Two-pion production in proton–proton collisions near threshold

Nuclear Physics A 712 (2002) 75–94 www.elsevier.com/locate/npe

Two-pion production in proton–proton collisions near threshold J. Johanson a , R. Bilger c , W. Brodowski c , H. Calén a , H. Clement c , C. Ekström b , K. Fransson a , J. Greiff e , L. Gustafsson a , S. Häggström a , B. Höistad a,∗ , A. Johansson a , T. Johansson a , A. Khoukaz a , I. Koch e , S. Kullander a , A. Kupsc f , P. Marciniewski f , B. Morosov g , W. Oelert d , A. Povtorejko g , R. Ruber a , W. Scobel e , T. Sefzick d , B. Shwartz i , J. Stepaniak f , A. Sukhanov g , G.J. Wagner c , J. Zabierowski h , J. Zloma´nczuk a a Department of Radiation Sciences, Uppsala University, S-75121 Uppsala, Sweden b The Svedberg Laboratory, S-75121 Uppsala, Sweden c Physikalishes Institut, Tübingen University, D-72076 Tübingen, Germany d IKP, Forschungszentrum Julich GmbH, D-52425 Jülich 1, Germany e Institut für Experimentalphysik Universität Hamburg, D-22761 Hamburg, Germany f Soltan Institute for Nuclear Studies, PL-00681 Warsaw, Poland g Joint Institute for Nuclear Research, Dubna, 101000 Moscow, Russia h Soltan Institute for Nuclear Studies, PL-90137 Lodz, Poland i Budker Institute of Nuclear Physics, Novosibirsk 630 090, Russia

Received 14 March 2002; received in revised form 16 August 2002; accepted 2 September 2002

Abstract Two-pion production reactions in proton–proton collisions have been studied using the PROMICE/ WASA detector and an internal cluster gas-jet target at the CELSIUS storage ring in Uppsala. The total cross sections for the pp → ppπ + π − , pp → ppπ 0 π 0 and the pp → pnπ 0 π + reactions are presented at beam energies ranging from 650 to 775 MeV. An isospin analysis of the amplitudes involved in these three reactions indicates that the excitation of the N ∗ (1440) followed by direct two pion emission can be the most important amplitude when allowed. However, large contributions from other production mechanisms must also be prevalent to explain the large pp → pnπ 0 π + cross section. The data are compared to an extensive model including non-resonant as well as resonant production via N ∗ and ∆ excitation.

* Corresponding author.

E-mail address: [email protected] (B. Höistad). 0375-9474/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 4 7 4 ( 0 2 ) 0 1 1 8 7 - 9

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 2002 Elsevier Science B.V. All rights reserved. PACS: 13.75.-n; 13.60.Le; 13.75.cs; 13.85.Lg Keywords: N UCLEAR REACTIONS 1 H(p, pπ + π − ), (p, p2π 0 ), (p, pπ 0 π + ), E = 650–775 MeV; Measured σ , σ (θ ); Deduced reaction mechanism features; Comparison with model predictions

1. Introduction Two-pion production in proton–proton collisions contains information about the nucleon–nucleon, pion–nucleon and pion–pion interactions, in particular the role of resonances in these systems can be elucidated. Data close to the energy threshold offers an opportunity to study the short-range part of these interactions, since high momentum transfers are involved in the production process. Studying two-pion production in the near threshold energy region also has the advantage that only a few partial waves contribute in the reaction processes, thus simplifying both the interpretation of the data and the theoretical calculations. However, the total cross sections are small which make the experiments difficult to perform. The new storage ring facilities with thin internal targets have opened up new possibilities for threshold experiments. The necessary combination of high luminosities and low background can be accomplished by using stored circulating beams passing through thin windowless internal targets. The existing data on two- pion production reactions in proton–proton collisions near threshold energies are scarce, especially for the reaction channels involving one or two neutral pions in the final state. In the present paper we present data on the total cross section for the two-pion production reactions pp → ppπ + π − , pp → ppπ 0 π 0 and pp → pnπ 0 π + at energies ranging from 650 to 775 MeV, i.e., very close to threshold, corresponding to about 20–85 MeV excess energy in the CM-system, where no previous data are available. The production mechanism for two-pion production in proton–proton collisions is likely to be dominated by resonance production. Data in the near threshold energy region could prove to be rather simple to interpret since only very few resonances dominate the reaction mechanism. The N ∗ (1440)P11 resonance appears at the lowest energy with an average threshold of about 1140 MeV, while the simultaneous excitation of two ∆(1232)P33 gives an average threshold of about 1360 MeV. One might therefore expect the N ∗ (1440) to dominate close to threshold for double pion production when allowed. However, the relative contributions from these resonances are also governed by the appropriate coupling strengths, which differ by an order of magnitude in favor of the ∆(1232). Most of the theoretical models describing two-pion production in the intermediate and near threshold energy region come from a theory group at the University of Valencia [1]. They have developed the only existing model describing all isospin-independent reaction channels of the NN → NNππ type, as well as models for the γ N → ππN and πN → ππN reactions. In their model calculations the production mechanism for the pp → ppπ + π − and pp → ppπ 0 π 0 reactions near threshold turns out to be completely dominated by the excitation of the N ∗ (1440) resonance via an effective σ exchange, and a decay of the resonance through the N ∗ (1440) → N(ππ)TS -=0 wave channel. If data

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supports such a reaction process, these double pion production channels would indeed give interesting information on the excitation of the N ∗ (1440) resonance and its decay properties. Note that the N ∗ (1440) resonance is being probed in the low mass region (up to 1239 MeV/c2 at Tp = 650 MeV and up to 1292 MeV/c2 at Tp = 775 MeV) by our choice of incident proton energies for the present experiment. The contribution from non-resonant production is reported [1] to be very small at all energies, whereas the contributions from processes where double ∆∆ are excited become important only at higher energies. For the reactions where the two pions have no isospin zero component, e.g., pp → pnπ 0 π + , the transition N ∗ (1440) → N(ππ)TS -=0 wave cannot occur, and subsequently the contribution to the cross section must come from transitions like NN → ∆∆ → NNππ , NN → NN ∗ → N∆π → NNππ or from non-resonant amplitudes. In those reaction channels their model predicts that the cross sections near threshold are much smaller than the cross sections from the reaction channels allowing the transition N ∗ (1440) → N(ππ)TS -=0 wave .

2. The experiment The experiments presented in this article were performed using the PROMICE/WASA experimental facility and an internal gas-jet target at the CELSIUS storage ring of the The Svedberg Laboratory (TSL) in Uppsala [2]. The PROMICE/WASA detector system, presented in detail in Ref. [3] and shown in Fig. 1, was designed to study meson production in the near threshold energy region.

Fig. 1. A top view is shown of the PROMICE/WASA detector system showing the different detector elements. The abbreviations stand for: central Electromagnetic Calorimeter (CEC), Forward Window Counter (FWC), Forward Proportional Counter (FPC), Forward Trigger Hodoscope (FTH), Forward Range Hodoscope (FRH), Forward Veto Hodoscope (FVH), Central E detector (CDE). Distances are given in mm.

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The charged outgoing particles were measured in the forward part (FD) of the detector. The neutral mesons were measured by their decay into two γ ’s in the central part (CD) of the detector. The FD consisted of window counters for triggering purposes (FWC), a tracker for high resolution particle track reconstruction (FPC), a forward trigger hodoscope for triggering purposes and particle identification (FTH), a forward range hodoscope to identify particles and measure their kinetic energy (FRH) and a forward veto hodoscope to veto against particles penetrating the FRH (FVH). The main purpose of the CD was to measure gammas from the decay of neutral mesons. The CD consisted of a central electromagnetic calorimeter (CEC) made from two boxes with CsI crystal arrays mounted on each side of the scattering chamber. E1 /E2 detectors were mounted in front of each box to detect charged particles. The total detector system comprised approximately 450 channels connected to ADCs and 1500 channels connected to TDCs. The stability of the scintillator detectors and their electronic read out system was monitored with a light pulser system [4]. The total signal rate in the experiments was of the order of 105 per second whereas the data acquisition system could process about 350 events per second. In a trigger system, used to reduce the signal rate and select the interesting events, all signals from the scintillator detectors could be included as primary and secondary triggers. Several different kinds of triggers were used in the experiments. Physics triggers were used to pick out the possible pp → ppπ + π − , pp → ppπ 0 π 0 and pp → pnπ + π 0 events. In addition, triggers to select elastically scattered protons for calibration and normalization purposes were used. A trigger from the light pulser was read out to monitor the stability of the detector response. Comprehensive Monte Carlo simulations were done to get quantitative information of all possible aspects of the detector. All parts of the detector system were implemented in full detail in the Monte Carlo code. Effects from nuclear reactions was given by the code GEANT. All possible event patterns in the experimental apparatus were also simulated by Monte Carlo simulations. Confidence in the Monte Carlo simulations has been obtained from previous studies of single meson production using the same detector. For the present experiment further confidence was obtained from comparisons between real data and predictions from simulations of numerous distributions in scattering angles and kinetic energies of the different outgoing particles in the measured reactions. The experimental details, the analysis of the data and the Monte Carlo simulations pertinent to this work are described in great detail in Ref. [5].

3. Analysis 3.1. Particle identification and event reconstruction A track reconstruction routine combined the available hits in the FPC to a number of possible track candidates. The routine was designed to work even in case of geometrical misalignment, bad timing or detection efficiency. Constraints were also put on the tracks after all possible track candidates had been formed and the most likely ones were selected for further analysis. The most difficult reaction to handle in the track reconstruction process was the pp → ppπ + π − reaction. If all outgoing particles ended up in the FD, four tracks

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had to be reconstructed. It was however difficult to reconstruct more than three tracks unambiguously in the FD, and therefore only events with three charged tracks in the FD were kept in the analysis. The subsequent event correction (less than 5%) was determined from the Monte Carlo Simulations. The other two reactions, pp → ppπ 0 π 0 and pp → pnπ + π 0 , gave at most two charged tracks in the FD, which were straightforward to reconstruct. The only neutral particles detected in the CD were gammas from the decay of neutral pions. A track was considered as a neutral track if it had a hit in a CsI detector but no hit in any of the E1 /E2 detectors in front of the CsI array. The charged outgoing particles were identified from their energy loss in the different layers of the FTH and FRH using the E1 /E2 method. This method was sufficient to identify protons. However, due to background from mostly electrons, pions needed an additional identification method. The pions were therefore also identified by detecting their decay particles using a method described in [3]. This technique only worked for positive pions, however, since negative pions were captured in atomic orbits and subsequently absorbed by the nuclei in the detector before they decayed. The slower signal from the positrons, in the decay π + → µ+ + νµ → e+ + ν¯ µ + νe + νµ was used in the delayed pulse technique. The drawback using the slower signal was that the time windows of the multi-hit TDCs [6] had to be large, in this case 160 ns–6 µs. Background particles entering the detector when the time window was open could be mistaken for delayed signals from the pion decay. To take care of delayed signals from general background, the third detector plane in the FTH, was used as a veto plane removing delayed hits not coming from the pion decays. The kinetic energies of the outgoing particles were reconstructed by measuring the deposited energy in the detector material. The calibration constants for the detector elements were obtained in a special calibration procedure. In the case of charged particles, the deposited energy was compensated for quenching and energy loss in dead material. The light pulser system was used to correct the energy calibration constants for any change in the gain of the detector elements during the run. The selection of protons and pions in the pp → ppπ + π − reaction is illustrated in Fig. 2. The main background in this reaction came from single neutral pion production, i.e., the reaction pp → ppπ 0 . The gammas from the decay of the π 0 can convert to electron-positron pairs in the material surrounding the interaction region. If an electron or a positron ended up in the FD together with the two outgoing protons, the trigger used to pick out charged two-pion production events was activated. The selection was further complicated by the fact that the energy loss behavior of electrons and positrons is similar to that of charged pions. The background from electrons and positrons can be seen in Fig. 2(a) as an island of entries in the lower left corner. Fig. 2(b) shows the pion data sample constrained by the identification of positive pions by the delayed pulse technique. Two other important background reactions were pp → pnπ + and pp → dπ + . A small enhancement of entries originating from deuterons can be seen just above the marked proton band in Fig. 2(a). The background reaction pp → pnπ + gave a significant contribution. The neutron in the pp → pnπ + reaction could undergo an n-p reaction in the forward cone of the scattering chamber or in the FWC. If the recoil proton ended up in the FD together with the outgoing proton and the positive pion, the trigger used to pick out events with three charged tracks in the FD was activated. Positive pions from

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(a)

(b) Fig. 2. (a) Shows the E/E distribution from an event sample from a run on the pp → ppπ + π − reaction at 650 MeV. E is measured in the third layer of the FTH (denoted by FTH3 in the figure), and E is measured in the FRH. The marked upper band corresponds to protons and the lower marked band corresponds to positive pions, the selection of which is guided by Monte Carlo simulations. (b) Shows the pion sample after applying the delayed pulse technique for positive pions.

the pp → pnπ + reaction form another island of events to the right of the island formed by electrons and positrons in Fig. 2(a). The identification of these high-energy pions is confirmed by Monte Carlo simulations. Regarding the pp → ppπ 0 π 0 and pp → pnπ + π 0 reactions, the only background reaction giving a significant contribution was the pp → ppπ 0 reaction. This is despite the

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fact that our geometrical detection acceptance for the pp → ppπ 0 reaction was very small (∼ 10−3 ) at the energies studied in this work. The total cross section for the pp → ppπ 0 reaction is however ∼ 103 larger than the total cross sections for the two-pion production reactions at our energies. Single neutral pions from the pp → pnπ + π 0 reaction could easily be identified from the invariant mass of the two gammas. For the pp → ppπ 0 π 0 reaction, the situation was more involved, since up to four gammas could end up in the CD. Moreover, due to the limited angular and energy resolution of the CD it was not possible to find out if the detected gammas came from the same π 0 or not. These circumstances lead to that only events with one gamma in each CsI box were kept in the analysis. This constraint reduced the detection acceptance by less than 5%. 3.2. Event selection 3.2.1. The pp → ppπ + π − reaction The missing mass distribution calculated from the two protons and one of the pions in the pp → ppπ + π − data for all selected events at 650 MeV is shown in Fig. 3(a). The presence of the pp → ppπ + π − reaction can be seen as a small increase of events around the mass of a charged pion. The events which remain when the pion is required to have a delayed pulse are shown by the histogram in Fig. 3(b). The peak around the mass of a charged pion is now apparent. The delayed pulse technique effectively removes the events from the dominating background reaction pp → ppπ 0 . The background events still present in Fig. 3(b) are mainly due to the pp → pnπ + reaction, where the positive pion is correctly identified by the delayed pulse technique. The background can be further reduced by making cuts on the proton–proton opening angle, the scattering angles of the protons, the kinetic energies of the protons and the kinetic energy of the positive pion. The events that remain after these kinematical cuts have been applied are shown by the shaded histogram in Fig. 3(b). The number of events used to calculate the total cross section at each energy for the pp → ppπ + π − reaction was extracted by selecting a region around the mass of a charged pion in the missing mass distribution of the two protons and the positive pion. The background was estimated by a smooth fit to the background on both sides of the peak. The error in this procedure is estimated by varying the contribution from the different background reactions in the Monte Carlo simulations. For the pp → ppπ + π − reaction the only remaining background in the final event sample comes from the pp → pnπ + reaction, and the error in subtracting that background is estimated to be 8 and 10% at 650 and 680 MeV, respectively. The events which are contained in the final kinematical distributions (see Figs. 6 and 8) were selected by making a cut on the missing mass calculated from the two protons and the pion as well as a cut on the missing mass of the two protons. The kinematical distributions will contain a small amount of background events which cannot be discarded by the kinematical cuts. 3.2.2. The pp → ppπ 0 π 0 reaction In the pp → ppπ 0 π 0 reaction, the missing mass distribution calculated from the two protons for all selected events at 725 MeV is shown by the solid line in Fig. 4. The

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(b) Fig. 3. Event selection in the pp → ppπ + π − reaction at 650 MeV presented as a missing mass distribution calculated from the two protons and the positive pion, MMppπ . (a) Shows all the events for which the protons and the pion are identified from E1 /E2 cuts. (b) Shows the data sample when the delayed pulse from the positive pion is applied in addition. The shaded area remains after cuts on opening angles, scattering angles and kinetic energies.

pp → ppπ 0 π 0 events show up as an enhancement of events around the summed mass of two neutral pions. The background events from the pp → ppπ 0 reaction gives a relatively large contribution. No kinematical cuts are meaningful at this energy due to the limited detection acceptance for protons from the pp → ppπ 0 reaction. Fortunately, the total cross section for the pp → ppπ 0 π 0 reaction rises sharply with increased beam energy whereas

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Fig. 4. The missing mass distribution calculated from the two protons, MMpp , for all selected events for the pp → ppπ 0 π 0 reaction at 725 MeV. The dotted line in the insert figure corresponds to the Monte Carlo simulations of the background of the neutral single pion production. The subtraction of this background gives the foreground contribution, which is represented by the dashed line.

the total cross section for neutral one-pion production only increases by a factor of two in the energy region between 650 to 775 MeV. The number of events used to calculate the total cross section at each energy was extracted by selecting all events in a region around the summed mass of two neutral pions in the missing mass distribution calculated from the two protons. The background from neutral one-pion production was subtracted and the shape of the background in the selected region was taken from Monte Carlo simulations of the background reactions, as shown in Fig. 4. 3.2.3. The pp → pnπ + π 0 reaction For the pp → pnπ + π 0 reaction the missing mass distributions calculated from the proton and the positive and neutral pions for all selected events, based on E1 /E2 constraints as well as a request for one photon in each CsI detector box, are shown at 750 MeV in Fig. 5(a). The events from this reaction should show up as an increase of events around the mass of a neutron in the missing mass distributions calculated from the proton and the two pions. Although the peak around the neutron mass is apparent, most of the events originate from the pp → ppπ 0 and pp → ppπ 0 π 0 reactions, where one of the protons was misidentified as a charged pion in the E1 /E2 selection. The left peak in the missing mass distributions corresponds to events from the pp → ppπ 0 reaction and the right peak corresponds to events from the pp → ppπ 0 π 0 reaction together with the wanted events from the pp → pnπ + π 0 reaction. The background from neutral oneand two-pion production can be removed with the delayed pulse technique. The shaded histogram in Fig. 5(a) shows the effect of the additional condition that the positive pions must have a delayed pulse.

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(a)

(b) Fig. 5. (a) Shows the missing mass distribution calculated from the proton and the two pions MMpπ + π 0 , for all selected events for the pp → pnπ + π 0 reaction at 750 MeV using E1 /E2 cuts and the photon trigger. The shaded area shows the remaining events when a delayed pulse from the positive pion is required. An angular distribution of the particle identified as a proton in the FD is shown in (b) for the final event sample, which includes a cut in MMpπ + π 0 around the neutron mass. The points represent real data, and the dotted and dashed

lines represent Monte Carlo generated data from the pp → pnπ + π 0 and pp → dπ + π 0 reactions, respectively. The deuteron in the second reaction can be misidentified as a proton in the FD or being broken up resulting in a real proton, which explains the enhancement of events at small angles. The solid line shows the sum of the two contributions.

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If the positive and neutral pions are correctly identified, only two reactions are possible, the pp → pnπ + π 0 and the pp → dπ + π 0 reactions. The separation between those two channels requires special effort. The pp → dπ + π 0 events can pass the event selection in two ways. Either the deuteron is misidentified as a proton in the E1 /E2 selection or the deuteron breaks up into a neutron and a proton in the detector material and the proton is subsequently identified in the E1 /E2 selection. Fortunately most of the background from the pp → dπ + π 0 events can be discarded by making a cut on the minimum scattering angle of the particle identified as a proton. The deuterons as well as the protons from deuteron breakup originating from the pp → dπ + π 0 reaction have small scattering angles. In fact, many of them disappeared in the beam pipe, thereby escaping detection. The scattering angles of the protons from the pp → pnπ + π 0 reaction on the other hand, were distributed over the available detector acceptance. The distribution in scattering angle of the particle identified as a proton for pp → pnπ + π 0 event candidates at 750 MeV, selected with a requirement of a delayed pulse from the pion and a cut on the missing mass calculated from the proton and the two pions, is shown by the points in Fig. 5(b). The dotted and dashed lines show the result of a full Monte Carlo simulation for the pp → pnπ + π 0 reaction and pp → dπ + π 0 reactions, respectively. It should be emphasized that final state interaction between the np-pair is included in the Monte Carlo simulation (see Section 3.4). The solid line shows the sum of the two Monte Carlo distributions. The agreement between the experimental distribution and the summed Monte Carlo distribution is reasonable. 3.3. Normalization The cross sections of two-pion production reactions were normalized by using elastically scattered protons recorded concurrently with the pion production data. The integrated luminosity was extracted by comparing the number of detected elastically scattered protons with known cross sections. The two main sources of background in the selected samples of elastically scattered protons came from the reactions pp → ppπ 0 and pp → pnπ + . If one of the protons from the pp → ppπ 0 reaction ends up in the FD and the other in the CD, the event is similar to an elastic scattering event. By using constraints on the opening angles for this reaction and the elastic scattering, almost all of the background from the pp → ppπ 0 reaction could be discarded. If the proton from the pp → pnπ + was detected in the FD and the positive pion is detected in the CD, the event can be mistaken for an elastic scattering event. The acceptance is however two orders of magnitude lower than the acceptance to detect the two protons from elastic scattering at all beam energies studied in this work. The small background (around 2%) from the pp → pnπ + π 0 reaction that remains in the final samples of elastically scattered protons is evenly distributed in opening angle. The differential cross sections needed to calculate the integrated cross sections in the selected angular region are taken from the partial-wave analysis by Arndt et al. [7] of the world data on NN elastic scattering. 3.4. Efficiencies and errors The measurements of the total cross section for two-pion production reactions rely on the fact that a large fraction of the phase space is covered by detectors so that the

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extrapolation to the 4π solid angle can be done with minimal errors. This was the case at all energies in our measurements. Inefficiencies of different kinds were evenly distributed over the phase space for the detected particles, except at small angles, (< 4◦ ), where the beam pipe created a detection void. The geometrical acceptance as well as the detection efficiency (around 35% together) and the reconstruction efficiency (around 15%) were estimated from Monte Carlo simulations. The trigger efficiencies (around 90%) were extracted from a systematic study of the simple triggers that made up the more complicated physics triggers. A full account of all those efficiencies is given in Ref. [5]. Monte Carlo simulations describe the selection of positive pions with the delayed pulse technique well, but overestimate the total efficiency by about 12% (this is the only case for which a discrepancy between Monte Carlo simulated data and real data ever was encountered). The total efficiency of the delayed pulse technique was therefore measured using positive pions from the reaction pp → pnπ + at 360 MeV. The distribution in scattering angle for the pions in this reaction is similar to the distribution of the positive pions from the pp → ppπ + π − reaction at the energies 650 and 680 MeV. In this way a value ∼ 65% was obtained for the total efficiency of the delayed pulse technique. Since the discrepancy between the experimental result and the Monte Carlo simulation is not understood, a total error of 12% is assumed in the efficiency to identify positive pions. In this context it should be mentioned that the measured mean life time of the muon using our delayed pulse technique gave excellent agreement with the known value. In order to enable an accurate compensation for the loss of events in the beam pipe, the final state interaction between the outgoing nucleons has to be taken into account. The final state interaction is implemented in the event generation by weighting each event with the square of the scattering wavefunction (in momentum space). Three types of final state interactions are implemented in the event generation, spin-triplet final state interaction, spin-singlet final state interaction with Coulomb interaction and spin-singlet final state interaction without Coulomb interaction. Two parameterizations of the square of the scattering wavefunction are included [8,9]. Both parameterizations take the scatteringwave function from the Paris nucleon–nucleon potential. The two parameterizations describe the effects of final state interaction well at all energies studied in this work. The effect of the attractive spin-singlet final state interaction can be seen in several kinematical distributions, e.g., in the proton–proton invariant mass distribution which is modified from phase space by an enhancement at low proton invariant masses and in the scattering angle distribution of the protons which is modified from phase space by an enhancement at lower scattering angles. As a result of the attractive final state interaction, some protons were lost in the beam pipe, thus decreasing the detection acceptance for the pp → ppπ + π − and pp → ppπ 0 π 0 reactions as well as the pp → pnπ + π 0 reaction. The event distribution from the pp → ppπ + π − reaction at 650 MeV is shown in Fig. 6(a) as a function of the proton–proton invariant mass, and the event distribution in proton scattering angles for the same reaction and energy is shown in Fig. 6(b). The points show the data and the solid and dashed lines show the results of the Monte Carlo simulations with and without final state interaction included. The distributions are clearly better described by the Monte Carlo which includes the final state interaction. The biggest error in the overall acceptance for the different two pion reaction channels comes from the determination of the detection acceptance, since this strongly depends on

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(a)

(b) Fig. 6. The effects of the proton–proton final state interaction are shown for the pp → ppπ + π − reaction at 650 MeV. The points show real data. The solid and dashed lines show the results of full Monte Carlo simulations with and without final state interaction. (a) Shows the event distribution as a function of the proton–proton invariant mass (Mpp ), and (b) shows the event distribution as a function of the proton scattering angle (lab).

a correct description of the final state interaction. The error in the detection acceptance is estimated by varying the strength in the final state interaction in the as described above. Given that the angular distributions of the outgoing protons (see Fig. 8(a)) in fact are becoming slightly non-isotropic with increasing energy there is a corresponding energy dependence in the overall acceptance. Since this energy dependence is of dynamic origin it is not accounted for in the phase space Monte Carlo including FSI. However, the error

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Table 1 The total cross sections for the pp → ppπ + π − , pp → ppπ 0 π 0 and the pp → pnπ 0 π + reactions at 650, 680, 725, 750 and 775 MeV together with statistical and systematic errors Cross section (nb) σ ± estat ± esyst

Energy (MeV) 650 680 725 750 775

pp → ppπ + π −

pp → ppπ 0 π 0

45 ± 3 ± 10 148 ± 6 ± 32

50 ± 7 ± 15

1650 ± 250 Ref. [10]

518 ± 22 ± 104 1038 ± 25 ± 158 1677 ± 42 ± 404

pp → pnπ 0 π +

831 ± 100 ± 201 1363 ± 78 ± 260 2288 ± 224 ± 790

introduced by not using the measured angular distributions in the Monte Carlo simulations, is small in comparison with the error from the uncertainty in the strength of the FSI. The statistical errors in the extracted cross sections differ for each reaction and beam energy whereas the systematic errors are similar for the different reactions and beam energies. The uncertainty in the beam energy is estimated to be below 0.5 MeV and is neglected in the analysis. For the pp → ppπ + π − reaction, the statistical errors are around 5% at our two energies. For the pp → ppπ 0 π 0 reaction, the statistical errors vary between 2 and 18% at our four energies. For the pp → pnπ + π 0 reaction, the statistical errors vary between 6 and 12% at our three energies. The statistical errors for each reaction and beam energy are shown in Table 1 as well as the total systematic errors. The total errors, including both statistical and systematic errors, are close to 22% for the pp → ppπ + π − reaction, between 16 and 30% for the pp → ppπ 0 π 0 reaction and between 27 and 32% for the pp → pnπ + π 0 reaction at the different beam energies for these reactions.

4. Results and remarks 4.1. The pp → ppπ + π − and pp → ppπ 0 π 0 reactions The total cross sections for the pp → ppπ + π − reaction at 650 and 680 MeV and for the pp → ppπ 0 π 0 reaction at 650, 725, 750 and 775 MeV are shown in Fig. 7(a) and (b), respectively, together with the previously existing low statistics bubble chamber data in the intermediate and near threshold energy region [10], as well as one datum point from an inclusive spectrometer measurement at 800 MeV. Also shown is a recent data point at 750 MeV for the pp → ppπ + π − reaction [11]. The solid and dashed curves show theoretical predictions from the model calculations by Alvarez-Ruso et al. [12]. These curves differ in the assumptions on the Lagrangian for the N ∗ (1440) → N(ππ )TS -=0 wave decay, and the difference thus reflects one theoretical uncertainty. The PROMICE/WASA data agree with the model calculations by Alvarez-Ruso et al. However, the theoretical calculations do not include final state interaction between the protons. Including final state interaction in the model would increase the predicted total cross section close to the threshold. The importance of the final state interaction is reflected in the kinematical distributions, shown in Fig. 6, which are well described by phase space Monte Carlo when proton–proton final state interaction is included.

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(b)

(c) Fig. 7. The total cross sections for the reactions (a) pp → ppπ + π − (b) pp → ppπ 0 π 0 and (c) pp → pnπ 0 π + from the PROMICE/WASA collaboration shown together with the previously existing data in the intermediate and near threshold energy region, and theoretical predictions from the model by Alvarez-Ruso et al. The error bars in the P/W data include both statistical and systematic errors.

4.2. The pp → pnπ + π 0 reaction The total cross sections for the pp → pnπ + π 0 reaction at 725, 750 and 775 MeV are shown in Fig. 7(c) together with the previously existing data in the intermediate and near threshold energy region. The larger errors in the measurements of the total cross section for the pp → pnπ + π 0 reaction as compared to the pp → ppπ 0 π 0 reaction are due to the more difficult background subtraction. With some surprise we note that the cross section

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for the pp → pnπ + π 0 reaction is as large as the cross sections for the pp → ppπ + π − and pp → ppπ 0 π 0 reactions. The solid and dashed curves in Fig. 7(c) show theoretical predictions from the model calculations by Alvarez-Ruso et al. The predicted total cross section is in this case considerably smaller than the experimental total cross section. The reason for the underpredicted total cross section near threshold is that the dominating production mechanism in the model, N ∗ (1440) → N(ππ )TS -=0 wave , is trivially forbidden by isospin conservation for the pp → pnπ + π 0 reaction, since the (π + π 0 ) pair has no isospin zero component. In fact, the same under-prediction of the cross section occurs for the same reason for the pn → ppπ − π 0 reaction [12]. Our new data indicate a larger contribution from other processes like NN → ∆∆ → NNππ , NN → NN ∗ → N∆π → NNππ or from nonresonant amplitudes, than predicted by the model. 4.3. Angular distributions Since all particles in the final states have been identified in the reactions, it is possible to extract various angular distributions for the final state particles. However due to the very low cross sections close to threshold the statistical errors are large. Nevertheless, it could be interesting to get a qualitative picture of some angular distributions. Such distributions are shown in Fig. 8. The distribution of events with respect to the proton angle, shown in (a), indicates a development of non-isotropic distributions with increasing energy. The significance of that feature in terms of reaction amplitudes can only be judged by detailed calculations. Model calculations at 750 MeV of the pp → ppπ + π − reaction show the same general feature as data, but there is unfortunately only a small sensitivity to the specific amplitude involved [12], which necessitates better data with good statistics. The pion distributions for pp → ppπ + π − shown in (b) are all isotropic, indicating an s-wave configuration, which is expected at this low energy. 4.4. General remarks The comparison between our data and the model calculation by Alvarez-Ruso et al. gives a mixed answer. Their predictions for the reaction channels pp → ppπ + π − and pp → ppπ 0 π 0 reactions are good, although the omission of final state interaction complicates the interpretation of this good prediction. The small cross sections predicted for the reaction channels when the N ∗ (1440) → N(ππ )TS -=0 wave transition is forbidden, is however not supported by the data. At this point it could therefore be useful to approach the problem in general terms and make a simple isospin analysis of the reaction in order to investigate if there exists any dominating amplitude, which could give a clue to the underling reaction dynamics. We therefore express the total NN → NNππ cross section in terms of isospin matrix elements MTi T2π Tf , where Ti denotes the isospin of the initial nucleon pair, Tf denotes the isospin of the final nucleon pair and T2π denotes the isospin of the produced pion pair. Using standard isospin coupling, and including factors due to the identity of outgoing particles, it is straight forward to show that the contributing matrix

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(a)

(b) Fig. 8. (a) Shows the angular distributions as a function of the overall CM angle of the emitted proton with respect to the incident beam. The curves are just cos2 (θ ) fits to the data to guide the eye. It should be noted that the data contain some background events, which could be the reason for the slight non-symmetric (unphysical) event distribution around 90 degrees. (b) Shows the angular distributions obtained at 680 MeV as a function of different relative angles in the overall CM system between the final particles indicated in the figure.

elements in our measured reactions are given by the expressions 
σ pp → ppπ + π − =

1 1 1 |M121 |2 + |M111 |2 + |M101 |2 120 8 6 1 +√ |M121||M101 | cos φ, 180

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1 1 1 σ pp → ppπ 0 π 0 = |M121|2 + |M101|2 − √ |M121||M101 | cos φ, 60 12 180
 3 1 1 σ pp → pnπ + π 0 = |M121 |2 + |M111 |2 + |M110|2 . 40 8 4 Here φ denotes the relative phase between the amplitudes M101 and M121 . Note that the weights by which the amplitudes M121 and M101 enter in the cross sections for these channels are dramatically different. Referring to the isotropic angular distributions shown in Fig. 8(b), and the proximity to the production threshold, we tentatively assume that 2π = 0 is the dominant pion pair configuration. Consequently T2π = 0 or 2, and the matrix elements M111 and M110 vanish. Our experimental data can now be used to determine the remaining amplitudes |M121 |2 and |M101 |2 . Displaying the data as a function of excess energy (total CM energy minus the sum of the rest masses of the final state particles), to avoid differences in Q-values in the reactions, one finds that the σ (pp → ppπ + π − ) cross section is roughly 50% larger than the σ (pp → pnπ + π 0 ) cross section, and that the σ (pp → ppπ 0 π 0 ) cross section is roughly 50% smaller than the σ (pp → pnπ + π 0 ) cross section at an excess energy of about 60 MeV. Denoting the σ (pp → pnπ + π 0 ) cross sections by σ , 20 2 2 we find that |M121 |2 = 40 3 σ and |M101 | = 3 σ . The amplitude |M121 | is thus twice as large as |M101 |2 . Observe now that the channel N ∗ (1440) → p + (2π)TS -=0 wave can only 2 be involved in |M101| , while the double ∆∆ excitation is allowed in both |M121 |2 and |M101 |2 . Given that the final state interaction between the nucleon pairs is the same (except for Coulomb), since they are all in a T = 1 state when T2π = 0 or 2, the large contribution from the |M121 |2 amplitude indicates that the excitation of a double delta ∆∆ could in fact be the dominating reaction amplitude close to threshold. Note also that a dominance of the Roper resonance N ∗ (1440) excitation, i.e., keeping only the M101 amplitude, would lead to a σ (pp → ppπ + π − ) cross section being twice as large as the σ (pp → ppπ 0 π 0 ) cross section, which is roughly supported by the data, but it would also lead to a vanishing σ (pp → pnπ + π 0 ) cross section, which is not supported by the data. However, the Roper resonance could still dominate the σ (pp → ppπ + π − ) cross section, for which the contribution from the |M101 |2 term is very much enhanced by its large isospin coupling factor, while the contribution from the |M121|2 term is suppressed by a small coupling factor. In fact, from the simple expression of the sum of the cross sections 1 σ (pp → ppπ + π − ) + σ (pp → ppπ 0 π 0 ) = 40 |M121 |2 + 14 |M101 |2 = 13 σ + 53 σ , we see that the largest part of the cross section comes from the |M101 |2 amplitude. Regarding the large σ (pp → pnπ + π 0 ) cross section, this is probably a consequence of the relatively large coupling factor appearing for the |M121 |2 term, which is the only term allowing swave pions. To get a better understanding of the relative contribution to the |M101 |2 term from the N ∗ (1440) → p + (2π)TS -=0 wave transition and from the other possible processes it is essential with new experimental input, since the present theory seems to underestimate the contribution from those amplitudes in the reaction channels where the transition N ∗ (1440) → p + (2π)TS -=0 wave cannot occur. A theoretically clean but experimentally difficult reaction channel is pp → nnπ + π + , which has been measured approximately at a few energies above 1 GeV (Shimizu et al. [10]). In this case there are only contributions

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3 from the double ∆∆ and non-resonant amplitudes since σ (pp → nnπ + π + ) = 20 |M121 |2 , i.e., this reaction could be used to understand the importance of those amplitudes. From + + the result |M121|2 = 40 3 σ above, one finds that the cross section σ (pp → nnπ π ) should + − be about 30% larger than the σ (pp → ppπ π ) cross section close to threshold. Such a large cross section for the σ (pp → nnπ + π + ) reaction channel seems however less probable in view of the available data at higher energies. Contribution from the amplitudes involving 2π = 1, might therefore not be negligible, since this would imply a smaller |M121 |2 amplitude and thus also a smaller σ (pp → nnπ + π + ) cross section.

5. Summary and final remarks Total cross sections for the pp → ppπ + π − , the pp → ppπ 0 π 0 and the pp → pnπ + π 0 reactions have been presented at energies very near the kinematical threshold. These cross sections are found to be surprisingly equal in magnitude. This result is partly compatible with the model calculations by Alvarez-Ruso et al., which indicates that the transition N ∗ (1440) → N(ππ )TS -=0 wave is a dominant part of the production mechanism for the double pion production channels pp → ppπ + π − and pp → ppπ 0 π 0 near threshold. However, for the reaction channels in which the two pions cannot couple to isospin zero, like pp → pnπ + π 0 , their model clearly underestimates the experimental cross sections. That means that the contributions from the double ∆∆ and/or the non-resonant terms are not fully accounted for in any of the reaction channels. Although, the very comprehensive model calculations by Alvarez-Ruso et al. are very promising, their results are presently somewhat difficult to assess, since no final state interaction of the outgoing nucleon pair is included in the predictions presented in Fig. 7, and since there is a possible underestimation of the contribution from the double ∆∆ and/or the non-resonant terms. On a more fundamental level, the prevailing uncertainties in the σ NN ∗ (1440) coupling strength must be resolved. The value gσ2 NN ∗ /4π = 1.33, used by Alvarez-Ruso et al. is obtained from a fit to inelastic α + p → α + X scattering data, where the Roper resonance is claimed to appear [13]. This value is in fact quite large compared to the strength obtained from the partial decay width of the N ∗ (1440) → N(ππ )TS -=0 wave channel (≈ 0.3–0.5) [14].

Acknowledgements We are grateful to the personnel at The Svedberg Laboratory for their kind support during the course of this experiment. Discussions with Göran Fäldt and Colin Wilkin are gratefully acknowledged. Financial support were given by the Swedish Natural Research Council, the Swedish Royal Academy of Sciences, the Swedish Institute, the German Bundesministerium für Bildung und Forschung, the Polish State Committee for Scientific Research and the Russian Academy of Sciences.

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References [1] L. Alvarez-Ruso, E. Oset, E. Hernandez, Nucl. Phys. A 633 (1998) 519; E. Oset, M.J. Vicente-Vacas, Nucl. Phys. A 446 (1994) 584; J.A. Gomez Tejedor, E. Oset, Nucl. Phys. A 571 (1985) 667. [2] TSL Progress Report, 1998–1999; D. Reistad, TSL Note 97-31 (1997); C. Ekström, et al., Nucl. Instrum. Methods A 371 (1996) 572. [3] H. Calen, et al., Nucl. Instrum. Methods A 379 (1996) 57. [4] J. Zabierowski, Nucl. Instrum. Methods A 338 (1994) 577. [5] J. Johanson, PhD thesis, Uppsala University, 2000. [6] LeCroy 1876, connected to each element in the FRH. [7] R. Arndt, et al., Phys. Rev. C 56 (1997) 635. [8] G. Fäldt, C. Wilkin, Phys. Rev. C 56 (1997) 2067. [9] J. Zlomanczuk, et al., Phys. Lett. B 436 (1998) 251. [10] F.H. Cverna, et al., Phys. Rev. C 23 (1980) 23; F. Shimizu, et al., Nucl. Phys. A 386 (1982) 571; D.C. Brunt, et al., Phys. Rev. 187 (1969) 1856; L.G. Dakhno, et al., Sov. J. Nucl. Phys. 37 (1983) 540. [11] W. Brodowski, PhD thesis, Tübingen University, 2001; W. Brodowski, et al., Phys. Rev. Lett. 88 (2002) 192301. [12] L. Alvarez-Ruso, PhD thesis, University of Valencia, 1999, and private communication. [13] H.P. Morsch, et al., Phys. Rev. Lett. 69 (1992) 1336; S. Hirenzaki, P. Fernández de Còrdoba, E. Oset, Phys. Rev. C 53 (1996) 277. [14] M. Soyeur, Nucl. Phys. A 671 (2000) 532.