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General Information

The NuBeam Physics list is a part of the recent initiative within Geant4 collaboration that aims to identify beneficial combinations
of Geant4 hadronic models in a form of a physics list for the needs of simulation of the Neutrino Beamlines.
The concept of a physics list arises from the fact that Geant4 can not offer a single algorithm for modeling hadronic interactions that
would cover the entire energy domain from zero to the TeV scale, for all known processes and particles.
Instead, models are valid only over finite energy ranges, and there maybe competing models in the same range or one model maybe working
better than the other for a specific group of particles, while its competitor may be better for other species. For this reason models
have to be combined to cover the large energy range; every two adjacent models may have an overlap in their validity range.
Additional information on Physics Lists can be found here:

Motivation

The motivation behind the NuBeam Physics List is to improve modeling of hadron production, in particular for the projectiles and the materials
that are typically used to compose the primary target in a Neutrino Beamline, including Fermilab NuMI beamline.

The neutrino flux is primarily determined by the production and subsequent decays of pions.
The pions are mainly coming from the 1st interaction of the primary proton beam with the primary target.
However, many secondary particles re-interact the target, which in turn also produce pions and significantly affect the flux.

Currently, the study focuses on modeling 2 aspects of hadron productions
  • production of pions by a high energy (>100GeV) proton beam on a Carbon target
  • possible re-interaction of secondary pions in the Carbon, assuming that their energy may range from several GeV to several tens of GeV

To make the case more general, this study also includes benchmarking Geant4 simulation of hadron production by a proton or a pion incident
on a Beryllium target; the beam momentum in this case ranges from 3GeV/c to 12GeV/c (we also call such energy range as intermediate energy).

Both Carbon and Beryllium are light nuclei of interest to the Fermilab Neutrino Beamline instrumentation.

Obviously, accurate modeling of production and re-interaction of other types of secondary is also an important aspect. This will be addressed
in the future rounds of the study.

It also needs to be pointed out that this study currently focuses on the light target nuclei, and any observations presented here apply only
to the group of targets in question.
Additional study would be necessary to address modeling of hadron production on heavier targets; observations and conclusions may or may not
be different in that case.

Simulation and Comparison vs Experimental Data

The study currently involves the following Geant4 hadronic models:
  • FTF and QGS, including variants, on the high energy end
  • Bertini Cascade, Liege Intranuclear Cascade (INCL++), and FTF in the intermediate energy range (since FTF validity extends as low as 3GeV).

One needs to remember that the high energy string models FTF and QGS are not “monolithic” but instead are made of several software sub-modules.
One such component that is mandatory for each string model is a String Fragmentation. In Geant4 there are two variants of String Fragmentation
code – an older G4QGSMFragmentation and a recent G4LundStringFragmentation that is being actively developed; in terms of software infrastructure
these two components are interchangeable.
We have included in the study two variants of QGSP, one with the traditional G4QGSMFragmentation (as it is typically used in all standard Geant4
physics lists) and a custom combination of QGSP with G4LundStringFragmentation.

Alternatives to Bertini Cascade in the intermediate energy range do exist as well, such as Binary Cascade or INCL++, but have their own limitations.
However, both models maybe of interest for further studies. This is especially true for the INCL++ model that is being actively developed and
is showing promising results in certain areas.

Experimental datasets used in this study are the following:
– M.G.Catanesi et al., Phys.Rev.C77:055207, 2008
– M. Apollonio et al., Phys.Rev.C80:035208, 2009
– M. Apollonio et al., Phys.Rev.C80:065207, 2009
– M. Apollonio et al., Nucl. Phys. A821: 118-192, 2009
– N.Abgrall et al., Phys.Rev. C84:034604, 2011
http://spshadrons.web.cern.ch/spshadrons
In the near future we also plan to add the following data:
– D.S. Barton et al., Phys. Rev. D27, 2580 (1983)

As a measure of agreement between the experimental data and the simulation we are using the chi2 divided by the number of degrees of freedom.
The chi2 is calculated as a sum Σ((Xi-Yi)/(σxi+σyi))**2 where X=sim., Y=exp.data; i=1,N, N=number of exp.data points.

Results of Statistical Testing of Geant4 Hadronic Models vs Experimental Data

The most recent results included in this document have been obtained with Geant4.10.1.p01.

Statistics is 1,000,000 events per sample.

Simulation assumes 0% systematics.

Results of statistical comparison of the Geant4 hadronic models vs experimental data are presented in a form of tables, showing chi2/NDF vs
beam momentum, for 3 types of projectile, proton, pi+ or pi-, and outgoing secondary pi+ or pi-.
This presents a comprehensive view across a wide range of energies (momenta).
Tables can be found in the Appendix 1, at the end of this document, for both Carbon and Beryllium targets.

For completeness, original results from Geant4.9.6.p03 are also preserved (except for INCL++ which was not included in that round of tests); please see Appendix 2
It should be pointed out that throughout the 4.10 development cycle a number of changes have been made to key Geant4 hadronic models, such as FTF and Bertini. For this reason specific results may somewhat vary between the two releases in question.

Traditional plots that overlay simulation and the data are also available via Geant4 Validation Repository, at the following URL: http://g4devel.fnal.gov:8080/G4WebAppNG/
Regression testing results are also available via Geant4 Validation Repository, to illustrate the evolution of Geant4 Hadronic models.

It is obvious from this study that, for a proton projectile, FTF produces results that, in the range 3-31GeV, are statistically much closer to the data
than other models in question.
However, at higher energy (e.g. beam momentum of 158GeV/c) QGSP+G4LundStringFragmentation produce more promising results.

Here it should be noted that for a proton projectile incident on a light nucleus INCL++ also produces reasonable results in the range 3-12GeV. Although at present it is difficult to claim these results to be clearly superior to those of FTF. At the same time INCL++ is substantially more expensive in term of CPU that FTF. For these reasons FTF remains the preferred choice for modeling interactions of a proton projectile of an intermediate energy/momenta with light targets such as Carbon or Beryllium. However, INCL++ is one of the modern developments in Geant4, and its progress will be closely monitored in the future study.

Similar trend is observed when modeling pion interaction with light nuclei, as results from FTF are statistically closer to the experimental data than those of Bertini or INCL++, in the entire range of their overlap in validity, i.e. from 3GeV and up.
The effect is somewhat more visible in the results from Geant4.10.1.p01 where several improvements have been made to FTF.

Composition of the NuBeam Physics List

Based on the study presented in this document it has been proposed to compose a new physics list NuBeam.

NuBeam is organized as a G4ModularPhysicsList, and uses a number of pre-fabricated components, as do other popular physics lists, such as
FTFP_BERT or QGSP_BERT.

In fact, NuBeam is largely similar to FTFP_BERT, with the exception of the following differences:
– It shifts the overlap Bertini/FTFP down to 3-3.5GeV for p,pi,K (as opposed to FTFP_BERT that sets the overlap at 4-5GeV)
– FTFP from 3GeV and up for pi, K,
– FTFP only at 3-101GeV for p
– QGSP+G4LundStringFragmentation from 100GeV and up for p

Please bear in mind that the 100-101GeV overlap region between FTFP and QGSP+G4LundStringFragmentation is an “educated guess”. This is subject
for future study and validation with the use of data from D.S. Barton et al., Phys. Rev. D27, 2580 (1983).

Starting Geant4.10.1, this physics list is available as part of standard distribution.

Appendix 1

Results included here have been obtained with Geant4.10.1.p01.

Tables 1-6 show results obtained at the process-level (single model).

Results obtained with realistic physics lists (combinations of models) are not currently included because earlier tests have demonstrated that they are very similar to those at the process-level.

Table 1. Chi2/NDF vs. beam momentum, as calculated for experimental vs. simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Carbon interactions for several Geant4 hadronic models at a given beam momentum.
pi+ production in proton on C interactions pi- production in proton on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c
Bertini 10.20 27.40 20.88 22.71 3.26 11.95 27.56 26.45
FTF 2.26 9.39 11.60 14.75 5.08 21.89 3.54 15.17 27.63 31.87 2.57 16.55
INCL++ 5.43 13.42 14.23 20.98 2.32 4.79 8.20 13.84
QGSP 35.17 58.83 44.36 54.12
QGSP+G4Lund 19.03 15.00 31.23 9.85

Table 2. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Carbon interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 29.18 39.27 45.84 13.82 20.40 37.81 20.85 7.48
FTF 9.22 7.29 8.44 4.10 9.51 12.62 9.11 2.82
INCL++ 29.29 40.12 46.17 12.29 23.82 37.50 25.17 6.40

Table 3. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Carbon interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 34.28 31.08 23.32 23.45 30.69 30.30 33.72 34.67
FTF 18.31 16.14 14.39 15.62 18.00 15.13 24.62 20.73
INCL++ 40.14 35.43 48.51 44.75 42.71 44.02 52.43 50.62

Table 4. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in proton on Be interactions pi- production in proton on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 8.9 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 8.9 GeV/c 12 GeV/c
Bertini 13.87 19.21 22.47 28.42 21.19 3.57 15.82 29.69 42.66 26.96
FTF 2.90 9.31 17.19 26.80 22.67 6.69 24.52 46.97 74.04 60.38
INCL++ 5.08 10.91 18.55 25.08 27.02 2.79 6.31 11.50 19.16 19.15

Table 5. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on Be interactions pi- production in pi+ on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 28.02 33.41 25.98 15.63 30.46 33.32 16.84 6.98
FTF 14.20 8.47 10.74 6.79 9.97 11.15 7.52 3.122
INCL++ 30.88 35.12 31.71 17.46 18.81 33.89 23.36 11.11

Table 6. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi- on Be interactions pi- production in pi- on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 32.64 29.18 26.09 24.48 33.31 37.42 39.21 43.85
FTF 15.76 12.06 13.91 9.06 26.56 16.45 31.17 25.04
INCL++ 45.33 35.65 56.46 74.10 47.05 47.14 50.06 108.83

Appendix 2

Results presented in this section have been obtained with Geant4.9.6.p03. They are preserved for completeness.

Tables 7-12 show results obtained at the process-level (single model).

Tables 13-18 show results obtained with realistic physics lists (combination of models) and a realistic target geometry, for the 1st beam-target
hadronic-inelastic interaction.
Results from NuBeam physics list are compared with predictions from popular standard physics lists FTFP_BERT and QGSP_BERT (where applicable).
Please note that results are also presented from several variants of NuBeam physics list, for different Bertini/FTF overlap region in the intermediate
energy range.

Table 7. Chi2/NDF vs. beam momentum, as calculated for experimental vs. simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Carbon interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in proton on C interactions pi- production in proton on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c
Bertini 10.44 22.16 10.84 19.05 2.36 9.62 23.64 32.43
FTF 4.27 6.82 7.97 9.71 18.06 43.33 3.36 4.20 5.42 5.44 12.83 40.23
QGSP 33.85 26.99 80.41 47.94
QGSP+G4Lund 21.24 15.39 49.51 10.66

Table 8. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Carbon interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 31.16 44.57 53.84 22.59 24.49 43.90 31.94 14.04
FTF 17.28 15.53 18.09 3.71 11.62 15.81 9.91 2.66

Table 9. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Carbon interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 33.67 22.86 26.79 38.50 35.87 34.59 55.37 66.42
FTF 28.57 14.87 16.28 18.70 25.11 22.1 22.53 15.45

Table 10. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in proton on Be interactions pi- production in proton on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 8.9 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 8.9 GeV/c 12 GeV/c
Bertini 14.10 17.97 20.38 25.06 20.57 4.31 16.41 29.07 41.92 27.59
FTF 3.80 5.93 8.76 13.09 9.93 5.07 7.82 10.19 17.08 13.74

Table 11. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi+ on Be interactions pi- production in pi+ on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 29.37 37.28 33.05 25.04 37.81 35.6 25.31 13.40
FTF 18.42 12.10 8.55 3.68 11.79 13.15 10.74 3.16

Table 12. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Beryllium interactions for several Geant4 hadronic models at a given beam momentum.

pi+ production in pi- on Be interactions pi- production in pi- on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c
Bertini 30.19 27.07 31.46 40.39 37.99 40.46 60.45 75.38
FTF 25.74 14.06 14.55 10.68 31.27 24.19 23.14 19.90

Table 13. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Carbon interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in proton on C interactions pi- production in proton on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 12 GeV/c 31 GeV/c 158 GeV/c
FTFP_BERT 12.19 6.36 7.56 8.66 4.9 37.18 4.91 5.91 5.79 6.01 8.48 34.03
NuBeam - FTF/BERT:7-10GeV 12.08 19.68 10.47 8.66 4.9 13.94 4.95 15.09 11.26 6.01 8.48 9.25
NuBeam - FTF/BERT:3-3.5GeV 7.84 6.44 7.66 8.66 4.9 13.94 4.00 5.11 5.98 6.01 8.48 9.25
QGSP_BERT 37.8 24.25 78.33 38.83

Table 14. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Carbon interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c
FTFP_BERT 30.20 16.06 18.33 22.60 13.28 8.75
NuBeam - FTF/BERT:7-10GeV 30.15 33.81 30.76 22.60 34.17 15.20
NuBeam - FTF/BERT:3-3.5GeV 30.18 16.97 18.44 22.09 13.90 8.96
NuBeam - FTF/BERT:3-6GeV 30.14 15.31 18.52 22.23 12.96 9.12

Table 15. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Carbon interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in pi+ on C interactions pi- production in pi+ on C interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c
FTFP_BERT 28.38 14.13 14.51 37.63 18.95 21.99
NuBeam - FTF/BERT:7-10GeV 28.48 25.33 14.60 37.98 30.33 27.37
NuBeam - FTF/BERT:3-3.5GeV 27.81 14.28 14.60 38.45 20.26 21.82
NuBeam - FTF/BERT:3-6GeV 28.34 13.62 14.61 37.77 12.40 21.93

Table 16. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from proton on Beryllium interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in proton on Be interactions pi- production in proton on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 8.9GeV/c 3 GeV/c 5 GeV/c 8 GeV/c 8.9GeV/c
FTFP_BERT 18.88 5.91 9.82 12.13 19.94 9.00 9.29 14.86
NuBeam - FTF/BERT:7-10GeV 18.79 17.32 12.03 12.14 19.73 20.41 13.37 11.43
NuBeam - FTF/BERT:3-3.5GeV 12.98 6.05 9.21 11.90 15.08 8.73 9.64 14.44
NuBeam - FTF/BERT:3-6GeV 12.98 5.98 9.31 12.37 15.08 8.57 8.76 14.68

Table 17. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi+ on Beryllium interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in pi+ on Be interactions pi- production in pi+ on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c
FTFP_BERT 29.28 13.88 9.09 33.51 10.75 2.71
NuBeam - FTF/BERT:7-10GeV 29.46 32.29 15.59 32.90 28.67 2.68
NuBeam - FTF/BERT:3-3.5GeV 29.08 14.23 9.22 32.35 10.95 2.74
NuBeam - FTF/BERT:3-6GeV 29.17 13.40 9.31 32.35 11.15 2.72

Table 18. Chi2/NDF vs beam momentum, as calculated for experimental vs simulated spectra of pi+ (left) and pi- (right)
resulting from pi- on Beryllium interactions for several Geant4 physics lists at a given beam momentum; several variants
of NuBeam physics lists are included.

pi+ production in pi+ on Be interactions pi- production in pi+ on Be interactions
Beam Momentum
3 GeV/c 5 GeV/c 8 GeV/c 3 GeV/c 5 GeV/c 8 GeV/c
FTFP_BERT 28.18 14.52 14.63 40.06 21.19 20.42
NuBeam - FTF/BERT:7-10GeV 28.04 25.63 17.84 40.23 34.99 28.33
NuBeam - FTF/BERT:3-3.5GeV 27.93 11.72 14.79 40.49 22.70 19.81
NuBeam - FTF/BERT:3-6GeV 27.87 14.94 14.71 40.75 15.54 20.18