Large-angle production of charged pions by 3 GeV/c - 12 GeV/c protons on carbon, copper and tin targets
aa r X i v : . [ h e p - e x ] S e p Large-angle production of charged pions by3 GeV / c–12 GeV / c protons on carbon, copper andtin targets HARP CollaborationOctober 22, 2018
Abstract
A measurement of the double-differential π ± production cross-section in proton–carbon, proton–copper and proton–tin collisions in the range of pion momentum 100 MeV /c ≤ p <
800 MeV /c andangle 0 .
35 rad ≤ θ < .
15 rad is presented. The data were taken with the HARP detector in theT9 beam line of the CERN PS. The pions were produced by proton beams in a momentum rangefrom 3 GeV /c to 12 GeV /c hitting a target with a thickness of 5% of a nuclear interaction length.The tracking and identification of the produced particles was done using a small-radius cylindricaltime projection chamber (TPC) placed in a solenoidal magnet. An elaborate system of detectors inthe beam line ensured the identification of the incident particles. Results are shown for the double-differential cross-sections d σ/ d p d θ at four incident proton beam momenta (3 GeV /c , 5 GeV /c ,8 GeV /c and 12 GeV /c ). (Submitted to The European Physical Journal C)1 ARP collaboration
M.G. Catanesi, E. Radicioni
Universit`a degli Studi e Sezione INFN, Bari, Italy
R. Edgecock, M. Ellis , S. Robbins , , F.J.P. Soler Rutherford Appleton Laboratory, Chilton, Didcot, UK
C. G¨oßling
Institut f¨ur Physik, Universit¨at Dortmund, Germany
S. Bunyatov, A. Krasnoperov, B. Popov , V. Serdiouk, V. Tereschenko Joint Institute for Nuclear Research, JINR Dubna, Russia
E. Di Capua, G. Vidal–Sitjes Universit`a degli Studi e Sezione INFN, Ferrara, Italy
A. Artamonov , P. Arce , S. Giani, S. Gilardoni, P. Gorbunov , A. Grant, A. Grossheim , P. Gruber ,V. Ivanchenko , A. Kayis-Topaksu , J. Panman, I. Papadopoulos, J. Pasternak, E. Tcherniaev, I. Tsukerman ,R. Veenhof, C. Wiebusch , P. Zucchelli , CERN, Geneva, Switzerland
A. Blondel, S. Borghi , M. Campanelli, M.C. Morone , G. Prior , R. Schroeter Section de Physique, Universit´e de Gen`eve, Switzerland
R. Engel, C. Meurer
Institut f¨ur Physik, Forschungszentrum Karlsruhe, Germany
I. Kato , University of Kyoto, Japan
U. Gastaldi
Laboratori Nazionali di Legnaro dell’ INFN, Legnaro, Italy
G. B. Mills Los Alamos National Laboratory, Los Alamos, USA
J.S. Graulich , G. Gr´egoire Institut de Physique Nucl´eaire, UCL, Louvain-la-Neuve, Belgium
M. Bonesini, F. Ferri, M. Paganoni, F. Paleari
Universit`a degli Studi e Sezione INFN Milano Bicocca, Milano, Italy
M. Kirsanov
Institute for Nuclear Research, Moscow, Russia
A. Bagulya, V. Grichine, N. Polukhina
P. N. Lebedev Institute of Physics (FIAN), Russian Academy of Sciences, Moscow, Russia
V. Palladino
Universit`a “Federico II” e Sezione INFN, Napoli, Italy
L. Coney , D. Schmitz Columbia University, New York, USA
G. Barr, A. De Santo , C. Pattison, K. Zuber Nuclear and Astrophysics Laboratory, University of Oxford, UK
F. Bobisut, D. Gibin, A. Guglielmi, M. Mezzetto
Universit`a degli Studi e Sezione INFN, Padova, Italy
J. Dumarchez, F. Vannucci
LPNHE, Universit´es de Paris VI et VII, Paris, France
U. Dore
Universit`a “La Sapienza” e Sezione INFN Roma I, Roma, Italy
D. Orestano, F. Pastore, A. Tonazzo, L. Tortora
Universit`a degli Studi e Sezione INFN Roma III, Roma, Italy
C. Booth, C. Buttar , P. Hodgson, L. Howlett Dept. of Physics, University of Sheffield, UK
M. Bogomilov, M. Chizhov, D. Kolev, R. Tsenov
Faculty of Physics, St. Kliment Ohridski University, Sofia, Bulgaria
S. Piperov, P. Temnikov
Institute for Nuclear Research and Nuclear Energy, Academy of Sciences, Sofia, Bulgaria
M. Apollonio, P. Chimenti, G. Giannini, G. Santin Universit`a degli Studi e Sezione INFN, Trieste, Italy
J. Burguet–Castell, A. Cervera–Villanueva, J.J. G´omez–Cadenas, J. Mart´ın–Albo, P. Novella, M. Sorel,A. Tornero
Instituto de F´ısica Corpuscular, IFIC, CSIC and Universidad de Valencia, Spain Now at FNAL, Batavia, Illinois, USA. Jointly appointed by Nuclear and Astrophysics Laboratory, University of Oxford, UK. Now at Codian Ltd., Langley, Slough, UK. Now at University of Glasgow, UK. Also supported by LPNHE, Paris, France. Now at Imperial College, University of London, UK. ITEP, Moscow, Russian Federation. Permanently at Instituto de F´ısica de Cantabria, Univ. de Cantabria, Santander, Spain. Now at SpinX Technologies, Geneva, Switzerland. Now at TRIUMF, Vancouver, Canada. Now at University of St. Gallen, Switzerland. On leave of absence from Ecoanalitica, Moscow State University, Moscow, Russia. Now at C¸ ukurova University, Adana, Turkey. Now at III Phys. Inst. B, RWTH Aachen, Aachen, Germany. On leave of absence from INFN, Sezione di Ferrara, Italy. Now at CERN, Geneva, Switzerland. Now at Univerity of Rome Tor Vergata, Italy. Now at Lawrence Berkeley National Laboratory, Berkeley, California, USA. K2K Collaboration. MiniBooNE Collaboration. Now at Section de Physique, Universit´e de Gen`eve, Switzerland, Switzerland. Now at Royal Holloway, University of London, UK. Now at University of Sussex, Brighton, UK. Now at ESA/ESTEC, Noordwijk, The Netherlands.3
Introduction
The HARP experiment [1] makes use of a large-acceptance spectrometer for a systematic study of hadronproduction on a large range of target nuclei for beam momenta from 1.5 GeV /c to 15 GeV /c . Themain motivations are the measurement of pion yields for a quantitative design of the proton driver ofa future neutrino factory [2], a substantial improvement of the calculation of the atmospheric neutrinoflux [3, 4, 5, 6, 7] and the measurement of particle yields as input for the flux calculation of acceleratorneutrino experiments, such as K2K [8, 9], MiniBooNE [10] and SciBooNE [11].The measurement of the double-differential cross-section, d σ π / d p d θ for π ± production by protons of3 GeV /c , 5 GeV /c , 8 GeV /c and 12 GeV /c momentum impinging on a thin carbon, copper or tin targetof 5% nuclear interaction length are presented.Especially for carbon targets it is interesting to measure pion production cross-sections in the frameworkof the HARP measurement programme for neutrino flux calculations. Carbon targets are frequently usedas hadron production targets in neutrino beam lines. In addition, measurements on carbon can be usedto predict pion production off nitrogen and oxygen nuclei without a large extrapolation in the productionmodels. The knowledge of the latter production cross-sections are needed to model atmospheric muon andneutrino fluxes. Owing to the relatively low incoming beam momenta the data are especially interestingfor the calculation of hadron production in secondary interactions in extended production targets and inatmospheric flux calculations. The comparison of the measurements on copper and tin targets with thecarbon data in this paper and with the tantalum data obtained with the same apparatus described inRef. [12] can be used to check the dependence on the atomic number A in hadron production models.Copper and tin are interesting target materials as their atomic numbers are midway between light targetmaterials, such as Be, Al and C (used in targets for conventional neutrino beams) and heavy targets suchas Ta (relevant for the optimization of neutrino factory designes).Data were taken in the T9 beam of the CERN PS. For this analysis, about 1,159,000 (1,066,000 and1,284,000) incoming protons were selected which gave an interaction trigger in the Large Angle spec-trometer, resulting in 235,000 (209,500 and 243,400) well-reconstructed secondary pion tracks for thecarbon (copper and tin) target. The different settings have been taken within a short running period sothat in their comparison detector variations are minimized.The analysis proceeds by selecting tracks in the Time Projection Chamber (TPC) in events with incidentbeam protons. Momentum and polar angle measurements and particle identification are based on themeasurements of track position and energy deposition in the TPC. An unfolding method is used tocorrect for experimental resolution, efficiency and acceptance and to obtain the double-differential pionproduction cross-sections, with a full error evaluation. A comparison with available data is presented.The analysis follows the same methods as the ones used for the determination of π ± production cross-sections by protons on a tantalum target described in Ref. [12]. We refer to Ref. [12] for a detaileddescription of the analysis, only the main points and differences with respect to the latter are describedhere. The HARP detector is shown in Fig. 1. The forward spectrometer is built around a dipole magnet formomentum analysis, with large planar drift chambers (NDC) [13] for particle tracking and a time-of-flightwall (TOFW) [14], a threshold Cherenkov detector (CHE) and an electromagnetic calorimeter (ECAL)used for particle identification. The forward spectrometer covers an acceptance for tracks originatingfrom the target with polar angles up to 250 mrad. This is well matched to the angular range of interestfor the measurement of hadron production to calculate the properties of conventional accelerator neutrinobeams [16, 17]. In the large-angle region a cylindrical TPC with a radius of 408 mm is positioned in asolenoidal magnet with a field of 0.7 T. The target is inserted into the inner field cage of the TPC. TheTPC is used for tracking, momentum determination and the measurement of the energy deposition d E/ d x for particle identification [18]. A set of resistive plate chambers (RPC) form a barrel inside the solenoid4igure 1: Schematic layout of the HARP detector. The convention for the coordinate system is shown inthe lower-right corner. The three most downstream (unlabelled) drift chamber modules are only partlyequipped with electronics and are not used for tracking.around the TPC to measure the arrival time of the secondary particles [19]. Beam instrumentationprovides identification of the incoming particle, the determination of the time when it hits the target,and the impact point and direction of the beam particle on the target. Several trigger detectors areinstalled to select events with an interaction and to define the normalization.In addition to the data taken with the thin carbon, copper and tin targets of 5% nuclear interaction length( λ I ), runs were also taken with an empty target holder, a thin 2% λ I target and a thick 100% λ I target.Data taken with a liquid hydrogen target at 3 GeV /c , 5 GeV /c and 8 GeV /c incident beam momentumtogether with cosmic-ray data were used to provide an absolute calibration of the efficiency, momentumscale and resolution of the detector. Moreover, tracks produced in runs with Pb and Ta targets in thesame period and with the same beam settings were used for the calibration of the detector, verificationof the event reconstruction and analysis procedures (see Ref. [12] for further details).The momentum of the T9 beam is known with a precision of the order of 1% [20]. The absolute normaliza-5ion of the number of incident protons was performed using 300 000, 240 000 and 280 000 ‘incident-proton’triggers for the carbon, copper and tin data, respectively. These are triggers where the same selection onthe beam particle was applied but no selection on the interaction was performed. The rate of this triggerwas down-scaled by a factor 64. A cross-check of the absolute normalization was provided by countingtracks in the forward spectrometer.A detailed description of the HARP apparatus is given in Ref. [15]. In this analysis the detector com-ponents of the large-angle spectrometer and the beam instrumentation are employed and are brieflysummarized in the following.A set of four multi-wire proportional chambers (MWPCs) measures the position and direction of theincoming beam particles with an accuracy of ≈ ≈ . /c anddetermines the initial time at the interaction vertex ( t ). The timing resolution of the combined BTOFsystem is about 70 ps. A system of two N -filled Cherenkov detectors (BCA and BCB) is used to tagelectrons at low energies and pions at higher energies. The electron and pion tagging efficiency is foundto be close to 100%. The proton fraction in the incoming beam varies from 35% at 3 GeV/c to 92% at12 GeV/c. The length of the accelerator spill is 400 ms with a typical intensity of 15 000 beam particlesper spill. The average number of events recorded by the data acquisition ranges from 300 to 350 per spillfor the four different beam momenta.The target is placed inside the inner field cage (IFC) of the TPC such that, in addition to particlesproduced in the forward direction, backward-going tracks can be measured. All three targets have anominal thickness of 5% λ I and a cylindrical shape with a nominal diameter of 30 mm. The 99.95% purecarbon target used for the measurement described here has a thickness of 18.94 mm with a variation of ± .
02 mm. Its density was measured to be 1.88 g/cm . The copper target has a purity of 99.99% witha thickness of 7.52 mm with a variation of ± .
01 mm and a density of 8.92 g/cm . The tin target has apurity of 99.99% with a thickness of 11.04 mm with a variation of ± .
04 mm and a density of 7.29 g/cm .A set of trigger detectors completes the beam instrumentation: a thin scintillator slab covering thefull aperture of the last quadrupole magnet in the beam line to start the trigger logic decision (BS); asmall scintillator disk, TDS, positioned upstream of the target to ensure that only particles hitting thetarget cause a trigger; and ‘halo’ counters (scintillators with a hole to let the beam particles pass) to vetoparticles too far away from the beam axis. A cylindrical detector (inner trigger cylinder, ITC) made of sixlayers of 1 mm thick scintillating fibres is positioned inside the inner field cage of the TPC and surroundsthe target. It provides full coverage of the acceptance of the TPC. The large-angle spectrometer consistsof a TPC and a set of RPC detectors inside the solenoidal magnet. The TPC detector was designed tomeasure and identify tracks in the angular region from 0.25 rad to 2.5 rad from the beam axis. Chargedparticle identification (PID) can be achieved by measuring the ionization per unit length in the gas(d E/ d x ) as a function of the total momentum of the particle. Additional PID can be performed througha time-of-flight measurement with the RPCs.In the present analysis, the TPC provides the measurement for the pattern recognition to find the particletracks, and to measure their momentum through the curvature of their trajectory. It also provides PIDusing the measurement of energy deposition. The RPC system is used in this analysis to provide acalibration of the PID capabilities of the TPC.In addition to the usual need for calibration of the detector, a number of hardware shortfalls, discoveredmainly after the end of data-taking, had to be overcome to use the TPC data reliably in the analysis. TheTPC is affected by a relatively large number of dead or noisy pads and static and dynamic distortions ofthe reconstructed trajectories. Static distortions are caused by the inhomogeneity of the electric field, dueto an accidental mismatch between the inner and outer field cage (powered by two distinct HV supplies)and other sources. Dynamic distortions are caused instead by the build-up of ion-charge density inthe drift volume during the 400 ms long beam spill. All these effects were fully studied and availablecorrections are described in detail in Ref. [12]. While methods to correct the dynamic distortions of the6PC tracks are being implemented, a pragmatic approach has been followed in the present analysis. Onlythe events corresponding to the early part of the spill, where the effects of the dynamic distortions arestill small, are used . The time interval between spills is large enough to drain all charges in the TPCrelated to the effect of the beam. The combined effect of the distortions on the kinematic quantities usedin the analysis has been studied in detail and only that part of the data for which the systematic errorscan be assessed with physical benchmarks was used, as explained in [12]. More than 40% of the recordeddata can be used on average in the current analysis.The absolute scale of the momentum determination is determined using elastic scattering data off ahydrogen target. The angle of the forward scattered particle (pion or proton) is used to give an absoluteprediction for the momentum of the recoil proton. This prediction is compared with the measurementin the TPC. To study the stability of this measurement protons are selected in a narrow band with arelatively large d E/ d x where the d E/ d x depends strongly on momentum. The average momentum forthe protons selected in this band remains stable within 3% as a function of time–in–spill over the part ofthe spill used for the analysis. The beam of positive particles used for this measurement contains mainly positrons, pions and protons,with small components of kaons, deuterons and heavier ions. Its composition depends on the selectedbeam momentum. The analysis proceeds by first selecting a beam proton hitting the target, not accom-panied by other tracks. Then an event is required to be triggered by the ITC in order to be retained.After the event selection the sample of tracks to be used for analysis is defined. Tracks are only consideredif they contain at least twelve space points out of a maximum of twenty. This cut is applied to ensurea good measurement of the track parameters and of the d E/ d x . Furthermore, a quality requirement isapplied on the fit to the helix. The latter requirement introduces a very small loss of efficiency. Fortracks satisfying these conditions, a cut is made on d ′ , the distance of closest approach to the extrap-olated trajectory of the incoming beam particle in the plane perpendicular to the beam direction and z ′ , the z -coordinate where the distance of the secondary track and the beam track is minimal. Finally,only tracks with momentum in the range between 100 MeV /c and 800 MeV /c are accepted. In addition,particles with transverse momentum below 55 MeV /c are removed.Table 1 shows the number of events and tracks at various stages of the selection. The total numberof events taken by the data acquisition (“Total DAQ events”) includes triggers of all types as well ascalibration events; the number of “Protons on target” represents the count of the incoming beam triggerafter off-line selection of accepted protons multiplied by the down-scale factor 64. The number of acceptedevents for this analysis (“Accepted protons with LAI (Large Angle Interaction)”) is obtained using thesame selection of incoming protons in coincidence with a trigger in the ITC. The large difference betweenthe rows “Total DAQ events” and “Accepted protons with LAI” is due to the relatively large fractionof pions in the beam and to the larger number of triggers taken for the measurements with the forwardspectrometer. These data will be the subject of other publications. The line “Maximum N evt ” refers to thelast number of events N evt in spill used to avoid dynamic distortion corrections, with the correspondingnumber of interaction triggers used in the analysis (“LAI in accepted spill part”) and the fraction ofthe data used given under “Fraction of triggers used”. The lines “Accepted momentum determination”and “In kinematic region and originating from target” give the number of tracks passing the momentumfit quality requirements and the selection of tracks originating in the target region. Finally, the rows“Negative particles”, “Positive particles ”, “ π − selected with PID” and “ π + selected with PID” show thenumber of accepted tracks with negative and positive charge and the ones passing in addition the pionPID criteria, respectively.To give an impression of the complexity of the events, one can define an ‘average multiplicity’ as the ratioof the number of tracks with at least twelve hits in the TPC (regardless of their momentum, angle orspatial position) and the number of events accepted by the selection criteria with at least one such track.With this definition, the average multiplicity is 2.2, 2.6, 3.1 and 3.4 for the 3 GeV /c , 5 GeV /c , 8 GeV /c this translates into a cut on the maximum number of events ( N evt ) to be retained λ I target data sets,and the number of protons on target as calculated from the pre-scaled trigger count. Data set 3 GeV / c 5 GeV / c 8 GeV / c 12 GeV / c Total DAQ events (C) 1304255 2648351 1878590 1875610(Cu) 992549 2166883 2599056 748123(Sn) 1636933 2827930 2780036 950582Protons on target (C) 1107456 4872896 6143552 7393024(selected min. bias ×
64) (Cu) 971840 3626048 7606272 2990656(Sn) 1379008 4598848 8260544 3842112Acc. protons with LAI (C) 56712 255922 337150 509713(Cu) 59873 237894 541852 226250(Sn) 83549 304949 600581 295053Maximum N evt (C) 140 140 170 150(Cu) 130 120 120 130(Sn) 110 110 120 110LAI in accepted spill part (C) 26231 108215 161331 217899(Cu) 27287 87974 175770 90752(Sn) 30029 98078 199209 100872Fraction of triggers used (C) 46 % 42 % 48 % 43 %(Cu) 46 % 37 % 32 % 40 %(Sn) 36 % 32 % 33 % 34 %Accepted momentum (C) 32483 154984 258338 304993determination (Cu) 37681 156847 374701 209043(Sn) 42949 188994 481436 274700In kinematic region and (C) 20508 95999 150444 173077originating from target (Cu) 23896 99652 229002 122273(Sn) 29090 125864 305214 167137Negative particles (C) 2873 20328 38892 48699(Cu) 3016 18242 52447 31239(Sn) 3352 20721 63846 39395Positive particles (C) 17635 75671 111552 124378(Cu) 20880 81410 176555 91034(Sn) 25738 105143 241368 127742 π − selected with PID (C) 2661 18513 35115 42994(Cu) 2728 16451 46820 27636(Sn) 3100 18762 56697 34595 π + selected with PID (C) 5554 28446 47165 54481(Cu) 4403 22087 57218 32234(Sn) 4439 23402 64410 38000 and 12 GeV /c beams in p–C data, respectively.The double-differential cross-section for the production of a particle of type α can be expressed in thelaboratory system as:d σ α d p i d θ j = 1 N pot AN A ρt X i ′ ,j ′ ,α ′ M − ijαi ′ j ′ α ′ · N α ′ i ′ j ′ , (1)where d σ α d p i d θ j is expressed in bins of true momentum ( p i ), angle ( θ j ) and particle type ( α ).The factor AN A ρt is the inverse of the number of target nuclei per unit area ( A is the atomic mass, N A is the Avogadro number, ρ and t are the target density and thickness) . The result is normalized to thenumber of incident protons on target N pot . We do not make a correction for the attenuation of the proton beam in the target, so that strictly speaking thecross-sections are valid for a λ I = 5% target. N α ′ i ′ j ′ is the number of particles of observed type α ′ in bins of reconstructed momentum( p i ′ ) and angle ( θ j ′ ). These particles must satisfy the event, track and PID selection criteria. Although,owing to the stringent PID selection, the background from misidentified protons in the pion sample issmall, the pion and proton raw yields ( N α ′ i ′ j ′ , for α ′ = π − , π + , p) have been measured simultaneously.This makes it possible to correct for the small remaining proton background in the pion data withoutprior assumptions concerning the proton production cross-section.The matrix M − ijαi ′ j ′ α ′ corrects for the efficiency and resolution of the detector. It unfolds the truevariables ijα from the reconstructed variables i ′ j ′ α ′ with a Bayesian technique [22] and corrects theobserved number of particles to take into account effects such as trigger efficiency, reconstruction efficiency,acceptance, absorption, pion decay, tertiary production, PID efficiency, PID misidentification and electronbackground. The method used to correct for the various effects is described in more detail in Ref. [12].In order to predict the population of the migration matrix element M ijαi ′ j ′ α ′ , the resolution, efficiencyand acceptance of the detector are obtained from the Monte Carlo. This is accurate provided the MonteCarlo simulation describes these quantities correctly. Where some deviations from the control samplesmeasured from the data are found, the data are used to introduce (small) ad hoc corrections to the MonteCarlo.Using the unfolding approach, possible known biases in the measurements are taken into account auto-matically as long as they are described by the Monte Carlo. For example the energy-loss of particlesinside the target and material around the inner field cage is expressed as an average shift of the measuredmomentum distribution compared to the physical momentum. Known biases are therefore treated in thesame way as resolution effects. In the experiment simulation, which is based on the GEANT4 toolkit [23],the materials in the beam-line and the detector are accurately described as well as the relevant featuresof the detector response and the digitization process. The Monte Carlo simulation compares well withdata, as shown in Ref. [12].The absolute normalization of the result is calculated in first instance relative to the number of inci-dent beam particles accepted by the selection. After unfolding, the factor AN A ρt is applied. The beamnormalization using down-scaled incident-proton triggers has uncertainties smaller than 2% for all beammomentum settings.The background due to interactions of the primary protons outside the target (called ‘Empty targetbackground’) is measured using data taken without the target mounted in the target holder. Owingto the selection criteria which only accept events from the target region and the good definition of theinteraction point this background is negligible ( < − ).The effects of these uncertainties on the final results are estimated by repeating the analysis with therelevant input modified within the estimated uncertainty intervals. In many cases this procedure requiresthe construction of a set of different migration matrices. The correlations of the variations between thecross-section bins are evaluated and expressed in the covariance matrix. Each systematic error source isrepresented by its own covariance matrix. The sum of these matrices describes the total systematic error. The measured double-differential cross-sections for the production of π + and π − in the laboratory systemas a function of the momentum and the polar angle for each incident beam momentum are shown in Fig. 2and 3, respectively. The error bars shown are the square-roots of the diagonal elements in the covariancematrix, where statistical and systematic uncertainties are combined in quadrature. Correlations cannotbe shown in the figures. The correlation of the statistical errors (introduced by the unfolding procedure)are typically smaller than 20% for adjacent momentum bins and smaller for adjacent angular bins. Thecorrelations of the systematic errors are larger, typically 80% for adjacent bins. Tables with the results The background of interactions of the primary proton outside the target can be suppressed for large angle tracksmeasured in the TPC owing to the good resolution in z . This is contrary to the situation in the forward spectrometer wherean interaction in the target cannot be distinguished from an interaction in upstream or downstream material [16, 17].
9f this analysis are also given in Appendix A. A discussion of the error evaluation is given below. Theoverall scale error ( < /c data the point–to–point statistical error is larger than the systematicerror, except for the lowest secondary momentum bin. Especially in the middle of the range (around400 MeV /c ), the systematic error is small. Thus the fluctuations between the points are expected tobe of statistical nature. In the first angular bins the momentum resolution is relatively large comparedto the bin size such that the unfolding procedure tends to display statistical fluctuations over two bins.Since the treatment of the data sets taken with different beam momenta is identical, structures visible inthe spectra at 3 GeV /c and not visible in the other data sets are not likely to be artefacts of the efficiencycorrections. Overall trends in the shapes, i.e. structures extending over more than two bins are, however,to be considered significant.To better visualize the dependence on the incoming beam momentum, the same data averaged over theangular range (separately for the forward going and backward going tracks) covered by the analysis areshown separately for π + and π − in Fig. 4. The spectrum of pions produced in the backward direction ismuch steeper than that in the forward direction.The increase of the pion yield per proton is visible in addition to a change of spectrum towards highermomentum of the secondaries produced by higher momentum beams in the forward direction.The dependence of the integrated pion yields on the incident beam momentum is shown in Fig. 5 andcompared with the p–Ta data taken with the same apparatus (Ref. [12]). The π + and π − yields integratedover the region 0 .
350 rad ≤ θ < .
550 rad and 100 MeV /c ≤ p <
700 MeV /c are shown in the left paneland the data integrated over the region 0 .
350 rad ≤ θ < .
950 rad and 250 MeV /c ≤ p <
500 MeV /c inthe right panel. The beam energy dependence of the yields is clearly different in the p–C data comparedto the p–Ta data. The dependence in the p–C data is much more flat with a saturation of the yieldbetween 8 GeV /c and 12 GeV /c (in both integration regions). The π + and π − production yields exhibita different behaviour. The p–Cu and p–Sn data are more similar to the p–Ta data than the p–C dataindicating a smooth transition between light and heavy target nuclei.The integrated π − / π + ratio in the forward direction is displayed in Fig. 6 as a function of secondarymomentum. The previously published p–Ta data are reproduced in addition to the measurements on thethree target nuclei presented in this paper. In the covered part of the momentum range more π + ’s areproduced than π − ’s. The π − / π + ratio increases with increasing beam momentum and, depending on thebeam momentum, a change of the sign of the slope of the ratio as a function of secondary momentum isvisible in the p–C data. The latter feature is not present in the p–Cu, p–Sn and p–Ta [12] data. The ratiois closer to unity for the heavier target nuclei and a smaller variation with beam momentum is observed.The dependence of the integrated pion yields on the atomic number A is shown in Fig. 7 combiningthe results with the p–Ta data (Ref. [12]) taken with the same apparatus and analysed using the samemethods. The π + yields integrated over the region 0 .
350 rad ≤ θ < .
550 rad and 100 MeV /c ≤ p <
700 MeV /c are shown in the left panel and the π − data integrated over the same region in the rightpanel for four different beam momenta. One observes a smooth behaviour of the integrated yields. The A -dependence is slightly different for π − and π + production, the latter saturating earlier, especially atlower beam momenta. The uncertainties are reported in some detail in Table 2 for the carbon target data and summarized forthe copper and tin target data in Table 3. One observes that only for the 3 GeV /c beam is the statisticalerror similar in magnitude to the systematic error, while the statistical error is negligible for the 8 GeV /c and 12 GeV /c beams. The statistical error is calculated by error propagation as part of the unfoldingprocedure. It takes into account that the unfolding matrix is obtained from the data themselves andhence contributes also to the statistical error. This procedure almost doubles the statistical error, but The migration matrix is calculated without prior knowledge of the cross-sections, while the unfolding procedure deter-mined the unfolding matrix from the migration matrix and the distributions found in the data. π + production in p–C, p–Cu and p–Sn interactions asa function of momentum displayed in different angular bins (shown in mrad in the panels). The resultsare given for four incident beam momenta (filled triangles: 3 GeV /c ; open triangles: 5 GeV /c ; filledrectangles: 8 GeV /c ; open circles: 12 GeV /c ). The error bars represent the combination of statisticaland systematic uncertainties. 11igure 3: Double-differential cross-sections for π − production in p–C, p–Cu and p–Sn interactions asa function of momentum displayed in different angular bins (shown in mrad in the panels). The resultsare given for four incident beam momenta (filled triangles: 3 GeV /c ; open triangles: 5 GeV /c ; filledrectangles: 8 GeV /c ; open circles: 12 GeV /c ). The error bars represent the combination of statisticaland systematic uncertainties. 12igure 4: Double-differential cross-sections for π + and π − production in p–C, p–Cu and p–Sn interactionsas a function of momentum averaged over the angular region covered by this experiment (shown in mrad).The left panel of each pair shows forward production (350 mrad ≤ θ < ≤ θ < /c ; open triangles: 5 GeV /c ; filled rectangles: 8 GeV /c ;open circles: 12 GeV /c ). The error bars obtained after summing the bins of the double-differentialcross-sections take into account the correlations of the statistical and systematic uncertainties.13igure 5: Left: The dependence on the beam momentum of the pion production yields in p–C, p–Cu, p–Sn, p–Ta interactions interactions integrated over the forward angular region (0 .
350 rad ≤ θ < .
550 rad)and momentum (100 MeV /c ≤ p <
700 MeV /c ). Right: The dependence on the beam momentum ofthe pion production yields integrated over the region (0 .
350 rad ≤ θ < .
950 rad and 250 MeV /c ≤ p <
500 MeV /c ) with the same meaning of the symbols. The results are given in arbitrary units, with aconsistent scale between the left and right panel. Although the units are indicated as “arbitrary”, for thelargest region (left panel), the yield is expressed as d σ/ d p dΩ in mb/(GeV /c sr). For the smaller region(left panel) the same normalization is chosen, but now scaled with the relative bin size to show visuallythe correct ratio of number of pions produced in this kinematical region with respect to the yield in thelarger kinematical region. Data points for different target nuclei and equal momenta are slightly shiftedhorizontally with respect to each other to increase the visibility.avoids an important systematic error which would otherwise be introduced by assuming a cross-sectionmodel a priori to calculate the corrections.The largest systematic error corresponds to the uncertainty in the absolute momentum scale, which wasestimated to be around 3% using elastic scattering (see detailed discussion in [12]). It is difficult to betterconstrain the absolute momentum scale, since it depends on the knowledge of the beam momentum(known to 1%) and the measurement of the forward scattering angle in the elastic scattering interaction.At low momentum in the relatively small angle forward direction the uncertainty in the subtraction of theelectron and positron background due to π production is dominant. This uncertainty is split betweenthe variation in the shape of the π spectrum and the normalization using the recognized electrons. Theassumption is made that the π spectrum is similar to the spectrum of charged pions. Initial π − and π + spectra are obtained in an analysis without π subtraction. The π − spectra are then used in the MC forthe π distributions. A full simulation of the production and decay into γ ’s with subsequent conversionin the detector materials is used to predict the background electron and positron tracks. In the regionbelow 120 MeV /c a large fraction of the electrons can be unambiguously identified. These tracks areused as relative normalization between data and MC. The remaining background is then estimated fromthe distributions of the simulated electron and positron tracks which are accepted as pion tracks withthe same criteria as used to select the data. These normalized distributions are subtracted from thedata before the unfolding procedure is applied. Uncertainties in the assumption of the π spectrum aretaken into account by an alternative assumption that their spectrum follows the average of the π − and π + distribution. An additional systematic error of 10% is assigned to the normalization of the π subtractionusing the identified electrons and positrons. 14igure 6: The ratio of the differential cross-sections for π − and π + production in p–C, p–Cu, p–Snand p–Ta interactions as a function of secondary momentum integrated over the forward angular region(shown in mrad). The results are given for four incident beam momenta (filled triangles: 3 GeV /c ; opentriangles: 5 GeV /c ; filled rectangles: 8 GeV /c ; open circles: 12 GeV /c ).15igure 7: The dependence on the atomic number A of the pion production yields in p–C, p–Cu, p–Sn,p–Ta interactions interactions integrated over the forward angular region (0 .
350 rad ≤ θ < .
550 rad) andmomentum (100 MeV /c ≤ p <
700 MeV /c ). The results are given in arbitrary units, with a consistentscale between the left and right panel. The vertical scale used in this figure is consistent with the one inFig. 5.The target region definition and the uncertainty in the PID efficiency and background from tertiaries areof similar size and are not negligible. Relatively small errors are introduced by the uncertainties in theabsorption correction, absolute knowledge of the angular and the momentum resolution. The correctionfor tertiaries (particles produced in secondary interactions) is relatively large at low momenta and largeangles. As expected, this region is most affected by this component.As already mentioned above, the overall normalization has an uncertainty of 2%, and is not reportedin the table. It is mainly due to the uncertainty in the efficiency that beam protons counted in thenormalization actually hit the target, with smaller components from the target density and beam particlecounting procedure. Very few pion production data sets are available in the literature for p–C, p–Cu and p–Sn interactions inthis energy region. Our data can be compared with results from Ref. [24] and [25] where measurementsof π − production are reported in 4.2 GeV /c and 10 GeV /c p–C interactions, respectively. The totalnumber of π − observed in the above references is about 1300 (5650) in the 4.2(10) GeV /c data. In thepapers cited above no tables of the double differential cross-sections were provided, the measurementsbeing given in parametrized and graphical form only. The authors of Ref. [24] and [25] give the results asa simple exponential in the invariant cross-section: EA d σ d p , where E and p are the energy and momentumof the produced particle, respectively, and A the atomic number of the target nucleus . Unfortunately, noabsolute normalization is given numerically. To provide a comparison with these data, the parametrization their spectra are parametrized in each angular bin with a function of the form f π − = c exp ( − T/T ), where T is thekinetic energy of the produced particle and T is given by T = T ′ / (1 − β cos θ ). For the 4.2 GeV /c data the values of theparameters are T ′ = (0 . ± . /c and β = 0 . ± .
04 and T ′ = (0 . ± . /c and β = 0 . ± .
02 forthe 10 GeV /c data. Momentum range (MeV /c )
100 – 300 300 – 500 500 – 700
Angle range: from (rad) to (rad)
Error source 3 GeV /c beam Absorption 1.0 0.7 0.6 0.5 0.3 0.1 0.3 0.5Tertiaries 2.9 2.2 1.3 2.6 2.2 0.9 0.4 0.0Target region cut 2.3 0.6 0.4 1.2 0.6 0.6 1.1 0.3Efficiency 1.5 1.8 1.5 1.4 2.4 2.6 1.7 2.8Shape of π π Total systematics
Statistics /c beam Absorption 1.0 0.6 0.5 0.5 0.2 0.0 0.3 0.6Tertiaries 2.8 1.9 0.9 2.5 2.2 1.5 0.3 0.3Target region cut 1.7 0.9 0.8 2.1 0.1 0.4 1.1 1.0Efficiency 1.7 2.1 1.7 1.2 2.1 3.0 1.2 2.5Shape of π π Total systematics
Statistics /c beam Absorption 1.0 0.6 0.4 0.5 0.2 0.0 0.3 0.7Tertiaries 2.8 1.8 0.5 2.5 2.1 1.4 0.5 0.4Target region cut 4.1 2.7 1.8 3.6 1.3 1.0 2.5 1.9Efficiency 1.5 2.1 1.4 1.1 1.8 2.3 1.2 2.1Shape of π π Total systematics
Statistics
12 GeV /c beam Absorption 1.0 0.6 0.3 0.5 0.2 0.0 0.2 0.6Tertiaries 1.6 1.2 0.1 1.8 1.3 0.7 0.2 0.8Target region cut 3.8 1.9 1.4 2.4 1.0 0.0 1.6 0.3Efficiency 1.4 1.9 1.4 1.1 1.7 2.4 1.0 2.1Shape of π π Total systematics
Statistics p (GeV /c ) Angle (mrad)
950 1550 2150 950 1550 2150 950 1550 /c Total syst.
Statistics /c Total syst.
Statistics /c Total syst.
Statistics
12 GeV /c Total syst.
Statistics was integrated over the angular bins used in our analysis and with an arbitrary overall normalizationoverlaid to our results. We compare the 4.2 GeV /c parametrization of Ref. [24] with our 5 GeV /c data and the Ref. [25] parametrization with our 12 GeV /c data. In the comparison with the 4.2 GeV /c parametrization the normalization c is a simple constant, while for the 10 GeV /c parametrization a smooth θ -dependence consistent with a graphical analysis of Ref. [25] was used. Thus only the comparison ofthe slopes with secondary momentum can be considered significant. Since the 8 GeV /c and 12 GeV /c p–C results are very similar, the lack of data with an exactly equal beam momentum does not play animportant role. The results of this comparison are shown in Fig. 8. The shaded band gives the excursionof the parametrization due to the error in the slope parameters ( ± σ ) with an additional assumed 10%error on the absolute scale. The latter additional error takes into account the fact that the errors on theslopes fitted to the individual angular bins in the cited data are at least a factor of two larger than inthe exponential slope obtained from their global parametrization. The agreement of our data with thesimple parametrization is good. To judge the quality of the comparison, one should keep in mind thatthe statistics of Ref. [24] and [25] is much smaller (1300 π − and 5650 π − , respectively) than the statisticsof the π − samples in our 5 GeV /c and 12 GeV /c data (18,000 and 43,000 π − , respectively). The errorson the slopes fitted to the individual angular bins in the cited data are at least a factor of two larger thanin the exponential slope obtained from their global parametrization. The bands in the figure extend overthe region where data from Ref. [24] and Ref. [25] are available.Our p–C and p–Cu data can also be compared with π + and π − production measurements taken with12 GeV /c incident protons from Ref. [26]. These data were taken with a magnetic spectrometer and onlymeasurements at 90 degrees from the initial proton direction are available. The statistical point–to–pointerrors are quoted to be 3%, while the overall normalization has a 30% uncertainty due to the knowledgeof the acceptance. In Fig. 9 their p–C data are shown together with the p–C data reported in this paper.The filled boxes show the data directly from Ref. [26], while the open boxes are scaled with a factor 0.72.This factor was defined by scaling the average of the π − and π + data from Ref. [26] at 179 MeV /c and242 MeV /c to the HARP data averaged over the same region. The scale factor is within one standarddeviation of the systematic normalization uncertainty of Ref. [26]. The latter data set compares well withthe data described in this paper (filled circles) in the angular region 1.35 rad ≤ θ < /c data of Ref. [24] with the 5 GeV /c data reportedhere; the right panel shows the comparison of the 10 GeV /c parametrization of [25] with the 12 GeV /c data. The absolute normalization of the parametrization was fixed to the data in both cases. Theband shows the range allowed by varying the slope parameters given by [24] and [25] with two standarddeviation and a 10% variation on the absolute scale. The angular ranges are shown in mrad in the panels.drawn, for the scaled data only their quoted statistical error of 3% is shown. The agreement of the twodata sets is excellent. The fact that the two scale factors are different may be due to the fact that thescale uncertainty in Ref. [26] holds separately for data sets taken with different target nuclei.Available data at 12.3 GeV/c from the E910 experiment [27] are in reasonable agreement with our p–Curesults as shown in Fig. 11. In order to take into account the different angular binnings which preventa direct comparison, a Sanford-Wang parametrization is fitted to our data. The fit is performed to thedata redefined as d σ π / d p dΩ . An area between two parametrizations is defined which contains our datapoints as shown in Fig. 11 (top panels). It is visible that the parametrization is not a perfect descriptionto our data. Therefore, we define a band of ±
15% around the best fit which contains almost all theHARP data points. The same parametrizations are then displayed in the binning of E910. While theshape of the distributions are similar for both π + and π − in HARP and E910 data sets, the absolutenormalizations disagree by 5%–10%. For the individual data sets the systematic errors are between 5%and 10% depending on the range of secondary momentum. Since these errors are correlated betweenbins, the discrepancy in the π + and π − data separately are of the order of one standard deviation.However, the effects are opposite in π + and π − , giving a 15% difference in the π + / π − ratio between twoexperiments which is of the order of two standard deviations. This effect may point to an underestimationof systematic effects on the absolute normalization in one of the experiments or in the PID efficiency.Part of the difference is also due to an imperfect parametrization of our data sample. Owing to thesymmetry of the HARP TPC, including its trigger counter, we do not expect a large systematic error inthe HARP data between π + and π − production cross-sections.19igure 9: Comparison of the HARP results with π + and π − production data at 90 degrees from Ref. [26]taken with 12 GeV /c protons. The left panel shows the comparison of the π + production data of Ref. [26]with the data reported here; the right panel shows the comparison with the π − production data. Thesmaller filled boxes show the data directly from Ref. [26], while the open boxes are scaled as explainedin the text. The latter data set compares well with the data described in this paper (filled circles) in theangular region 1.35 rad ≤ θ < An analysis of the production of pions at large angles with respect to the beam direction for protons of3 GeV /c , 5 GeV /c , 8 GeV /c and 12 GeV /c impinging on thin (5% interaction length) carbon, copperand tin targets is described. The secondary pion yield is measured in a large angular and momentumrange and double-differential cross-sections are obtained. A detailed error estimation has been discussed.Results on the dependence of pion production on the target atomic number A are also presented.The use of a single detector for a range of beam momenta makes it possible to measure the dependenceof the pion yield on the secondary particle momentum and emission angle θ with high precision. The A dependence of the cross-section can be studied using the combination of the present data with the dataobtained with tantalum [12].Very few pion production measurements in this energy range are reported in the literature. The onlycomparable results found in the literature agrees with the analysis described in this paper. Hadronicproduction models describing this energy range can now be compared with our new results and, if needed,improved. Data taken with different target materials and beam momenta will be presented in subsequentpapers. We gratefully acknowledge the help and support of the PS beam staff and of the numerous technical col-laborators who contributed to the detector design, construction, commissioning and operation. In partic-ular, we would like to thank G. Barichello, R. Brocard, K. Burin, V. Carassiti, F. Chignoli, D. Conventi,G. Decreuse, M. Delattre, C. Detraz, A. Domeniconi, M. Dwuznik, F. Evangelisti, B. Friend, A. Iaciofano,20igure 10: Comparison of the HARP data with π + and π − production data at 90 degrees from Ref. [26]taken with 12 GeV /c protons. The left panel shows the comparison of the π + production data of Ref. [26]with the data reported here; the right panel shows the comparison with the π − production data. Thesmaller filled boxes show the data directly from Ref. [26], while the open boxes are scaled as explainedin the text. The latter data set compares well with the data described in this paper (filled circles) in theangular region 1.35 rad ≤ θ < π + and π − production data from Ref. [27] taken with12.3 GeV /c protons. The top panels show a parametrization of the π + (left) and π − (right) productiondata described in this paper. The data have been normalized to represent d σ π / d p dΩ . The shaded bandrepresents the area between two parametrization which contain the data points. The bottom panels showthe comparison of the same parametrization, now binned according to the E910 data. The bottom left(right) panel shows the π + ( π − ) production data of Ref. [27]. The angular regions are indicated in mradin the upper right-hand corner of each plot. 22 Cross-section data
Table 4: HARP results for the double-differential π + production cross-section in the laboratory system, d σ π + / ( dpdθ ) for carbon. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin,where p and θ are the pion momentum and polar angle, respectively. The central value as well as thesquare-root of the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± π − production cross-section in the laboratory system, d σ π − / ( dpdθ ) for carbon. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin,where p and θ are the pion momentum and polar angle, respectively. The central value as well as thesquare-root of the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± π + production cross-section in the laboratory system, d σ π + / ( dpdθ ) for copper. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin,where p and θ are the pion momentum and polar angle, respectively. The central value as well as thesquare-root of the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± π − production cross-section in the laboratory system, d σ π − / ( dpdθ ) for copper. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin,where p and θ are the pion momentum and polar angle, respectively. The central value as well as thesquare-root of the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± π + production cross-section in the laboratory system, d σ π + / ( dpdθ ) for tin. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin, where p and θ are the pion momentum and polar angle, respectively. The central value as well as the square-rootof the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π + / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± π − production cross-section in the laboratory system, d σ π − / ( dpdθ ) for tin. Each row refers to a different ( p min ≤ p < p max , θ min ≤ θ < θ max ) bin, where p and θ are the pion momentum and polar angle, respectively. The central value as well as the square-rootof the diagonal elements of the covariance matrix are given. θ min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± min θ max p min p max d σ π − / ( dpdθ )(rad) (rad) (GeV /c ) (GeV /c ) (barn/(GeV /c rad)) GeV / c 5 GeV / c 8 GeV / c 12 GeV / c ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± eferences [1] M. G. Catanesi et al. , HARP Collaboration, “Proposal to study hadron production for the neutrinofactory and for the atmospheric neutrino flux”, CERN-SPSC/99-35 (1999).[2] A. Blondel et al. , CERN-2004-002, ECFA/04/230.[3] G. Battistoni, Nucl. Phys. Proc. Suppl. B100 (2001) 101.[4] T. Stanev, Rapporteur’s talk at the 26th Int. Cosmic Ray Conference (Salt Lake City, Utah, USA;eds. B.L. Dingus et al. , AIP Conf. Proceedings 516, (2000) 247).[5] T. K. Gaisser, Nucl. Phys. Proc. Suppl.
B87 (2000) 145.[6] R. Engel, T. K. Gaisser and T. Stanev, Phys. Lett.
B472 (2000) 113.[7] M. Honda, Nucl. Phys.
B77 (1999) 140.[8] M. H. Ahn et al. , K2K Collaboration, Phys. Rev. Lett. (2003) 041801.[9] M. H. Ahn et al. , K2K Collaboration, Phys. Rev. D74 (2006) 072003, arXiv:hep-ex/0606032.[10] E. Church et al. , BooNe Collaboration, “A proposal for an experiment to measure muon-neutrino → electron-neutrino oscillations and muon-neutrino disappearance at the Fermilab Booster: BooNE”,FERMILAB-PROPOSAL-0898, (1997));A. A. Aguilar-Arevalo et al. , BooNE Collaboration, arXiv:0704.1500, 2007.[11] A. A. Aguilar-Arevalo et al. , SciBooNE Collaboration, “Bringing the SciBar detector to the Boosterneutrino beam,” FERMILAB-PROPOSAL-0954, (2006), arXiv:hep-ex/0601022.[12] M. G. Catanesi et al. , HARP Collaboration, Eur. Phys. J. C51 (2007) 787, arXiv:0706.1600.[13] M. Anfreville et al. , Nucl. Instrum. Meth. A481 (2002) 339.[14] M. Baldo-Ceolin et al. , Nucl. Instrum. Meth.
A532 (2004) 548;M. Bonesini et al. , IEEE Trans. Nucl. Sci. NS-50 (2003) 1053.[15] M. G. Catanesi et al. , HARP Collaboration, Nucl. Instrum. Meth.
A571 (2007) 527;
A571 (2007)564.[16] M. G. Catanesi et al. , HARP Collaboration, Nucl. Phys.
B732 (2006) 1, arXiv:hep-ex/0510039.[17] M. G. Catanesi et al. , HARP Collaboration, Eur. Pys. J. C52 (2007) 29, arXiv:hep-ex/0702024.[18] E. Radicioni, presented at NSS2004, IEEE Transaction on Nuclear Science, Vol 52, N 6 (2005) 2986.[19] M. Bogomilov et al. , Nucl. Instrum. Methods
A508 (2003) 152;G. Barr et al. , Nucl. Instrum. Methods
A533 (2004) 214;M. Bogomilov et al. , IEEE Transaction on Nuclear Science (2007) 342.[20] L. Durieu, A. Mueller and M. Martini, PAC-2001-TPAH142 Presented at IEEE Particle AcceleratorConference (PAC2001), Chicago, Illinois, 18-22 Jun 2001 ;L. Durieu et al. , Proceedings of PAC’97, Vancouver, (1997);L. Durieu, O. Fernando, CERN PS/PA Note 96-38.[21] K. Pretzl et al. , Invited talk at the “International Symposium on Strangeness and Quark Matter”,Crete, (1999) 230.[22] G. D’Agostini, Nucl. Instrum. Meth.
A362 (1995) 487.[23] S. Agostinelli et al. , GEANT4 Collaboration, Nucl. Instrum. Meth.
A506 , (2003) 250.[24] G. H. Agakishiev et al. , (in Russian), Sov. J. Nucl. Phys. (1990) 1009; JINR-P1-89-793, 1989.3525] D. Armutliiski et al. , “Hadron spectra in hadron–nucleus collisions” (in Russian), JINR-P1-91-191,1991.[26] T.-A. Shibata et al. , Nucl. Phys. A 408 (1983) 525.[27] I. Chemakin et al. , E910 Collaboration, Phys. Rev.