Absolute Momentum Calibration of the HARP TPC
aa r X i v : . [ phy s i c s . i n s - d e t ] A p r Preprint typeset in JINST style - HYPER VERSION
Absolute Momentum Calibration of the HARP TPC
M.G. Catanesi, E. Radicioni
Università degli Studi e Sezione INFN, Bari, Italy
R. Edgecock, M. Ellis , F.J.P. Soler Rutherford Appleton Laboratory, Chilton, Didcot, UK
C. Gößling
Institut für Physik, Universität 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 Università degli Studi e Sezione INFN, Ferrara, Italy
A. Artamonov , S. Giani, S. Gilardoni, P. Gorbunov , A. Grant, A. Grossheim ,V. Ivanchenko , A. Kayis-Topaksu , J. Panman, I. Papadopoulos, E. Tcherniaev,I. Tsukerman , R. Veenhof, C. Wiebusch , P. Zucchelli , CERN, Geneva, Switzerland
A. Blondel, S. Borghi , M.C. Morone , G. Prior , R. Schroeter Section de Physique, Université de Genève, Switzerland
C. Meurer
Institut für Physik, Forschungszentrum Karlsruhe, Germany
U. Gastaldi
Laboratori Nazionali di Legnaro dell’ INFN, Legnaro, Italy
G. B. Mills Los Alamos National Laboratory, Los Alamos, USA
J.S. Graulich , G. Grégoire Institut de Physique Nucléaire, UCL, Louvain-la-Neuve,Belgium
M. Bonesini, F. Ferri
Sezione INFN Milano Bicocca, Università degli Studi Milano Bicocca, Milano, Italy – 1 – . 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
Università “Federico II” e Sezione INFN, Napoli, Italy
L. Coney , D. Schmitz Columbia University, New York, USA
G. Barr, A. De Santo Nuclear and Astrophysics Laboratory, University of Oxford, UK
F. Bobisut, D. Gibin, A. Guglielmi, M. Mezzetto ∗ Università degli Studi e Sezione INFN, Padova, Italy
J. Dumarchez
LPNHE, Universités de Paris VI et VII, Paris, France
U. Dore
Università “La Sapienza” e Sezione INFN Roma I, Roma, Italy
D. Orestano, F. Pastore, A. Tonazzo, L. Tortora
Università degli Studi e Sezione INFN Roma III, Roma, Italy
C. Booth, 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
Università degli Studi e Sezione INFN, Trieste, Italy
J. Burguet–Castell, A. Cervera–Villanueva, J.J. Gómez–Cadenas, J. Martín–Albo,P. Novella, M. Sorel – 2 – nstituto de Física Corpuscular, IFIC, CSIC and Universidad de Valencia Now at FNAL, Batavia, Illinois, USA. Now at University of Glasgow, UK. Also supported by LPNHE, Paris, France. Now at Imperial College, University of London, UK. ITEP, Moscow, Russian Federation. Now at SpinX Technologies, Geneva, Switzerland. Now at TRIUMF, Vancouver, Canada On leave of absence from Ecoanalitica, Moscow State University, Moscow, Russia. Now at Çukurova 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. MiniBooNE Collaboration. Now at Section de Physique, Université de Genève, Switzerland, Switzerland. Now at Royal Holloway, University of London, UK. A BSTRACT : In the HARP experiment the large-angle spectrometer is using a cylindrical TPC asmain tracking and particle identification detector. The momentum scale of reconstructed tracksin the TPC is the most important systematic error for the majority of kinematic bins used forthe HARP measurements of the double-differential production cross-section of charged pions inproton interactions on nuclear targets at large angle. The HARP TPC operated with a number ofhardware shortfalls and operational mistakes. Thus it was important to control and characterize itsmomentum calibration. While it was not possible to enter a direct particle beam into the sensitivevolume of the TPC to calibrate the detector, a set of physical processes and detector propertieswere exploited to achieve a precise calibration of the apparatus. In the following we recall themain issues concerning the momentum measurement in the HARP TPC, and describe the cross-checks made to validate the momentum scale. As a conclusion, this analysis demonstrates that themeasurement of momentum is correct within the published precision of 3%.K
EYWORDS : Time projection chambers, Detector alignment and calibration methods. ∗ Corresponding author, e-mail: [email protected] ontents
1. Introduction 1
2. Elastic scattering data 4
3. Track residuals with positive and negative settings 124. Consistency checks of the momentum calibration with d E / d x
5. Comparison with time-of-flight measurements 166. Conclusions 197. Acknowledgments 20A. Appendix: Treatment of the Dynamic Distortions 21
1. Introduction
The HARP experiment [1, 2] at the CERN PS was designed to make measurements of hadronyields from a large range of nuclear targets and for incident particle momenta from 1.5 GeV / c to15 GeV / c . The main aims are to measure pion yields for a quantitative design of the proton driverof a future neutrino factory, to provide hadron production cross-sections for precision calculationsof the atmospheric neutrino flux [3] and to measure particle yields as input for the flux calculationof accelerator neutrino experiments, such as K2K [4], MiniBooNE and SciBooNE [5].– 1 – igure 1. Left panel: schematic layout of the TPC. The beam enters from the left. Starting from the outside,first the return yoke of the magnet is seen, closed with an end-cap at the upstream end, and open at thedownstream end. The field cage is positioned in the middle of the magnetic volume. The inner field cage isvisible as a short cylinder entering from the left. The ITC trigger counter and target holder are located insideof the inner field cage. Right panel: mechanical drawing of a sector of the TPC pad plane, the layout of thepads is indicated.
The HARP experiment makes use of a large-acceptance spectrometer consisting of a forwardand large-angle detection system. A detailed description of the experimental apparatus can befound in reference [2]. The forward spectrometer — based on large area drift chambers [6] anda dipole magnet complemented by a set of detectors for particle identification (PID): a time-of-flight wall [7] (TOFW), a large Cherenkov detector (CHE) and an electromagnetic calorimeter —covers polar angles up to 250 mrad which is well matched to the angular range of interest for themeasurement of hadron production to calculate the properties of conventional neutrino beams.The large-angle spectrometer — based on a Time Projection Chamber (TPC) and ResistivePlate Chambers (RPCs), located inside a solenoidal magnet — has a large acceptance in the mo-mentum and angular range for the pions relevant to the production of the muons in a neutrinofactory. It covers the large majority ( ∼ The HARP TPC was designed and built in a record time of about 1.5 years. Its main design featuresare an almost full solid angle acceptance and high-event rate capabilities. It was operated in theyears 2001 and 2002 at the CERN PS. Additional specialized calibration runs were performed in2003.The TPC consists of a cylindrical volume 1.5 m long and 0.8 m diameter filled with a 91% Ar,9% CH gas mixture positioned in a solenoidal magnet with a field of 0.7 T. A 12 kV electric fielddrives the ionization charges at a velocity of 5 cm / m s to the read-out plane, where the inductionsignals are collected by 3972 pads arranged in 20 concentric rows. The pad signals are digitizedin 100 ns time bins, corresponding to about 5 mm bins in the longitudinal direction. A sketch ofthe HARP TPC and of its pad plane is shown in Fig. 1. More technical details can be found inreference [2]. The TPC is the key detector for the analysis of tracks emerging from the target atlarge angles with respect to the incoming beam direction.– 2 –he HARP TPC suffered from a number of shortcomings that were discovered during andafter the data taking [2]:1. A rather large number of deficient electronic channels ( ∼ d ′◦ ). This provides very little penalty in measuring cross sections because already with thisstatistics systematic errors dominate in most of kinematic bins [8, 9].Under these experimental conditions, in the absence of an appropriate calibration system andwithout the possibility of exposing the TPC to test-beams, a wide range of experimental cross-checks has been employed to assess the momentum scale in the HARP TPC, as described in thefollowing. The momentum measurement in the HARP TPC is a direct result of the calculation based on themeasured track curvature and the known magnetic field, no ad hoc correction factor has beenapplied to make the measurement agree with the benchmarks. Thus, the determination of the scaleshould be considered as a cross-check rather than a calibration.A bias on the momentum scale as measured by a TPC is typically related to a sagitta error: d ( p T ) / p T = s · · q · p T / ( . · B · L ) (1.1)Where the sagitta s and the track length L are in meters (0.5 m is the typical track length in HARP),the magnetic field B in Tesla (0.7 T in HARP), the track momentum p T is in GeV / c , q is the signof the charge of the particle.Unfortunately, it was not possible to send a direct beam of particles into the sensitive volumeof the TPC. In the absence of such a beam, well defined procedures were used to determine theabsolute calibration of the absolute momentum calibration of the TPC.– 3 – The momentum scale in the TPC was characterized by using proton–proton elastic scatteringdata as benchmark, see Section 2, in two different ways:1. By using the incident proton momentum and direction (measured by the beam MWPCs)and the momentum and direction of the proton scattered at large angle, measured bythe TPC, the missing mass squared M x is determined for every event (see Section 2.1).A bias in the momentum scale would reflect in a bias in the M x calculation.2. The angle of the forward scattered particle is used (measured by the forward spectrom-eter) together with the momentum and direction of the incoming proton to predict fromthe kinematics of the elastic scattering the recoil proton momentum and direction. Thisprediction is then compared with the measured momentum of the recoil proton (seeSection 2.2). Special care has been devoted in this test to avoid any bias due to thedifferent energy losses of protons (measured in elastic scattering events) against pions(cross section measurements), as described in Section 2.2.3. • As an additional cross-check, one can also look at the d E / d x distribution, see Section 4. Asatisfactory description of the p –d E / d x distribution is obtained after the TPC calibration. Al-though less precise than the elastic scattering kinematics this method can be used to excludelarge biases. • A sagitta error would have opposite sign for positively and negatively charged particles andwould grow linearly with p T . It would thus be detectable, regardless of the absolute scale,by a dependence of the measured total momentum on the track angle for samples of trackswith different angles for which one can ensure that they have the same total momentum.These samples, as discussed in Section 4.2, can be defined using protons in fixed regions ofrelatively high d E / d x (d E / d x depends only on the total momentum). • The p – b relation using the time-of-flight measurement with the RPCs can also be used asa relatively weak cross-check, see Section 5. The precision of this method is limited bythe understanding of the detector physics of the RPCs in combination with the very shortflight-path.
2. Elastic scattering data
This analysis has been already published in [2] and it is only briefly summarized here. Eventsfrom the 3 GeV / c momentum runs are selected by requiring standard beam selection criteria forprotons and only 1 or 2 prong events in the TPC. The 2-prong events are determined by veryloose kinematical cuts: | ( f − f ) − p | < . ( q + q ) < .
75 rad, where f , f , q , q are, respectively, the azimuthal and polar angles of the two tracks. Further selection criteria areapplied to the large-angle track, that is used for the final analysis: the particle is positively charged In principle it is enough to measure the angle of the scattered proton to predict its momentum. We did not followthis method because a) we use the angle to select a clean sample of elastic scattering events and b) the angle of protonsis affected by multiple scattering in the material around the target – 4 – igure 2.
Missing mass in 3 GeV / c pp scattering. The result (solid line) is centered very close to the PDGvalue of the squared proton mass. An artificial shift of 15% of the momentum measured was applied toobtain the dashed histogram. Such a shift is clearly excluded by the data (see the text). and well measured over a minimum of 10 points; the reconstructed momentum is in the range320 MeV / c ≤ p <
620 MeV / c . The tracks must come from the target and must be recognizedas a proton with a d E / d x selection.The missing mass is then computed as: M x = ( p beam + p target − p TPC ) (2.1)where p beam , p target , p TPC are the 4-momenta of the incoming beam particle, target particle and theparticle scattered at large angle and measured in the TPC, respectively.The result of this analysis is shown in Fig. 2. A fit to the distribution of Fig. 2 provides h M x i = . ± . / c ( c / ndof = . /
17 in the 0 . − . / c range for a fitusing a Gaussian plus a linear background as description) in agreement with the PDG value of0 . / c .To study the effect of a momentum scale bias over the reconstructed missing mass, we havereconstructed the same distribution by displacing the momentum of the reconstructed track by 15%.As shown in Fig. 2 such a bias would produce a displacement of about 0 .
085 GeV / c on M x .Systematic errors to this measurement come from uncertainties on the primary beam particlemomentum, correction for proton energy losses in the material of the cryogenic target and innerfield cage. As a result, the momentum scale is estimated to be correct to better than 3.5% (at onestandard deviation). Longitudinal position of the point of minimum distance between the beam axis and the track extrapolation in thedirection of the interaction vertex must be in the range of −
50 mm ≤ z <
70 mm, where z is the coordinate along thebeam direction – 5 – .2 Comparison of the measured proton momentum with the elastic scattering predictions Elastic scattering interactions of protons and pions off hydrogen provide events where the kinemat-ics is fully determined by any of the kinematic quantities and in particular by the direction of theforward scattered beam particle. These kinematic properties of the elastic scattering reaction wereexploited to provide a known ‘beam’ of protons pointing into the TPC sensitive volume. Data weretaken with liquid hydrogen targets at beam momenta of 3 GeV / c , 5 GeV / c and 8 GeV / c . A good fraction of forward scattered protons or pions in the elastic scattering reaction enter intothe acceptance of the forward spectrometer (about 50% depending on the beam momentum).Both direction and momentum of the recoil proton are then predicted.Selecting events with one and only one track in the forward spectrometer and requiring that themeasured momentum and angle of the forward track are consistent with an elastic reaction alreadyprovides an enriched sample of elastic events. To be counted, tracks need not to be inside theacceptance of the dipole magnet, but need only to be detected in the upstream drift chamber whichcovers the full acceptance of particles exiting the aperture of the solenoid magnet which houses theTPC. By requiring that only one barrel RPC hit is recorded at the position predicted for an elasticevent (the precision of the prediction from the forward spectrometer is within the RPC pad size)and within a time window consistent with a proton time-of-flight, a sample of recoil protons withknown momentum vector is obtained with a purity of about 99%.The requirement of one RPC hit is relaxed for events where the recoil proton momentum ispredicted to be low enough that it can be absorbed in the material in front of the RPCs. In suchcases also events without any RPC hit are accepted. The additional requirement that the recoilangle is consistent with elastic scattering is then used to ensure a pure sample. At beam momentain the range 3 GeV / c –8 GeV / c the kinematics are such that these protons point into the TPC withangles of ≈ ◦ with respect to the beam direction.The correlation of the forward scattering angle and recoil proton momentum introduces an un-avoidable threshold in recoil proton momentum ( ≈
350 MeV / c ) which translates into a minimumangle for the scattered particle. The threshold is relatively high due to the need to detect the protonalso in the barrel RPC system outside the outer field cage of the TPC. As mentioned above, thisrequirement can be removed only in cases where a somewhat larger background can be tolerated.Due to the geometry of the rectangular aperture of the dipole magnet of the forward spec-trometer only two small horizontal sectors of the TPC can be populated with recoil protons abovethreshold momentum in the 3 GeV / c beam. In the 5 GeV / c beam the situation is much betterand all azimuthal angles can be populated, although not yet homogeneously. In the 8 GeV / c beamthe population is homogeneous in f , but the error propagation of the measurement of the forwardscattering angle into the prediction of momentum and angle of the recoil proton becomes less fa-vorable.The numbers of selected elastic events amount to about 15,000 for the 8 GeV / c data sam-ple, and 5,000 for each of the 5 GeV / c and 3 GeV / c data samples. The exposures with highermomentum beams have not been used for this study.– 6 – igure 3. Left panel: p T of the recoil protons in used in the proton and pion elastic scattering data (5 GeV / c runs) using the forward spectrometer to determine the kinematics. Right panel: typical distribution of the p T of pion tracks used in the cross section measurement for 8.9 GeV / c p–Be interactions in the angular rangeof the analysis before p and p T cuts. With elastic scattering we can check the reconstructed momentum of protons, while in cross sectionmeasurements we are interested in the momentum of pions. If the momentum scale is influencedby a bias, however, protons are a robust check provided that their momentum in elastic scatteringevents is similar to the momentum of pions in cross section measurements and that their higherenergy losses do not influence the measurement. The comparison of the p T of protons from elasticevents and the p T of pions in a typical setting, Fig. 3, shows that with elastic scattering most of therange of interest is covered.The possibility that the energy loss of low momentum protons can alter the momentum recon-struction is discussed in the following section. Since the energy loss in the material of the cryogenic target, trigger counter, and inner field cageis large for protons in the energy range covered by elastic scattering, there is a significant changeof curvature of their trajectory in that region of the detector. This effect introduces a bias in themeasurement of the momentum if one uses the vertex constraint for these low-momentum protons.Therefore, the behaviour of the momentum measurement for protons was studied without makinguse of the vertex constraint. If one would use a vertex constraint in the fit for these protons onewould either have to modify the algorithm to take into account the change of curvature induced bythe large energy loss in the inner field cage or one would have to correct a posteriori for the bias.– 7 – igure 4.
Comparison of the unconstrained ( p
1) and constrained ( p
2) momentum ( p / p −
1) for pions(above 350 MeV / c ) using data (from different target materials) and the corresponding Monte Carlo. Thedata are indicated by the black histogram and the Monte Carlo by the dashed histogram. The position of thepeak is at zero well within 1% and the mean is 2% both for data and MC. The first 50 events in the spill areused. The former option, the use of a modified algorithm, would not validate the standard code used forthe minimum ionizing pions. The latter option is used in the analysis described in Section 2.1.Inside the TPC gas volume the energy losses of protons are negligible so that they can indeed beused to validate the procedures in a way also applicable to the situation for pions.Constrained and unconstrained fits are sensitive in the identical way to any sagitta error, sincethe vertex position is not influenced by distortions in the TPC.For pions and high momentum protons it was checked independently that the constrained fitis unbiased with respect to the unconstrained fit for tracks reconstructed in the real data and in thesimulated data. In Fig. 4 it is shown that the vertex constraint does not introduce biases for thoseparticle trajectories and that the simulation provides an excellent description of the behaviour of theresolution function. The comparison of the unconstrained ( p
1) and constrained ( p
2) momentum( p / p −
1) for data and Monte Carlo shows that the position of the peak is centered at zero wellwithin 1% and that the average is about 2% both for data and MC.
In this comparison, only the first 50 events in the spill were used in order to avoid the effect ofdynamic distortions in the unconstrained fit (see also Appendix A). Given the beam conditionsof the run under study here, this condition guarantees the same data quality as in the analyses ofreferences [8, 9]. – 8 – igure 5.
The momentum bias of the fit without vertex constraint measured with elastic scattering data(3 GeV / c : open squares, 5 GeV / c : open circles) as a function of the momentum predicted by the forwardscattered track. In the absence of a clear trend, the average of the points constrains the bias to be smallerthan 3%. For these comparisons only the first 50 events in the spill are used since the unconstrained fit issensitive to dynamic distortions beyond this value. The comparison of predicted momentum and the momentum reconstructed without vertex con-straint is shown as a function of predicted momentum in Fig. 5. The relative average difference is(2 ± To improve the statistics of this check, we make use of the full statistics by applying the correctionof the dynamic corrections (see Appendix A) and we add elastic scattering p + − p events to theproton elastic scattering sample and analyse separately p − − p events . One should note thatthe effect of a trajectory distortion creates the same momentum shift if a systematic shift on thesagitta is caused by an E × B effect, since both the effect and the curvature for protons changesign simultaneously. Therefore these two settings are expected to provide consistent results. The In the following figures the label “positives” indicates the recoil protons in elastic scattering events in the positivebeam, and “negatives” is used to label the protons in the negative beam. – 9 – igure 6. D ( p − ) / p − plot for protons produced in p + p and pp elastic scattering, combining data from the3, 5 and 8 GeV / c primary beam momenta. Left panel: first 50 events in the spill, no corrections for dynamicdistortions. Central panel: first 100 events in the spill, with corrections for dynamic distortions. Right panel:events 101–200 in the spill, with corrections for dynamic distortions. Figure 7. D p − / p − plot for p − p elastic scattering, combining data from the 3, 5 and 8 GeV / c primarybeam momenta, computed with the corrections for dynamic distortions of the TPC. Left panel: first 100events in the spill, right panel: events 101–200 in the spill. difference between the predicted and the measured 1 / p (after corrections for the energy loss of theproton prior to entering the TPC), is shown in Fig. 6. As mentioned above, this procedure has anintrinsic 2% systematic error coming from the determination of the incoming beam momentum andfrom the angle measurement with the forward spectrometer.The following results were obtained: • The elastic scattering sample using the first 50 events (without corrections for dynamic dis-tortions) and the elastic scattering sample using the events, corrected for dynamic distortions,from 1 to 100 and from 101 to 200 are fully compatible (see Fig. 6); • With the larger statistics allowed by the use of 200 events per spill it is now possible to– 10 – igure 8.
Average momentum of particles with a d E / d x in the TPC corresponding to 7-8 MIP, as measuredin 31 different settings. The horizontal dashed lines correspond to a variation of ±
2% around the averagevalue of 340 MeV / c . The different settings are labeled with the material of the target and the momentum, inGeV / c , of the incident beam. compare “positives” ( p + p and pp) (Fig. 6) and “negatives” ( p − p) (Fig. 7).The distribution for “positives” has an average D ( p − ) / p − equal to − . ± . h D ( p − ) / p − i = . ± . h D ( p − ) / p − i = − . ± . To check that the results obtained with the elastic events on the hydrogen target are stable in theother data taking settings, we have selected a narrow d E / d x region corresponding to 7–8 MIP. Inthis region the pion contamination is negligible and protons have an average momentum of 340MeV / c .The average reconstructed momentum of protons in this band is shown in Fig. 8 for 31 differentsettings. All the settings provide an average momentum within ±
2% around the average value of340 MeV / c , demonstrating the stability of the momentum scale measured with elastics during theoverall HARP data taking. Particles were only accepted when they were nearly perpendicular tothe beam direction, so that the average p T of this sample is 310 MeV / c .– 11 – igure 9. Left panel: the mean residual D ( R f ) for each pad row of the TPC measured using a B field positivepolarity setting (+5 GeV / c Carbon target data). Top: D ( R f ) in mm. Bottom: D ( R f ) in fraction of RMS .Right panel: Same using a B field negative polarity setting ( − / c Carbon target data). Changing the B field polarity, the swap in sign of the mean residuals in the innermost and outermost pad ring is clearlyvisible
3. Track residuals with positive and negative settings
A way to monitor the presence of residual distortions (when the dynamic distortion correction isnot applied) is to look at the D ( R f ) difference between the coordinate of the track measured in eachpad row of the TPC and the trajectory estimated by the circular fit. To do this we have selectedtracks (vertex constrained) hitting the center of the RPC overlap to be able to fix an external point.The cuts applied in the standard analysis have been used. The same residual distributions can beobtained separately for positive and negative magnetic field direction. In this case an E × B effectchanges sign for the two polarities. For this test we used a carbon 5% nuclear interaction length( l I ) target with beam momenta of ± / c respectively.The analysis of the distributions of the residuals shows that the biases are small (in the rangeof ±
200 microns). As expected row number 1 (the innermost) and row number 20 (the outermost)display edge effects ( − m m and +300 m m respectively) which are not fully addressed by thedistortion correction for static misalignment between the inner and outer field cage voltages. Thefact that the residual is larger in the inner row and of opposite sign to that in the outer row isconsistent with the hypothesis that the effect is due to a residual electrostatic field, see Fig. 9 (left).A further confirmation was obtained by looking at the residual distribution for the tracks of the − / c sample where the magnetic field polarity was inverted. In this last case the behaviouris the same but the sign of the residual of the innermost and outermost row is now inverted (+380 m m and − m m respectively), see Fig. 9 (right).By excluding rows 1 and 20 from the fit, one can place a limit of less than 1% on the effect ofthe residual distortion effects on the momentum measurement.– 12 – igure 10. d E / d x − p plot of HARP data, 5% Ta target at 5 GeV / c , fitted with the modified Bethe-Blochfunction (see the text), including the resolution bars for every fitted slice in momentum and d E / d x . The barsare computed from the published momentum resolution and d E / d x resolution for all points. The dashedcurve is the 1 / b curve.
4. Consistency checks of the momentum calibration with d E / d x The d E / d x cannot be used in HARP to estimate the momentum scale with a precision similar to theelastic scattering method because both the scale and offset calibration of d E / d x are free parametersand the resolution in d E / d x , about 17%, is insufficient to achieve such a precision. Nevertheless,the d E / d x – p plot provides a qualitative cross-check of the TPC momentum calibration. Indeed wefind good agreement as shown in Fig. 10.It has been claimed that the disagreement of the d E / d x plots we published in [8] with a 1 / b curve is a clear symptom of a TPC momentum bias, up to 15% [10]. Since the free parameters ofthe d E / d x curve can only be fixed using the point at which particles are minimum ionizing, it willbe immediately clear that a 1 / b description, which reaches its minimum asymptotically, cannotbe an adequate approximation as shown in the comparison of the correct curve and this simpleapproximation in Fig. 10. Since this was not immediately obvious to the authors of Ref. [10], weinclude here a rather pedantic discussion of d E / d x . The average energy loss is described with thestandard Bethe-Bloch formula [11]: − dEdx = Kz ZA b (cid:20)
12 ln 2 m e c b g T max I − b − d ( bg ) (cid:21) . (4.1)For particle identification a truncated mean is tuned to correctly estimate the Landau peakposition (discarding the 20% of points with the highest d E / d x ), and not the mean d E / d x (for– 13 – igure 11. Average reconstructed momentum as a function of event number in spill for protons using a highvalue of d E / d x for the selection. The analysis is performed for the combined data set taken with 3 GeV / c ,5 GeV / c , 8 GeV / c and 12 GeV / c beams on Be, C, Cu, Sn, Ta and Pb targets. The solid line shows theaverage for protons for the first 100 events in the spill. The two dotted lines show the ±
3% variation aroundthe average. which the standard Bethe-Bloch theory applies). Hence each point on the d E / d x – p scatter-plotrepresents the calculation of the most probable d E / d x per TPC pad row, integrated over the tracks’effective path length across each pad row (therefore it represents the peak value of a convolution ofLandau distributions). Its phenomenology can be described sufficiently accurately by a modifiedBethe-Bloch formula [12], as shown in Fig. 10: the d E / d x for protons, pions, the positions of thed E / d x of a minimum ionizing particle (MIP), and intersection points of the bands for differentparticle types are all consistent.To avoid the effect of dynamic distortions the above analyses were done using only the first50 events in each spill. It was checked that the constrained fit remains stable, well within 3%, forabout 100 events in the spill as will be described in the following section. One can select samples of tracks with a well defined momentum by accepting narrow enoughd E / d x intervals in the region of high values (the so-called “1 / b ” region). The d E / d x resolutionis sufficient to select such a proton sample with only a 10% RMS spread in “true” momentum. Ifthe measured average momentum of such samples is compared as a function of event number inthe spill N evt strong constraints on the influence of dynamic distortions on the momentum measure-ments can be obtained.In this analysis particles were selected in narrow bands of d E / d x in regions where d E / d x depends strongly on momentum. To select a sample with the highest possible momentum, theprotons were further required to reach the RPC system (low momentum protons would be absorbedbefore reaching the RPCs). A further selection 1.0 rad < q < T . In addition to a momentum selection also a PID-selection is performed with the same cuts.The analysis was performed for the combined data set taken with 3 GeV / c , 5 GeV / c , 8 GeV / c and12 GeV / c beams on Be, C, Cu, Sn, Ta and Pb targets.The average momentum obtained from a Gaussian fit to the momentum distribution shows thatthe average momentum stays constant within a few percent up to N evt =
100 at p T ≈
350 MeV / c (see Fig. 11).One observes that the behaviour is not compatible with a linear dependence as a function oftime but the average momentum stays constant over a long period before a downward trend setsin. One of the reasons is the fact that the distortion effect does not have a linear dependence atthe beginning of the spill, owing to the fact that the first ions need to exit the amplification zonebefore they distort the field in the drift zone. This is shown in a little more detail in the Appendix.This effect “protects” the first fifty events in the spill very efficiently. Another reason for increasedstability of the constrained fit under the condition of distortions is simply that the weight of thevertex constraint compensates very well for the distortions, up to the point where, when dynamiccorrections are not applied, the tracks are so distorted that the reconstruction efficiency is affected.It has been shown with elastic scattering that the absolute track finding efficiency does notchange as a function of event number in the spill. This result indicates that the distortions arecontinuous and smooth as a function of z and R . However, once quality criteria are applied, mainlythe requirement that the tracks emerge from the target, the efficiency is reduced when the distortionsare increasing during the growth of the ion charge. Since this requirement removes tracks shiftingout of the acceptance at one side, and since the measurements of curvature and of the minimumdistance to the interaction point are correlated, the deviation of the average measured momentumfrom a constant is thus a single-sided efficiency effect.The p T -range covered by this cross-check represents a large range of the kinematic domainused in the analysis. Using a sample of tracks within a fixed interval of d E / d x where the average momentum is ∼
340 MeV / c , and considering that p T = p tot sin q , it is possible to look for a sagitta bias (acting on p T ) through any correlation between h p i and sin q . Unlike previous analyses where the RPC hitswere used to set a minimum range, here such a requirement was avoided not to introduce an angulardependence in the definition of the average energy of the sample. From the fits to Fig. 12 (left) weconclude that a null bias is measured with a precision of about 3%. This analysis has been repeatedusing positive and negative pions and the correction for dynamic distortions with incoming p + inthe positive beam and p − in the negative beam (Ta target, 8 GeV / c ). As shown in Fig. 12 (right),for both magnet polarities there is no significant dependence on sin q .Since the curvature of the protons and of distortions (if of the E × B type) are both inverted,the slope for protons (if any) is expected to have the same sign for positive and negative beams.The fact that there is no significant dependence on sin q confirms the reliability of the HARP TPCcalibration. – 15 – igure 12. Left panel: average momentum in a fixed slice of d E / d x as a function of sin q . Data are collectedwith Be, C, Cu, Sn, Ta and Pb targets at 3, 5 and 8 GeV / c , no correction for dynamic distortions. A fixedshift in sagitta would show up as a linear change of average momentum. These data have been fitted with aconstant term, with a linear function (the best fit corresponds to a momentum bias of ∼ .
5% at 500 MeV / c )and with a linear function with a slope corresponding to a 10% bias (dashed line). While the constant termis compatible with the linear function ( D c = . D c ≃
20. Thus, it is excluded at morethan 5 sigma level. Right panel: same analysis for p + (black squares) and p − (open circles) incident beamsand with the full spill correction for dynamic distortions. These data were taken with opposite magnetic fieldpolarities. Data are collected for 8 GeV / c incident beam on Ta target only. A fixed shift in sagitta wouldshow up with the same slope for positives and negatives. In this case, given a smaller statistics, a 10% biasis excluded at about 90% C.L. ( D c ≃ .
5. Comparison with time-of-flight measurements
The HARP RPC system [13] is positioned as a barrel around the TPC chamber, about 50 cm fromthe interaction target. It can in principle be used to check the momentum calibration comparing the b – p relation of pions and protons, where b is measured using the time-of-flight to reach the RPCsystem.This cross-check is limited in precision due to the short flight distance of the particles and therather large corrections needed to convert the measured threshold crossing time into a measurementof time-of-arrival of the particle. For example the range of the correction for the “time-slewing” ofthe threshold crossing time for different measured integrated charge collected in the RPCs is 2 ns,similar to the total time-of-flight of pions to reach the RPCs [13]. As an additional complication,the momentum range of the particles for which a p – b comparison can be made is in the regionwhere pions are minimum ionizing and where protons are heavily ionizing (with a different d E / d x by a factor of up to 8). Thus one first has to ascertain that the response of the RPC system is wellunderstood before one can use the time-of-flight as a mean to calibrate the momentum measurement– 16 – igure 13. Analysis of D TOF = (measured − predicted) time-of-flight for pions (left panel) and protons(right panel). The measured time is provided by the RPC signal time and the predicted time is based on thetrack momentum measured in the TPC. The numbers refer to RPC pad ring (equivalent to Z position; withpad 3 in the most backward direction). Whereas the pion data are centered near zero, the proton data areshifted to negative times with a positive slope. The dashed line is the prediction for D TOF for a sagitta biasof 1 mm and a track length of 0.5 m. in the TPC.Fig. 13 taken from reference [13] shows the difference of the time-of-arrival measured withthe RPCs, t m , and the time-of-arrival predicted using the momentum measured in the TPC, t p .This plot had been used in [10] to claim a 15% bias in the HARP TPC momentum scale.If a momentum bias would be caused by an error in the measurement of the trajectory sagitta,it would reflect on the b of protons and not on the b of pions, which already saturate b at theHARP momenta. The RPC calibration has been performed using pions, so that one would expectthat these display a vanishing average offset as is the case in Fig. 13. However, the behaviour of themeasured D ( T OF ) for protons does not agree with that predicted by the sagitta model, see Eq (1.1).While data, Fig. 13, exhibits a clear slope, the sagitta model predicts a rather flat dependence of D ( T OF ) on the measured momentum. This flatness comes from the particular momentum rangeof the protons where d ( p ) / p increases linearly with p , while D ( T OF ) decreases with p because b of the protons saturates.The question whether the RPC time measurement suffers from systematic effects due to thelarge difference in primary ionization caused by pions and protons in the momentum range availablefor these calibrations had been addressed with a dedicated RPC calibration analysis studying protonand pion elastic scattering off the cryogenic hydrogen target and reported in reference [14].As for the measurement of the momentum scale, see Section 2, such a measurement makes itpossible to send a “controlled beam” of slow protons through the TPC and towards the RPC system– 17 – igure 14. The difference of the time offset measured in pad ring 3 from the expected time offset forprotons as a function of the momentum along its flight path (in the gas volume of the TPC). The filledcircles show the results of measurements using elastic scattering on hydrogen, the points without markerrepresent the simulation of the measurement using the same reconstruction procedure. The momentum waspredicted using the kinematics of elastic scattering. Consistency of the simulated time difference with zeroshows that the prediction of the flight time (and thus of the momenta) using the elastic scattering kinematicsand Monte Carlo corrections in the reconstruction procedure for respective energy losses are correct. Fromreference [14]. without the need to measure the momentum of the recoil proton with the TPC.An exposure of the HARP detector where a 5 GeV / c beam of protons and pions is directedonto a 60 mm long liquid hydrogen target was used.Results of this analysis are shown in Fig. 14. Due to the kinematics of elastic scattering thevast majority of selected recoil protons which reach the RPC system is measured in pad ring 3.The data exhibit a clear deviation pointing to a difference in RPC time response to protons asa function of the momentum. The difference can only be due to the different response of the RPCsto heavily ionizing compared to minimum ionizing particles. The observed effect accounts for thelargest fraction of the absolute values and the shape of the deviations observed in Fig. 13.The remaining difference observed between the points of Fig. 13 and Fig. 14 is of the orderof (150 ± / c , where the error is estimated from the spread of the points forthe different pad rings. The central value of 150 ps corresponds to a momentum shift of ≈ / c .Several important systematic errors affect this measurement: • The momentum prediction with elastic scattering needs a correction for energy loss in theregion of the inner field cage of the TPC. Although the description of the physical processesis very accurate it is possible that a slightly larger amount of material is present than that– 18 –ccounted for in the calculations (the opposite is excluded). If the calculation is repeatedwith 10% more material a 1%–2% shift in predicted momentum is induced which would reduce the apparent difference. • Background hits in the RPC pads can only create an earlier time measurement, since single-hit TDCs were used to read out the system. Given the charged track multiplicities and thecorresponding number of converted photons from p decays this overlap probability is esti-mated to be ≈ • There is a 20 ps–30 ps difference in measured arrival time for ∼
400 MeV / c p + versus p − .However in the negative beams this is as small as 0 ps–10 ps. The difference with oppositeB field shows already that the RPCs have this kind of systematic. The latter can be due tothe position-dependent slewing correction to the amplifier position which has as maximumswing 180 ps, and assumes exact knowledge of where the first electron was detected. (thereis a symmetry breaking due to the amplifier position always to one side.) • There is a 1% difference in the average pulse-height for p + and p − with ∼
400 MeV / c in the90 ◦ direction. There the production cross-sections are equal. The difference can come fromthe E × B effect for the avalanche electrons which can induce a different space-charge effectdue to the different angle of incidence of the p + and p − in the RPC measurement gap due tothe opposite curvature of their trajectories in the TPC. This can explain a ±
15 ps differenceof threshold crossing, keeping in mind that the threshold was relatively high, considering thatthe full time slewing correction is ∼
6. Conclusions
Asserting the correctness of the momentum reconstruction in the HARP TPC has not been easy, ascan be expected from a chamber affected by a large number of dead channels, cross-talk, static anddynamic distortions in the absence of the possibility to use a direct particle beam for calibration.By a series of dedicated cross-checks with benchmarks, the experimental verification could never-theless be made. This allowed us to conclude that the TPC momentum reconstruction developedby the HARP collaboration is correct within the precision of ± • reconstruction of the missing mass squared of pp elastic scattering data;– 19 – comparison of the momentum of the proton scattered at large angle as measured by the TPCand as calculated from the scattering angle of the forward particle in pp and p ± p elasticscattering events; • dependence of residuals upon polar angle and upon magnetic field polarity reversal, for tracksreconstructed with and without vertex constraint during the fit; • absence of slope in the momentum versus sin q plots in a fixed slice of d E / d x ; • comparison of the d E / d x curves in the region of high ionization where the ionization variesvery quickly with momentum, allowing a sensitive verification of the momentum scale.We also revisited methods of lesser precision, such as d E / d x in the region near the minimumionization, for which we found that it is crucial to use a complete Bethe-Bloch formula to reachreasonable conclusions. Once this is done we find a good match between d E / d x theoretical curvesand our data, in comfort of our momentum reconstruction.Finally a careful analysis of the time response of the RPC system ascertains that no momentumbias is present beyond the uncertainties of this method. While investigating any possibility ofsystematic effect on the momentum measurement, the presence of a systematic effect in the timemeasurement of the RPCs has been demonstrated.As a conclusion, none of the benchmarks has revealed any significant bias in the momentummeasurement beyond a systematic error of 3% for the momentum scale in the TPC.
7. Acknowledgments
We gratefully acknowledge the help and support of the PS beam staff and of the numerous technicalcollaborators who contributed to the detector design, construction, commissioning and operation.In particular, we would like to thank G. Barichello, R. Brocard, K. Burin, V. Carassiti, F. Chig-noli, D. Conventi, G. Decreuse, M. Delattre, C. Detraz, A. Domeniconi, M. Dwuznik, F. Evange-listi, B. Friend, A. Iaciofano, I. Krasin, D. Lacroix, J.-C. Legrand, M. Lobello, M. Lollo, J. Loquet,F. Marinilli, J. Mulon, L. Musa, R. Nicholson, A. Pepato, P. Petev, X. Pons, I. Rusinov, M. Scan-durra, E. Usenko, and R. van der Vlugt, for their support in the construction of the detector.The collaboration acknowledges the major contributions and advice of M. Baldo-Ceolin, M.T. Mu-ciaccia and A. Pullia during the construction of the experiment.The collaboration is indebted to V. Ableev, P. Arce, F. Bergsma, P. Binko, E. Boter, C. But-tar, M. Calvi, M. Campanelli, C. Cavion, A. Chukanov, A. De Min, M. Doucet, D. Düllmann,R. Engel, V. Ermilova, W. Flegel, P. Gruber, Y. Hayato, P. Hodgson, A. Ichikawa, A. Ivanchenko,I. Kato, O. Klimov, T. Kobayashi, D. Kustov, M. Laveder, L. Linssen, M. Mass, H. Meinhard,T. Nakaya, K. Nishikawa, M. Paganoni, F. Paleari, M. Pasquali, J. Pasternak, C. Pattison, M. Pla-centino, S. Robbins, G. Santin, S. Simone, A. Tornero, S. Troquereau, S. Ueda, A. Valassi, F. Van-nucci and K. Zuber for their contributions to the experiment and to P. Dini for his contribution toMC production.We acknowledge the contributions of V. Ammosov, G. Chelkov, D. Dedovich, F. Dydak,M. Gostkin, A. Guskov, D. Khartchenko, V. Koreshev, Z. Kroumchtein, I. Nefedov, A. Semak,– 20 – igure 15.
Average d ′ as a function of event number in spill for 8.9 GeV / c Be data. (left panel uncorrected;right panel: dynamic distortion corrections applied.) After the “default” correction for the static distortions(equal for each setting) a small residual effect at the beginning of the spill is visible at N evt = J. Wotschack, V. Zaets and A. Zhemchugov to the construction and operation of the HARP detec-tor. The experiment was made possible by grants from the Institut Interuniversitaire des SciencesNucléaires and the Interuniversitair Instituut voor Kernwetenschappen (Belgium), Ministerio deEducacion y Ciencia, Grant FPA2003-06921-c02-02 and Generalitat Valenciana, grant GV00-054-1, CERN (Geneva, Switzerland), the German Bundesministerium für Bildung und Forschung(Germany), the Istituto Nazionale di Fisica Nucleare (Italy), INR RAS (Moscow) and the Par-ticle Physics and Astronomy Research Council (UK). We gratefully acknowledge their support.This work was supported in part by the Swiss National Science Foundation and the Swiss Agencyfor Development and Cooperation in the framework of the programme SCOPES - Scientific co-operation between Eastern Europe and Switzerland.
A. Appendix: Treatment of the Dynamic Distortions
Given the beam intensity, the data acquisition rate and the target length (5% of the nuclear inter-action length), it is computed that HARP operated dead time larger than 90%. The electrons arenormally amplified near the TPC pad plane with an amplification factor of the order of 10 , pro-ducing an equivalent number of Argon ions. Any inefficiency of the gating grid at the level of 10 − or even 10 − would let an overwhelming number of ions drift into the TPC gas volume.This indeed turns out to be the case. The dynamic distortions can be monitored using theaverage value of the extrapolated minimum distance of secondary tracks from the incoming beam– 21 – igure 16. Analysis of Q / p T for the highest statistics data sample: p-Be at 8.9 GeV / c . Left panel: distor-tions are not corrected; six curves are drawn, each for the next 50 events in the spill. Right panel: dynamicaldistortions are corrected; the six curves are almost not distinguishable particle trajectory d ′ . This is a similar procedure as the one being used for the STAR TPC [15].Using calibration data sets, the deterioration of the performance of the detector, see Fig. 15 (left),is determined as a function of the strength of the distortions characterized by an average value of d ′ : for each particular setting only that part of the data for which the systematic error was undercontrol was used for the first analysis (of the order of 30% of available statistics) [8, 9]. As a secondstep, a physics model fully describing the time development of dynamic distortions during physicsspills has been developed and benchmarked, as well as a correction algorithm [16] implemented.In addition to the physics model, direct measurements of the displacements of the positionsmeasured at the pad plane of the TPC were performed by predicting the full track trajectory in spaceusing elastic scattering kinematics. The direct measurement and the model show good agreement,indicating that the effect is fully understood. The effects of this correction can be appreciated inFig. 15 (right). The comparison of results obtained using the uncorrected first part of the spill, asin the first HARP analysis, with those using the full corrected spill (see Fig. 16) shows excellentagreement. This provides an a posteriori confirmation with 2 to 3 times better statistics that theapproach used in the first HARP analysis was correct. This is not unexpected, since, owing to theirlimited mobility the first ions created in the amplification region need about 25 ms to reach the driftregion and subsequently the steady flow of ions into this region only starts approximately 100 msafter the start of the spill, with a gradual transition between these two regimes. References [1] M.G. Catanesi et al. [HARP Collaboration],
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