERN Summer student project Ørjan Dale 29 / 29