**Table of contents**- General Information
- At-rest processes (capture and annihilation)
- Gamma-nuclear interactions
- Hadronic interactions in the intermediate energy range (1.4GeV/c to 12GeV/c)
- Hadronic interactions at high energies

# General Information¶

This writeup contains short description of datasets used to benchmark and validate various aspects of Geant4 modeling of hadronic processes (models),

as in the responsibility of the FNAL-Geant4 group.

The dataset includes errors and uncertainties, as published.

If both statistical and systematic uncertainties are know, in our benchmarking and analysis we use, by default, the total errors that are calculated

as a quadratic sum of the statistical and systematic errors.

**At-rest processes (capture and annihilation)**¶

### pi- capture at rest on various nuclear targets (C, N, O, Al, Cu, Ta, Pb)¶

Kinetic energy spectra of secondary neutrons have been extracted from the table published in this paper:- R.Madey et al., Phys.Rev.C25, 3050 (1982)

NOTE: the numbers in the table are per 100 pions stopped in the target (the numbers are properly scaled in the analysis application).

Errors are statistical.

Overall systematic uncertainty is 6.3%.

No other datasets that can be directly used in validation have been found so far.

### **Antiproton annihilation on H**¶

Multiplicity of secondary pions and momentum spectra of charged secondary pion have been extracted from these papers:
- C. Amsler, Rev. Mod. Phys. 70, 1293 (1998)
- C. Amsler and F. Myher, Ann. Rev. Nucl. Part. Sci. 41, 219 (1991)
- C.B. Dover et al., Prog. Part. Nucl. Phys., Vol.29, pp.87-173 (1992)

None of these publications states if the errors are statistical, or if the systematic uncertainties are included. We assume that the errors include

statistical and systematic uncertainties.

NOTE: Datasets have been extracted from published graphs.

Other datasets on pbar annihilation should be available from experiments at LEAR (Crystal Barrel).

Those published data can be researched and added in the future, to expand the test bench and further fine-tune the Geant4 modeling.

**K- interactions at rest on H target**¶

The data on the branching ratios for several exclusive topologies resulting from K- on p interactions at rest, as well as energy spectrum (production rate) of pi0’s resulting from K- on p interactions.

The data have been extracted from this paper:

- K.Larson et al., Phys.Rev.D47,799(1993)

(combined with information from A.J.Noble et al., Phys. Rev. Lett 69, 414 (1992)).

No errors have been explicitly reported for the branching ratios for the topologies of interest.

The pi0 spectrum has been extracted from the published graph. At the time, errors could not be extracted from the graph due to technical difficulties.

Due to the lack of errors, the datasets are useful for illustrative purposes only, for example, to show that the spikes in the simulated pi0 spectra

correspond to those pi0’s coming from K- on p resulting in Sigma0 pi0 or K- on p resulting in Lambda pi0.

No other experimental datasets on K- at rest interactions, suitable for MC validation, are know at present.

**Sigma- interactions at rest on H target**¶

The data on production ratios of Lambda0 and Sigma0 have been extracted from this paper:
- M.Goossens et al., in in Low and Intermediate energy kaon physics, ed.E.Ferrari and G.Violini (Riedel, Holland, 1980), p.243

Statistical errors are reported. Systematic error is said to be of the same level as statistical error (~10-11%).

No other publications on this matter are know at present.

**mu- capture at rest on various nuclear targets**¶

Neutron multiplicities resulting from mu- capture on various nuclear targets (Al, Si, Ca, Fe, Ag, I, Au, Pb) have been extracted from the tables published

in the following paper:

P.Singer, Springer Tracts in Modern Physics, 71, 39 (1974)

It’s not explicitly stated whether the published errors are statistical only or if they include statistical and systematic uncertainties; we assume that

the errors include all uncertainties.

- R.M.Sundelin et al., Phys.Rev.Lett, Vol.20, Number 21, 1198 (1968)

It’s not explicitly said if the errors are of statistical origin, or if they also include systematic uncertainties; we assume that the errors include both

statistical and systematic uncertainties.

# Gamma-nuclear interactions¶

Experimental data on proton production in gamma-Cu interactions at 300MeV have been extracted from this paper:- R. Schumacher et al., Phys. Rev. C 25, 2269 (1982)

Double differential production cross sections as a function of kinetic energy of the secondary proton have been measured in different angular bins.

The errors are statistical.

Overall systematic uncertainty is 7%.

- K. Baba et al., Nucl. Phys. A322, 349 (1979)

Double differential production cross sections as a function of momentum of the secondary pion have been measured at different angles of the outgoing pion

(angle is measured with respect to the projectile).

Errors in the tables are statistical.

Systematic error is said to be uniformly 9% for all data points.

NOTE: similar result at different gamma energies (418-718MeV) are also available from this publication, and can be extracted and used if needed.

We’ve chosen 668MeV because it’s the highest available energy point where data for both pi- and pi+ production are available.

- K. Baba et al., Nucl. Phys. A306, 292 (1978)

It’ll give a useful reference for gamma interactions on a light target.

# Hadronic interactions in the intermediate energy range (1.4GeV/c to 12GeV/c)¶

In the intermediate energy range we benchmark Geant4 hadronic models vs data on inclusive proton/neutron production in p, pi+, or pi- interactions witha various nuclear target, for beam momenta between 1 and 9 GeV/c.

The data are from ITEP-771 experiment, and are available from the following publications:

- Yu.D.Bayukov et al, Preprint ITEP-148-1983 Sov.J.Nucl.Phys. 42 116, 1985

Statistical and systematic errors are provided separately for each data point.

By default, the total errors are calculated as a quadratic sum of statistical and systematic errors.

- 1.4GeV/c or 7.5GeV/c proton on C or U
- 1.4GeV/c or 5GeV/c pi+ or pi- on C or U

Data on other targets (Al, Be, Cu, Fe, Nb, Pb, Ta, Sn) are also available, and can be used if needed for specific studies.

NOTE: A large collection of data is also available from the HARP collaboration, and includes pion and proton production in pion or proton induced reactionson various nuclear targets, for a beam momentum in the range from 3GeV/c to 12GeV/c:

- M. Apollonio et al., Nucl. Phys. A821 118, 2009
- M. Apollonio et al., Phys.Rev.C80 065207, 2009
- M. Apollonio et al., Phys.Rev.C80 035208, 2009
- M.G. Catanesi et al., Phys.Rev.C77 055207, 2008

- M. Appolonio et al., Phys.Rev. C82 (2010) 045208 (forward proton production by proton or pion beam on nuclear target)

**total**, i.e. they include both statistical and systematic uncertainties, as stated in this document:

We use HARP data of pion production by a proton or pion beam on C or Be, in the 3-12GeV/c beam momentum range, as it is important for tuning Geant4 hadronic

models and Geant4 physics lists for the needs of FNAL Neutrino Beamline simulation.

# Hadronic interactions at high energies¶

We benchmark Geant4 predictions vs the following datasets:- NA61 collaboration, proton interactions on C at 31GeV/c of beam momentum
- NA49 collaboration, proton interactions on C at 158GeV/c of beam momentum (p+p data are also available)

**NA61 datasets**, results on charged pions and charged kaons production, as well as K+/pi+ ratio, have been extracted from the following publications:

- N.Abgrall et al., Phys.Rev. C84, 034604 (2011) (pions)
- N.Abgrall et al., Phys.Rev. C85, 035210 (2012) (kaons)

Double differential production cross sections as a function of momentum of the secondary particle have been measured in different bins of the polar angle

(with respect to the projectile).

Statistical and systematic errors are reported separately for each data point.

Data on proton production in p+C interactions at 31GeV/c beam momentum have been obtained via semi-private communications with the NA61 collaboration;

the results have been presented at the Neutrino 2012 conference and published in the conference proceedings; the NA61 collaboration considers them public.

Errors on the data points are said to be total (i.e. incl. stat. & sys.).

**NA49 datasets**are conveniently available in the ASCII format from this web site:

Errors on the data points are statistical.

Integrated systematic errors vary from 2% to 3.8%, depends on the subset of data.

NOTE: Links to the NA49 publications are also available via this site.

We have been using in validation pt-integrated distributions that describe production of pions, protons, antiprotons, and neutroms in the p+C interactions

at the 158GeV/c of beam momentum.

We use average multiplicities of the secondary particle as a function of Feynman variable xF. We also use average pt-spectra vs xF for pions, protons, and antiprotons.

We have recently started using in the statistical analysis double differential pt-spectra in different xF-bins, for secondary pions (as modeling pion production

in p+C interactions at high energies is critical for proper neutrino flux predictions, which is important to the FNAL IF program).

We are in the process of incorporating double differential pt-spectra in different xF bins for secondary protons and antiprotons, as serve as good reference points.

NA49 also offers data for p+P (p on H) interactions at 158GeV/c. We’ve started incorporating a subset of those data, e.g. for pion production, in the validation procedure,

although at present we don’t use it in validation regularly. However, these data provide a very useful reference, and they can also serve for benchmarking Geant4 hadronic

models vs other particle-particle generators.

nuclear targets at 100GeV.

This data set is expected to serve as an important reference and to “bridge the gap” between 31GeV and 158GeV.

The data will be extracted from the following publication:

Starting internal release 10.2.ref08, validation also includes benchmarking MC results vs data on inclusive pion, kaon, p, and pbar production by a pi+, p, or K+ beam on various

nuclear targets at 100GeV:

- D.S. Barton et al., Phys. Rev. D27, 2580 (1983), https://inspirehep.net/record/12592