Hadroproduction data parameterisations for fast neutrino beams calculations

M. Bonesini -NUFACT05 1

Hadroproduction data parameterisations for fast

neutrino beams calculations

M. BonesiniSezione INFN Milano

Dipartimento di Fisica G. OcchialiniUniversita’ di Milano-Bicocca


Conventional beams (from decay)

p+

Exp.

Decay Pipe

+

Rock

Hadron

Absorb.

Horns

Target

Problem in conventional beams: a lot of minority components -> needs better knowledge of sec. production in target

WANF


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)

Fast simulation (parametrization of hadron production data, re-int models)

Good for beamline optimization

Good for study of systematics


Some examples

Fluka full simulation (+ reweighting with SPY data): WANF for NOMAD

BMPT fast simulation: CHARM II

Both points to goodhadron production data


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 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)


+1.5 GeV/c

10%100%

LSND: H2O

+8.9 GeV/c+12.9 GeV/c

5%50%

100%Replica

5%50%

100%Replica

MiniBoone: BeK2K: Al

SOLID targets:

CRYOGENIC targets: EXP replica target:

HARP took data at the CERN PS T9 beamline in 2001-2002 Total: 420 M events, ~300 settings

Data taking summary


Higher energy data Barton et al., Phys. ReV. D27(1983),2580

Study of inclusive production of , K, p, pbar in 100 GeV/c ,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)


The Na56/SPY experiment

Measure , kaon fluxes by 450 GeV/c p on Be ( 5% precision)

->knowledge of neutrino spectra Measure k/ ratio (3% precision) ->

knowledge e/ 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 -> ...) (< 2%)

• Beam momentum determination and K lifetime->uncertainty on K decay correction (1 %)

• Protons on target (2 %)


Some NA56/SPY results: the K/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)heavy sample(p/natural


Some NA56/SPY resultsK/pinclusive 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%


Low Energy: The Sanford-Wang Parameterization

)cos(

1

2 8765

43

2 )1(

cpc

pP

cPc

PcPc

p

c eP

PPc

dpd

d

• 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


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


Comparisons

Cho et al. data Marmer et al.

dataFrom Mc-Gregor talk at NBI03


HARP preliminary S-W fit to p-Al data at 12.9 GeV/c

DRAFT

DRAFT

• small statistical and syst errors

•data compatible with older ones

•Useful for understanding of K2K beamline


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

)51()1(

)1(422

2

Dx

t

A

Be eMp

xBx

ddp

Nd

)2

2)((

22max

2tCpBxBe ex

CBeAp

ddp

Nd


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: + and K+ invariant cross-section data derived from Atherton et

al. & NA56/SPY Collaboration data (Be target), –/ + and K–/K+ data K0

L 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:


The invariant cross section for + and K+ Empirical formula based on general physical

arguments.

Approximate factorization in x and pt

(1-x) behavior in the forward direction for x 1 (quark counting rule)

x 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)

βR

)xR

Bx(1

)t

pγ

Rx

a(

e

)2t

pδ

R2x

2at

pγ

Rx

a(1α)

RxA(1

Be)

3dp

σ3d(E


The invariant cross section for -, K- and K0

L

Empirical formula describing +/- and K+/K- ratios:

function of x only R() and R(K) shapes supported by analysis of pp data

by Ochs (Nucl. Phys. B118 (1977) 397)

R() 1 for x 0; R() 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)

))3N(K)(N(K4

1

2n

)1)N(K(2n)N(K)N(K 0

L

r1

R0

r1

R0 )x(1rR(K);)x(1rR(π(


Invariant cross sections: Invariant cross sections: a) pions, b) kaonsa) pions, b) kaons


Parametrization extrapolations

Extension to other target material: Known dependence of the invariant cross section on atomic

number A:

From data on several nuclei: (x) ≈ (0.74- 0.55 x + 0.26 x2)).( 0.98+0.21 p2

T)

(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)

(E

d3dp3

)A1(

A1

A2

) (Ed3dp3

)A2


Comparison of BMPT with other energies

Courtesy of A. Marchionni

Eichten et al. (24 GeV/c)

Barton et al. (100 GeV/c)


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


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


A fast neutrino beam simulation:phase-space weighting

Hadron decay probability inside the

tunnel

Zdet

Rdet

Ldet

Decay tunnel

h

Focusingdevices

Target

Lh

Lh,MAX

P (1 e

Lh ,MAX

h )e

Lh

h

e

Lmat

int

BR ex

(

mh

E h ph cosh

)2

0

mh2 m,x

2

2mh

mh

E h ph cosh

Rdet2

4Z det2

N AdetLdet

Interact. in

material

2/3 body decay

branching ratio

Probability that the is emitted in

the detector direction

Total cross-section

momentum in lab frame

Solid angle Nucleon

target density in

the detector


An application to WANF: Proton int in target

450 GeV protonsBeryllium target30 mrad acceptance

Exit point from target:Black: FlukaBlue: Secondaries onlyRed: with Tertiaries

+ –

K+ K-


WANF: proton interactions in target

450 GeV p on Be target

30 mrad acceptance

p,pT secondary mesons from target

+

+

K+

K+


WANF: Comparison with CHARM II data

450 GeV p on Be

8 mrad acceptance

Detector at 881 m Positive focusing

beam (105 pot) CHARM II data Anti-

contamination

The CHARM II collab., Eur. Phys. J. C11 (1999), 18


WANF:comparison with CHARM II data

450 GeV p on Be 8 mrad acceptance Detector at 881 m Negative focusing

CHARM II data Anti- beam (105

pot) contamination

The CHARM II collab., Eur. Phys. J. C11 (1999), 18


An application to CNGS: Comp with Fluka+Geant MC

400 GeV protons on graphite target

Positive focusing Detector at 732

Km This simulation Fluka+Geant MC

R. Bailey et al., CERN-SL-99-034-DI, 1999


An application to NUMI (from M. Messier et al.)

Comparison BMPT, Mars, GFLUKA in Minos near/far detecor


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)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

2 2.5 3

LTVBuyckFort FrancesKenora

m13= x10-3 eV2


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 ...)


Many thanks to F. Pietropaolo,T. Tabarelli and A. Marchionni with

whom most of this work was done in some old and happy days

Documents

Hadroproduction data parameterisations for fast neutrino beams calculations