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

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

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

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

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

Data taking summary HARP took data at the CERN PS T9 beamline in 2001-2002 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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) ≈ (0.74- 0.55 x + 0.26 x2)).( 0.98+0.21 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

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

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

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

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

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

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

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

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

An application to CNGS: Comp with Fluka+Geant MC R. Bailey et al., CERN-SL-99-034-DI, 1999 400 GeV protons on graphite target Positive focusing Detector at 732 Km This simulation Fluka+Geant MC M. Bonesini -NUFACT05

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

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

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

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