The E852 Collaboration

The ηπ system has been studied in the reaction πp → ηπp at 18 GeV/c. A large asymmetry in the angular distribution is observed indicating interference between L-even and L-odd partial waves. The a2(1320) is observed in the J = 2 wave, as is a broad enhancement between 1.2 and 1.6 GeV/c in the 1 wave. The observed phase difference between these waves shows that there is phase motion in addition to that due to a2(1320) decay. The data can be fitted by interference between the a2(1320) and an exotic 1 −+ resonance with M = (1370 ±16 +50 −30 ) MeV/c and Γ = (385 ±40 +65 −105 ) MeV/c. 13.60.Le, 13.85.Fb, 14.40.Cs Typeset using REVTEX 2 The question of whether or not hadrons outside the scope of the constituent quark model exist is one whose answer speaks directly to the fullness of our understanding of quantum chromodynamics (QCD) [1]. However, non-qq mesons (or exotic mesons) have proven difficult to distinguish from the many conventional qq states which populate the various mesonic spectra. For this reason, much attention has been focused on those states with manifestly exotic J quantum numbers. A qq meson with orbital angular momentum l and total spin s must have P = (−1) and C = (−1). Thus a resonance with J = 0, 0, 1, 2, ... must be exotic. Such a state could be a gluonic excitation such as a hybrid (qqg) or glueball (2g, 3g, ...), or a multiquark (qqqq) state. In a relative P wave (L=1), the ηπ system has J = 1. Having isospin I=1, it could not be a glueball, but it could be a hybrid or a multiquark state. Production and decay properties of exotic states have been predicted using several models [2–8]. A calculation based upon the MIT bag model predicts [3] that a 1 hybrid (qqg) will have a mass near 1.4 GeV/c. On the other hand, the flux-tube model [4,5] predicts the mass of the lowest-lying hybrid state to be around 1.8 GeV/c. Characteristics of bag-model S-wave multiquark states (which would have J = 0, 1, or 2) have been predicted [7] but those for a 1 state have not. Finally, recent lattice calculations [8] of the 1 hybrid meson estimate its mass to be in the range of 1.7 to 2.1 GeV. The ηπ system has been studied in several recent experiments, with apparently inconsistent results. Alde et al. [9], in a study of πp interactions at 100 GeV/c at CERN (the GAMS experiment), claimed to observe a 1 state in the ηπ system at 1.4 GeV/c produced via unnatural parity exchange (the P0 partial wave—the naming convention is discussed below) [10]. Aoyagi et al. [11], in a πp experiment at 6.3 GeV/c at KEK, observed a rather narrow enhancement in the ηπ system at 1.3 GeV/c in the natural parity exchange 1 spectrum (P+). Beladidze et al. [12], in the VES experiment at IHEP, (π N interactions at 37 GeV/c) also reported a P+ signal in the ηπ − state, but their signal was broader and had a significantly different phase variation from that of the KEK experiment. While the 3 phase difference between the P+ and D+ waves was independent of ηπ mass in the KEK analysis, that phase difference did show significant mass dependence in the VES analysis. (Since the phase variation for the D+ wave follows a classic Breit-Wigner pattern for the a2(1320) meson, the phase difference between these waves can determine the phase variation of the unknown P+ wave.) Here we study the ηπ system in the reaction πp → ηπp at 18 GeV/c. Our data sample was collected in the first data run of E852 at the AGS at Brookhaven National Laboratory with the Multi-Particle Spectrometer (MPS) [13] using a liquid hydrogen target. The MPS, which was equipped with six drift-chamber modules [14] and three proportional wire chambers, was augmented by: a four-layer cylindrical drift chamber surrounding the target [15]; a soft-photon detector consisting of 198 blocks of thallium-doped cesium iodide [16] also surrounding the target; a window-frame lead-scintillator photon-veto counter; a large drift chamber; and a 3045-element lead-glass detector (LGD) [17] downstream of the MPS. Further details are given elsewhere [18]. A total of 47 million triggers which required one forward-going charged track, one recoil charged track, and an LGD trigger-processor signal enhancing high electromagnetic effective mass was recorded. Of these, 47,200 events were reconstructed which were consistent with the ηπp (η → 2γ) final state. These events satisfied topological and fiducial volume cuts, as well as energy/momentum conservation for production and for the η → 2γ decay with a confidence level > 10% [19]. The 2γ mass resolution at the η mass is σ = 0.03 GeV/c. The a2(1320) is the dominant feature of the ηπ − mass spectrum shown in Fig. 1a. Background has been estimated using side bands in both the 2-γ mass distribution and the missing-mass distribution, thus taking into account background from non-η sources as well as from sources due to production of other final states. The background level is approximately 7% at 1.2 GeV/c, falling to 1% at 1.3 GeV/c. The acceptance-corrected distribution of |t| = |t| − |t|min, where t is the the fourmomentum-transfer, is shown for |t| > 0.08(GeV/c) in Fig. 1b. (Our acceptance is quite low below 0.08 (GeV/c) due to a trigger requirement.) The shape of this distribution is con4 sistent with previous experiments and has been shown to be consistent with natural-parity exchange production in Regge-pole phenomenology [20,21]. The acceptance-corrected distribution of cos θ, the cosine of the angle between the η and the beam track in the Gottfried-Jackson frame [22] of the ηπ system, is shown in Fig. 2a for 1.22 < M(ηπ) < 1.42 GeV/c. There is a forward-backward asymmetry in cos θ. The asymmetry for | cos θ| < 0.8 is plotted as a function of ηπ mass in Fig. 2b. The asymmetry is large, statistically significant and mass dependent. Since the presence of only even values of L would yield a symmetric distribution in cos θ, the observed asymmetry requires that odd-L partial waves be present to describe the data. A partial-wave analysis (PWA) [23,24] based on the extended maximum likelihood method has been used to study the spin-parity structure of the ηπ system. The partial waves are parameterized in terms of the quantum numbers J as well as m, the absolute value of the angular momentum projection, and the reflectivity ǫ (which is positive (negative) for natural (unnatural) parity exchange [25]). In our naming convention, a letter indicates the angular momentum of the partial wave in standard spectroscopic notation, while a subscript of 0 means m = 0, ǫ = −1, and a subscript of +(−) means m = 1, ǫ = +1(−1). Thus, S0 denotes the partial wave having J m = 00, while P− signifies 11, D+ means 2 1, and so on. We consider partial waves with m ≤ 1, and we assume that the production spin-density matrix has rank one. The experimental acceptance is determined by a Monte Carlo method. Peripherallyproduced events are generated [26] with isotropic angular distributions in the GottfriedJackson frame. After adding detector simulation [27], the Monte Carlo event sample is subjected to the same event-selection cuts and run through the same analysis as the data. The experimental acceptance is then incorporated into the PWA by using these events to calculate normalization integrals (see ref. [23]). Goodness-of-fit is determined by calculation of a χ from comparison of the experimental moments with those predicted by the results of the PWA fit. A systematic study has been performed to determine the effect on goodness-of-fit of adding and subtracting partial waves 5 of J ≤ 2 and m ≤ 1. All such waves have been included in the final fit. We have also performed fits including partial waves with J = 3 and J = 4. Contributions from these partial waves are found to be insignificant for M(ηπ) < 1.8 GeV/c. Thus, PWA fits shown or referred to in this letter include all partial waves with J ≤ 2 and m ≤ 1 (i.e. S0, P0, P−, D0, D−, P+, and D+). The background described above was included as a non-interfering, isotropic term of fixed magnitude. The results of the PWA fit in 40 MeV/c bins for 0.98 < M(ηπ) < 1.82 GeV/c and 0.10 < |t| < 0.95 GeV are shown in Fig. 3a-c. Here, the acceptance-corrected numbers of events predicted by the PWA fit for the D+ and P+ waves and their phase difference ∆Φ(D+ − P+) are shown as a function of M(ηπ ). There are eight ambiguous solutions in the fit [24,28,29], each of which leads to the same angular distribution. We show the range of fitted values for these ambiguous solutions in the vertical rectangular bar at each mass bin, and the maximum extent of their errors is shown as the error bar. The a2(1320) is clearly observed in the D+ partial wave (Fig. 3a). A broad peak is seen in the P+ wave at about 1.4 GeV/c (Fig. 3b). ∆Φ(D+ − P+) increases through the a2(1320) region, and then decreases above about 1.5 GeV/c (Fig. 3c). The intensities for the waves of negative reflectivity (not shown) are generally small and are all consistent with zero above about 1.3 GeV/c. These results are quite consistent with the VES results [12]. In particular, the shape of the phase difference is virtually identical to that reported by VES. (The magnitude of the phase difference is shifted by about 20 relative to that of VES.) Consistency checks and tests of the data have been carried out to determine whether the observation of the structure in the P+ wave could be an artifact due to assumptions made in the analysis or to acceptance problems. These include: fitting the data in restricted ranges of the decay angle; inclusion of higher angular momentum states; fitting the data with various t cuts; fitting the data using different parametrizations of the background; making cuts on other kinematic variables such as the πp or the ηp effective masses; and fitting data using events with η → πππ decays (with rather different acceptance from the 2γ events). The results are very stable and, in particular, the behavior of ∆Φ(D+ − P+) does not change in 6 any of these checks. Fits were also carri