The pp ->pp pi pi pi reaction channels in the threshold region

The cross section for prompt neutral and charged three pion production in pp interactions was measured at excess energies in the range 160 - 217 MeV. That comprises the first measurement of the pp->pp pi0pi0pi0 reaction and the comparison with the pp->pp pi+pi-pi0 reaction, in a very direct way. The experiment was performed above the eta meson production threshold and the cross section normalization was obtained from a concurrent measurement of the reaction pp->pp eta with the eta decaying into 3 pions. Since the same final states are selected, the measurement has a low systematical error. The measured cross section ratio sigma(pp->pp pi+pi-pi0)/sigma(pp->pp pi0\pi0\pi0) is compared to predictions of dominance of different isobars in the intermediate state.


Introduction
Production of three pions in proton-proton interactions, where the pions do not originate from decays of narrow meson resonances (like η or ω), has not received proper attention yet, neither experimentally nor theoretically. Experimentally there are only very few data on the pp → ppπ + π − π • and pp → pnπ + π + π − reactions and no data on the other reaction channels: pp → ppπ • π • π • , pp → pnπ + π • π • and pp → nnπ + π + π • . On the theory side there exists a complete microscopic model covering all reaction channels of two pion production in pN interactions [1], but so far no such models have been developed for the three pion case. In the isobar model the process pp → ppπππ should proceed by an excitation of one or two baryon resonances followed by the subsequent decays [2] and in the low energy region a mechanism with a simultaneous excitation of N * and ∆(1232)P 33 resonances is expected to dominate. The N * involved has to decay into Nππ and therefore the lowest lying Roper (N(1440)P 11 ) and N(1520)D 13 resonances could be considered. There is however a significant difference between their decay pattern. The Roper decays predominantly into ∆π whereas for the N(1520) the Nρ channel is equally important [3,4].
The influence of the resonances in the intermediate state can be studied in the invariant mass distributions of the subsystems of the outgoing protons and pions. Such studies were done for the pp → ppπ + π − π • and pp → pnπ + π + π − reactions in bubble chamber experiments performed at higher energies (beam kinetic energies of 4.15 GeV and 9.11 GeV) with up to thousand events [5][6][7]. In these studies, only one or two of the pions were considered to originate from decays of N * or ∆ resonances. However, such kind of analysis is complicated and may not be conclusive due to many possible scenarios and due to large widths of the involved resonances. A simple starting point for analyzing the three pion production close to threshold is to assume a constant value for the matrix element. The dependence of the cross section on the beam energy is then given by the phase space volume divided by a flux factor. For a proper description of the reactions in the threshold region it is required to take into account the final state interaction (FSI) between the outgoing protons [8,9]. The Nπ FSI on the other hand is expected to be negligibly small [10]. A hint about the production mechanism of the three pions could then be obtained by studying the ratio of the cross sections for the different charge states. The three pion production amplitude NN → NNπππ can be written in terms of the isospin amplitudes M T i T 3π T f , where T i (T f ) denotes the initial (final) isospin of the nucleon pair and T 3π denotes the isospin of the produced pion triplet. It is now straightforward to show that where cross terms between M 121 and M 101 amplitudes are neglected. In the simple statistical approach [11], with all amplitudes : σ(pp → pnπ + π + π − ) = 8 : 1 : 10. There were so far experimental data on σ(pp → ppπ + π − π • ) : σ(pp → pnπ + π + π − ) only. At 2.0 GeV this ratio is 1:2.53±0.46 [12] and at 2.85 GeV it is 1:1.59±0.27 [13]. This suggests a deviation from the statistical approach, especially at lower energies. Similar conclusions can also be drawn from experiments on double pion production at excess energies below 100 MeV [14] where the statistical approach fails. We discuss the cross section ratios under different assumptions about the dominating reaction mechanism in section 3 of this paper.
With a 4π facility such as WASA [15], aiming for measurements of decays of η and η ′ mesons produced in pp interactions, the understanding of the pp → ppπππ reactions becomes very important as they constitute a severe background for the studies of η and η ′ decays into three pions. Those decays provide key ingredients for determining the ratios of the light quark masses m u /m s and m d /m s [16,17], since the decay widths are proportional to the u and d quark mass difference squared. In order to estimate the effect of the background for the decay experiments, the properties of the pp → ppπππ reactions for beam proton energies from 1.254 GeV (corresponding to the η production threshold) to 3 GeV are important. There are no experimental points for the cross section of the pp → ppπ • π • π • reaction in that energy range, and only three points for pp → ppπ + π − π • all coming from old bubble chamber experiments [12,13,18]. The experiment performed at the lowest energy, 1.48 GeV, identified a single event [18] (corresponding to 20µb). Moreover in the bubble chamber experiments, the prompt three pion production was not separated from the η → πππ decays.

Measurement
The analysis is based on data collected with the WASA facility at CELSIUS [19]. The target system provides small (φ ≈ 30 µm) hydrogen pellets that interact with the circulating proton beam. The protons have nominal kinetic energies of 1.30, 1.36 and 1.45 GeV (corresponding to excess energies, Q, in the center of mass system around 200 MeV for the pp → ppπππ reactions).
The integrated luminosities at each energy were: 27 nb −1 , 414 nb −1 (data on pp → ppπ + π − π • reaction are based on a sample corresponding to 80 nb −1 ) and 221 nb −1 respectively. The WASA detector system consists of a multilayer forward detector (FD), for measurement of the outgoing protons scattered in an angular range of 2.5-18 • , and a central detector (CD) containing an electromagnetic calorimeter and a drift chamber/solenoid for measuring the produced mesons and their decay particles in an angular range of 20-140 • . The experimental method for extracting the cross section of the pp → ppπππ reaction, relies on normalizing to the simultaneously measured pp → ppη reaction, with subsequent decay of the eta into π + π − π • (branching ratio 22.7% [4]) or into π • π • π • (32.5%). In this way, the reference reaction has the same particles in the final state, and most of the efficiency corrections cancel. The final state is selected by the requirement that two protons are detected in the forward detector. In addition the selected events should have six γ hit clusters (with energy depositions of at least 20 MeV) in the calorimeter, for the 3π • case, or two γ hit clusters and two tracks with opposite bending in the central detector drift chamber, for the π + π − π • case. After identification of the two proton tracks in the FD no additional cuts on the proton-proton system are applied. The specific cuts for neutral and charged CD particles systems aim to select a clean 3π final state. In case of the ppπ • π • π • channel, already the requirement of the six neutral hit clusters in the CD results in a fairly clean data sample. The π + π − π 0 sample was obtained by requiring the invariant mass of the two photons to be located in the π 0 mass region, and the missing mass of the two protons plus the two photons to be greater than two pion masses.
Two pion production, pp → ppππ, is the major physical background which has to be considered in the analysis in view of its much higher cross section. The final state can be misidentified as a three pion event only in case of two additional hit clusters in the calorimeter, due to cluster split-offs, pile-up or noise. To reject the background strict time cuts are applied, as well as additional kinematical conditions -such as reconstruction of the total energy. The final contribution of the background is on the per cent level, in agreement with expectations from the Monte Carlo simulations. Therefore the uncertainty in   the exact value of the total cross section for the two pion channels, as well as in the reaction mechanism, only gives a minor contribution to the systematical error.
The derivation of the cross sections for the pp → pp3π reaction is based on the fact that the resolution in the pp missing mass determination is very good (4 MeV/c 2 FWHM at 1.30 GeV) and that the missing mass distribution is practically insensitive to the mechanism of the pp → ppη reaction.
After the selection of the ppπππ final states, the pp missing mass distribution is constructed from experimental data, and from Monte Carlo simulated data of the reaction channels pp → ppπππ, pp → pp(η → 3π), and pp → ppππ as the main background contribution. The individual Monte Carlo distributions were then fitted to the measured spectrum, with the pp → ppπππ to pp → ppη ratio as parameter. The pp → ppππ contribution was fixed relative to the pp → ppη channel based on the cross section values listed in table 1. Fig. 1 shows the result of the best fit at the three beam energies for the pp → ppπ • π • π • reaction and at 1.36 GeV for the pp → ppπ + π − π • reaction. Several studies were done in order to determine uncertainties and check consistency: • For 1.36 GeV, data from two well separated run periods were analyzed and gave consistent results.  of the χ 2 distribution (7 constrains (7C) fit for the π • π • π • and 5C fit for the π + π − π • ). • Variation of the nominal beam energy and of the energy resolution of the detectors assumed in the analysis.
The applied method to obtain the cross section ratio relies heavily on the Monte Carlo simulations. Their accuracy is demonstrated in fig. 2 by comparing distributions of some variables with the result of the simulation, taking into account all three mentioned reaction channels. The normalization factors for the three channels are the same for each distribution, and were obtained from the fit of the pp missing mass distribution ( fig. 1). The simulation describes well detector effects such as the structure at 0.3 GeV, which is due to an ambiguity in distinguishing stopped protons from punch through protons in the FD. The angular distribution of the γs shows two distinct, well reproduced structures. Near 40 • the binning changes to account for different sizes of the CsI scintillators in the CD; at 90 • the detection efficiency is reduced by the pellet target components. The major geometric acceptance limitation is imposed by the angular acceptance for protons (3 • -17 • ). The good agreement between simulated and real data both in the gamma and proton scattering angle distribution indicates that the acceptance correction is under good con-  [20] tuned to describe the TOF data [21] and dotted line the pp FSI. trol.
In order to extract the total cross section, a model has to be used to extrapolate data outside of the measured range of the proton scattering angles. For the pp → ppη reaction the largest deviation from the phase space behavior is expected due to the strong pp final state interaction. We use a full calculation of the pp FSI of A. Deloff [20] with the Reid NN-potential, which yields a perfect reproduction of the 1 S 0 phase shifts for relative pp momenta up to 0.3 GeV/c. This calculation reproduces the pp angular distribution much better, but not yet the squared missing mass (M 2 pp ) distributions obtained for Q = 15.5 MeV [22] and Q = 41 MeV [21]. Agreement was then obtained in [20] by expanding the production amplitude in the η momentum relative to the pp pair. The proportionality constant was optimized for a best fit of the M 2 pp distribution, cf. fig. 3. Application of this approach to the M 2 pp distribution of this work yields a very similar result for Q = 41 MeV (see fig. 3) and Q = 17 MeV (not shown). This fit at the same time gives a good description of the pp opening angle distribution ( fig. 2c), where the pp FSI leads to an enhancement at the lowest angles. For the pp → pp3π, the outgoing protons can have scattering angles up to 30 • at those beam energies. This means that extraction of the total cross section involves some extrapolation into unmeasured kinematical regions. However, it was checked that e.g. the inclusion of a broad resonance in the Nπ system in the reaction mechanism changes the total acceptance by a few per cent only.

Results and discussion
The main result of the experiment is the ratio between the pp → ppπππ and pp → ppη cross sections for which values are given in table 2 with statistical and systematical uncertainties. One can extract the total cross section values Table 1 Total cross sections for two pion and eta production used in the analysis. The data for π o π o production are extracted from bubble chamber experiments [18,23] and from CELSIUS/WASA [24]. The data for π + π − production are from ref. [25]. The data for eta production are from CELSIUS, COSY and Saclay [22,[26][27][28]. Some values were obtained by interpolation to the energies used in this experiment.
Beam kinetic ppη ppπ + π − ppπ 0 π 0  Table 2 The results for the ratio of the cross sections of the pp → ppπππ reaction and the pp → ppη reaction with the corresponding η decay into 3π. Both statistical and systematical uncertainties are shown. In addition the extracted cross sections for pp → ppπ • π • π • and pp → ppπ + π − π • reactions are listed.
Beam kinetic using the known σ ppη from table 1 together with the relevant η decay branching ratio into 3π. For the beam proton energy at 1.30 GeV the η cross section points come from four experiments [22,[26][27][28]. At 1.36 GeV there is only one data point [26] to compare with. The cross section value at 1.45 GeV, is an interpolation using the data from PINOT [27]. The extracted values of cross sections for the production of the three pions are also given in table 2.
As a cross check of the acceptance corrections for the pp → ppη reaction, the cross sections have also been estimated using the luminosity derived from the simultaneously measured pp elastic scattering events [29]. The scattering cross sections were taken from the precision experiment EDDA [30].  Fig. 4. Measurements of the pp → ppπ + π − π • and pp → ppπ • π • π • cross section in the beam proton energy range 1-3 GeV. The four experimental points below 1.5 GeV are from the present experiment, while the data at 2 GeV and at 2.85 GeV for the pp → ppπ + π − π • reaction are from bubble chamber experiments [12,13]. Dotted lines are predictions of the statistical model [11] (phase space and flux factor). Dashed and solid line predictions are with pp FSI from Deloff [20] and from Fäldt and Wilkin [8] respectively. with the σ ppη results from literature, which indicates that detection acceptances are well under control. Figure 4 summarizes the results for the reactions pp → ppπ + π − π • and pp → ppπ • π • π • . The solid lines include the pp FSI calculated according to the parameterization from Fäldt and Wilkin [8] and the dashed lines the pp FSI calculated with the Reid wave function [20] (here, for pp relative momenta in center of mass greater than 300 MeV/c, pure phase space is used). The lines from the model predictions are normalized to the experimental data points at 1.36 GeV. In addition the dotted lines give the energy dependence of the cross section calculated from the statistical model and are normalized at high energies to the dashed lines. Two data points for pp → ppπ + π − π • from bubble chamber experiments in the energy range 2-3 GeV [12,13] are also shown. The data point at 2 GeV [12] has been corrected by subtracting the fraction of events expected from the pp → ppη reaction [31].
The experimental value obtained for the ratio of the cross sections for pp → ppπ + π − π • and pp → ppπ • π • π • at 1.36 GeV is 5.2±0.5(stat)±0.8(syst). To have a compar-ison at the same Q, the result should be corrected for the difference between the charged and neutral pion masses, which makes the phase space volume at 1.36 GeV for the pp → ppπ • π • π • reaction 18% larger than for pp → ppπ + π − π • . The threshold corrected value for the ratio σ(pp → ppπ + π − π • )/σ(pp → ppπ • π • π • ) thus becomes 6.3±0.6±1.0. As mentioned in the introduction a similar ratio is expected in the statistical approach with all amplitudes being equal. The simplest two baryon excitation mechanism involves the formation of an intermediate ∆ and an N * (1440), where the N * (1440) decays either to N(ππ) T =0 s−wave or via an intermediate ∆π state [4]. In the N * (1440) → N(ππ) T =0 s−wave scenario T 3π has to be 1. Then only the amplitude M 111 can contribute and a cross section ratio of 4 is expected from the expressions given in section 1. This decay branch can thus certainly be a major part of the total reaction mechanism. For the scenario N * (1440) → ∆π, T = 0,1 or 2 is permitted, and thus all M 101 , M 111 and M 121 amplitudes can be involved and the ratio for the 3π system can not be calculated without further assumptions. Note however that in this case the experimental ratio can easily be reproduced by choosing certain values of the amplitudes M 101 and M 121 . For example the choice |M 101 | 2 ≈ 0.7|M 111 | 2 and |M 121 | 2 = 0 gives the observed ratio 6.3. Accordingly, also the reaction diagram involving N * (1440) → ∆π might well be the leading part of the reaction mechanism. This conclusion is further supported by calculations within the isobar model by Sternheimer and Lindenbaum [2] which lead to the ratio 7. In case of N(1520) in the intermediate state one expects a much larger value, since the additional Nρ decay mode can contribute only to the pp → ppπ + π − π • channel.