1. Dipartimento di Fisica G. Occhialini Universita’ di Milano-Bicocca
NuFact 05
Hadroproduction data parameterisations for fast neutrino beams calculations
M. Bonesini
Sezione INFN Milano
Dipartimento di Fisica G. Occhialini
Universita’ di Milano-Bicocca
M. Bonesini -NUFACT05

2. Conventional nm beams (from p decay)
WANF
Problem in conventional beams: a lot of minority components -> needs better knowledge of sec. production in target
Exp.
Decay Pipe
Hadron m+ p+ n p
Absorb.
Target
Rock
Horns
M. Bonesini -NUFACT05

3. Simulation of neutrino beams
1. Primary
target production
2. re-interactions
in target
3. re-interactions
in beamline
Full Montecarlo simulation (MARS, FLUKA, Geant 3 or 4)
Good for study of systematics
Fast simulation (parametrization of hadron production data, re-int models)
Good for beamline optimization
M. Bonesini -NUFACT05

4. hadron production data
Some examples
BMPT fast simulation: CHARM II
Both points to good
hadron production data
Fluka full simulation (+ reweighting with SPY data): WANF for NOMAD
M. Bonesini -NUFACT05

5. Low Energy data: Harp is coming
2-15 GeV/c incident p beam on nuclear targets (Be, C,Al, Cu, Sn, Ta, Pb, Miniboone &
K2K replica)
Full solid angle acceptance
PID for p/p separation
Aims: cross sections at a 2% precision
See E. Radicioni talk for details
(thin Al target results)
Some old datasets:
J. Allaby et al., CERN-70-12
G. Eichten et al.,Nucl. Phys. B44(1972) 333
All datasets useful, but suffer from low statistics and high systematics (15 % on cross sections)
M. Bonesini -NUFACT05

6. Data taking summary
HARP took data at the CERN PS T9 beamline in Total: 420 M events, ~300 settings
SOLID targets:
CRYOGENIC targets:
 EXP replica target:
+1.5 GeV/c
10%
100%
LSND: H2O
+8.9 GeV/c
+12.9 GeV/c 5%
50%
Replica
MiniBoone: Be
K2K: Al
M. Bonesini -NUFACT05

7. Higher energy data Barton et al., Phys. ReV. D27(1983),2580
Study of inclusive production of p, K, p, pbar in 100 GeV/c p+,K+,p collisions with C,Al,Cu,Ag,Pb targets
Single arm M6E Fermilab spectrometer
Skubic et al., Phys. ReV. D18 (1978), 3115
Strange particle production in 300 GeV/c p collisions with
Be,Cu,Pb
H.W. Atherton et al. (NA20), CERN 80-07, 1980
p = 60, 120, 200, 300 GeV/c; pt = 0, 500 MeV/c
target plate length = 40, 100, 300, 500 mm
G. Ambrosini et al. (NA56/SPY), Eur. Phys. J. C10 (1999) 605
p = 7, 10, 15, 20, 30, 40, 67.5, 135 GeV/c (at pt = 0); pt = 0, ±75, ±150, ±225, ±337, ±450, +600 MeV/c (for p = ±15, ±40 GeV)
target plate length = 100, 200, 300 mm
WANF “T9-like” target (3 rods 10 cm long, 3 mm thick)
M. Bonesini -NUFACT05

8. The Na56/SPY experiment Critical points for such an experiment
Measure p, kaon fluxes by 450 GeV/c p on Be ( 5% precision)
->knowledge of neutrino spectra
Measure k/p ratio (3% precision) ->
knowledge ne/nm ratio
Equipped H6 beamline from NA52
experiment in North Area
Primary p flux measured by SEM
Different Be targets (shapes, L)
PID by TOF counters (low momenta) and Cerenkov (high momenta)
Critical points for such an experiment
beamline simulation (spectrometer acceptance) (5 – 10 % precision)
Particle misidentification ( < 1%)
Subtraction of long lifetime particles decaying outside the target (K0s -> pp, ...) (< 2%)
Beam momentum determination and K lifetime->uncertainty on K decay correction (1 %)
Protons on target (2 %)
M. Bonesini -NUFACT05

9. Some NA56/SPY results: the K/p ratio
Solid points negatives,
open points positives
Errors 3 %
K content (depleted by
decays) enriched by trigger prescaling
2 samples (one trigger natural composition, the other heavy particles K,p,..)
K/p=(K/p)heavy sample(p/p)natural
M. Bonesini -NUFACT05

10. Some NA56/SPY results:p/K/p inclusive invariant cross sections
Forward invariant cross sections
Model independent extrapolation to zero target thickness with data itself (L=100,200,
300 mm targets)
Total error 10%
M. Bonesini -NUFACT05

11. Low Energy: The Sanford-Wang Parameterization
Empirical parameterization with 8 free parameters:
where:
Pπ is the pion momentum.
Pp is the incident proton momentum.
Θπ is the pion production angle in the lab frame.
c1-8 are the fit parameters
Original S-W
M. Bonesini -NUFACT05

12. S-W Fit Results
Available S-W fits for p-Be (usually made with a compilation of data):
Original S-W fit
Modified Cho S-W fit
K2K S-W fit …
For p-Al 12.9 GeV/c new S-W fit from Harp data is coming
From Mc-Gregor talk at NBI03
M. Bonesini -NUFACT05

13. Comparisons Cho et al. data Marmer et al. data
From Mc-Gregor talk at NBI03
M. Bonesini -NUFACT05

14. HARP preliminary S-W fit to p-Al data at 12.9 GeV/c
small statistical and syst errors
data compatible with older ones
Useful for understanding of K2K beamline
DRAFT
DRAFT
M. Bonesini -NUFACT05

15. The existing parameterizations of secondary particle yield at higher energy
Simple formulas fitting the yield of charged secondary particles from 400 GeV/c protons on Be targets:
Data above 60 GeV/c (x ≈ 0.15) at pt = 0 and 500 MeV/c
H.W. Atherton et al., CERN 80-07, 1980: thin target approximation
A.J. Malensek, FN-341,1981: thick target approximation (500 mm)
Both fail at low x
M. Bonesini -NUFACT05

16. A new parameterization of secondary particle yield from thick targets: the BMPT parametrization
Goal: improvement with respect to previous models at low x (and pT  0). H.W. Atherton et al., CERN 80-07, 1980, A.J. Malensek, FN-341,1981
Secondary yield from fit of:
p+ and K+ invariant cross-section data derived from Atherton et al. & NA56/SPY Collaboration data (Be target),
p–/ p+ and K–/K+ data
K0L evaluation from simple parton model.
Evaluation of tertiary particles production:
Comparison of secondary production from targets of different thickness (100, 200, 300 mm and T9) in Na56/SPY.
Extrapolation to other target material and incident p energy:
M. Bonesini -NUFACT05

17. The invariant cross section for p+ and K+
Empirical formula based on general physical arguments.
Approximate factorization in x and pt
(1-x)a behavior in the forward direction for x  1 (quark counting rule)
x-b behavior in for x  0 (non direct hadron formation mechanism )
Exponential fall in pt for soft interaction
xR=E*/E*max (greatly extends scaling to sub-asymptotic energies, Yen Phys. ReV. D10 (1974) 836)
M. Bonesini -NUFACT05

18. The invariant cross section for p-, K- and K0L
Empirical formula describing p+/p- and K+/K- ratios:
function of x only
R(p) and R(K) shapes supported by analysis of pp data by Ochs (Nucl. Phys. B118 (1977) 397)
R(p)  1 for x  0; R(p)  5 for x  1;
R(K) (1-x)-3 for x  1;
K0L production evaluated from simple parton model
(n = u/d ≈ 2 assuming isospin symmetry)
M. Bonesini -NUFACT05

19. Invariant cross sections: a) pions, b) kaons
M. Bonesini -NUFACT05

20. Parametrization extrapolations
Extension to other target material:
Known dependence of the invariant cross section on atomic number A:
From data on several nuclei:
a(x) ≈ ( x x2)).( p2T)
(D.S. Barton et al., Phys. Rev. D35 (1987) 35, Skubic et al., Phys. ReV. D18(1978) 3115)
≤ 5% systematic error from Be to C
Comparison with data at different incident proton energy:
100 GeV/c proton on Carbon (D.S. Barton et al., Phys. Rev. D27 (1983) 2580)
24 GeV/c proton on Beryllium (T.Eichten et al., Nucl. Phys. B44 (1972) 333)
M. Bonesini -NUFACT05

21. Comparison of BMPT with other energies
Eichten et al. (24 GeV/c)
Barton et al. (100 GeV/c)
Courtesy of A. Marchionni
M. Bonesini -NUFACT05

22. Empirical model for tertiary particles production on thick targets (SPY data)
Experimental evidences:
Comparison of secondary production from targets of different thickness (100, 200, 300 mm and T9) in SPY
Naive absorption model inadequate at large thicknes
Empirical assumptions (for long “needle-like” targets):
Tertiary particles produced mostly by re-interaction of leading secondary particle in the forward direction -> model to reproduce NA56/SPY data
M. Bonesini -NUFACT05

23. A fast neutrino beam simulation (based on BMPT parametrization)
Secondary meson production from BMPT parametrization
3-dimensional description of all beamline elements
Tracking of parent mesons
Neutrino production from parent meson decay (2/3 body decay included)
Useful to check parametrization, fast simulation tool
to “debug” beamlines
M. Bonesini -NUFACT05

24. A fast neutrino beam simulation: phase-space weighting
Hadron decay probability inside the tunnel
Interact. in material
2/3 body decay branching ratio
Probability that the n is emitted in the detector direction
n momentum in lab frame
Solid angle
Total n cross-section
Nucleon target density in the detector
Focusing
Decay tunnel
devices L
det R
det
Target q nh L Z
det h L
h,MAX
M. Bonesini -NUFACT05

25. An application to WANF: Proton int in target
450 GeV protons
Beryllium target
30 mrad acceptance
Exit point from target:
Black: Fluka
Blue: Secondaries only
Red: with Tertiaries K+ K-
M. Bonesini -NUFACT05

26. WANF: proton interactions in targetK+
450 GeV p on Be target
30 mrad acceptance
p,pT secondary mesons from target p+ K+
M. Bonesini -NUFACT05

27. WANF: Comparison with CHARM II data
The CHARM II collab., Eur. Phys. J. C11
(1999), 18
450 GeV p on Be
8 mrad acceptance
Detector at 881 m
Positive focusing
nm beam (105 pot)
CHARM II data
Anti- nm contamination
M. Bonesini -NUFACT05

28. WANF:comparison with CHARM II data
The CHARM II collab., Eur. Phys. J. C11 (1999), 18
450 GeV p on Be
8 mrad acceptance
Detector at 881 m
Negative focusing
CHARM II data
Anti-nm beam (105 pot)
nm contamination
M. Bonesini -NUFACT05

29. An application to CNGS: Comp with Fluka+Geant MC
R. Bailey et al., CERN-SL DI, 1999
400 GeV protons on graphite target
Positive focusing
Detector at 732 Km
This simulation
Fluka+Geant MC
M. Bonesini -NUFACT05

30. An application to NUMI (from M. Messier et al.)
Comparison BMPT, Mars, GFLUKA in Minos near/far detecor
M. Bonesini -NUFACT05

31. An off-axis calculation (from S. Wojcicki)
Physics potential of different sites for NuMI off-axis detector in term of FOM=S/sqrt(B)
Fast simulation based on BMPT (3Kevt/s on a laptop)
Dm13=
x10-3 eV2
M. Bonesini -NUFACT05

32. Conclusions
Full or fast simulation need good quality hadroproduction data in the forward direction: call it parametrization or reweighting …
Parametrization of available high-energy data on particle production on light nuclei (BMPT):
Fits satisfactory the 400 & 450 GeV p-Be experimental data over a wide x and pT range.
Can be safely extrapolated to thick target and to different proton momentum (≈ 24 GeV/c) and target material: we will check soon with HARP data down to 8-10 GeV/c
Can be applied to neutrino beam simulations:
Efficient (fast) alternative to full hadronic cascade codes
Reproduces existing data within ≈ 10% (CHARM II and ...)
M. Bonesini -NUFACT05

33. Acknowledgements
Many thanks to F. Pietropaolo,T. Tabarelli and A. Marchionni with whom most of this work was done in some old and happy days
M. Bonesini -NUFACT05