Lineshape of the Lambda(1405) Hyperon Measured Through its Sigma0 pion0 Decay

The pp ->p K+ Y0 reaction has been studied for hyperon masses m(Y0)<1540 MeV/c2 at COSY-Juelich by using a 3.65 GeV/c circulating proton beam incident on an internal hydrogen target. Final states comprising two protons, one positively charged kaon and one negatively charged pion have been identified with the ANKE spectrometer. Such configurations are sensitive to the production of the ground state Lambda and Sigma0 hyperons as well as the Sigma0(1385) and Lambda(1405) resonances. Applying invariant- and missing-mass techniques, the two overlapping excited states could be well separated, though with limited statistics. The shape and position of the Lambda(1405) distribution, reconstructed cleanly in the Sigma0 pion0 channel, are similar to those found from other decay modes and there is no obvious mass shift. This finding constitutes a challenging test for models that predict Lambda(1405) to be a two-state resonance.

The excited states of the nucleon are a topical field of research, since the full spectrum contains deep-rooted information about the underlying strong colour force acting between the quarks and gluons. In addition to searching for missing resonances predicted by quark models [1], it is important to understand the structure of certain well established states, such as the Λ(1405) hyperon resonance.
Although a four-star resonance [2], and known already for many years, the dynamics of the Λ(1405) are still not fully understood. Within the quark model it can be explained as a P -wave q 3 baryon [3]. It is also widely discussed as a candidate for aKN molecular state [4], or for one with a more intrinsic q 4q pentaquark structure [5]. If the Λ(1405) is a dynamically generated resonance produced viaKN rescattering within a coupled-channel formalism [6,7], it may consist of two overlapping I = 0 states [8,9,10]. Its decay spectrum would then depend upon the production reaction. Due to the opening of theKN channels, the Λ(1405) lineshape is not represented satisfactorily by a Breit-Wigner resonance [4,11,12,13]. Nevertheless, if the Λ(1405) were a single quantum state, as in the quark model or molecular pictures, its lineshape should be independent of the production method.
Part of the difficulty in elucidating the nature of the Λ(1405) is due to it overlapping the nearby Σ 0 (1385). The interference between these two states can distort significantly the Σ + π − and Σ − π + spectra [6], for which there are experimental indications [14]. This interference can be eliminated by taking the average of Σ + π − and Σ − π + data [11] but the cleanest approach is through the measurement of the Σ 0 π 0 channel, since isospin forbids this for Σ 0 (1385) decay. This is the technique that we want to develop here and, although our statistics are rather poor, these are already sufficient to yield promising results.
We have used data obtained during high statistics φ-production measurements with the ANKE spectrometer [15] to study the excitation and decay of lowlying hyperon resonances in pp collisions at a beam momentum of 3.65 GeV/c in an internal-ring experiment at COSY-Jülich. A dense hydrogen cluster-jet gas target was used and over a four-week period this yielded an integrated luminosity of L = (69 ± 10) pb −1 , as determined from elastic pp scattering that was measured in parallel and compared with the SAID 2004 solution [16].
The detection systems of the magnetic three-dipole spectrometer ANKE simultaneously register and identify both negatively and positively charged particles [17]. Forward (Fd) and side-wall (Sd) counters were used for protons, telescopes and side-wall scintillators for K + , and scintillators for π − . Since the efficiencies of the detectors are constant to 2% (σ) across the momentum range of registered particles, any uncertainty in this can be neglected in the further analysis.
In the Σ 0 (1385) case, the residue is X 0 = π 0 , while for the Λ(1405), X 0 = π 0 γ. The resonances overlap significantly because the widths of 36 MeV/c 2 for Σ 0 (1385) and 50 MeV/c 2 for Λ(1405) are much larger than the mass difference [2]. The strategy to discriminate between them is to: (i ) detect and identify four charged particles p F d , p Sd , K + and π − in coincidence, thereby drastically reducing the accidental background at the expense of statistics, (ii ) select those events for which the mass of a (p Sd π − ) pair corresponds to that of the Λ, (iii ) select the mass of the residue m(X 0 ) to be that of the π 0 to tag the Σ 0 (1385), and m(X 0 ) > m(π 0 ) + 55 MeV/c 2 for the Λ(1405). Figure 1a shows the two-dimensional distribution of the four-particle missing mass MM(pK + π − p) of the p Sd π − pairs versus the invariant mass M(p Sd π − ). A vertical band corresponding to the Λ, is visible around a mass of 1116 MeV/c 2 . The features of this band are illustrated clearly in the projection onto the M(p Sd π − ) axis shown in Fig. 1b. The Λ peak, with a FWHM of ∼ 5 MeV/c 2 , sits on a slowly varying background, much of which arises from a false pπ − association (the combinatorial background).
Data within the invariant-mass window 1112-1120 MeV/c 2 were retained for further analysis and, in Fig. 2, MM(p F d K + ) is plotted against MM(pK + pπ − ) for these events. The triangular-shaped domain arises from the constraint MM(p F d K + ) ≥ MM(pK + pπ − ) + m(Λ). Despite the lower limit of 50 MeV/c 2 on MM(pK + pπ − ), there is a background from Σ 0 production at the bottom of the triangle, but this can be easily cut away. The enhancement for MM(p F d K + ) ∼ 1400 MeV/c 2 corresponds to Σ 0 (1385) and Λ(1405) production. The two vertical bands show the four-particle missing-mass MM(pK + pπ − ) criteria used to separate the Σ 0 (1385) from the Λ(1405). The left band is optimised to identify a π 0 whereas, in view of the missing-mass resolution, the right one selects masses significantly greater than m(π 0 ).
Since the properties of the Σ 0 (1385) are undisputed [2], we first present and discuss results for this hyperon as a test case for the Λ(1405) analysis. In Fig. 3 we show the experimental missing-mass MM(p F d K + ) spectrum for  [2]. The resonance is located half way between the Σπ andKN thresholds, indicated by arrows in Fig. 3, and no significant influence of either threshold is observed in the data.
To investigate possible contributions to the spectrum other than from the Σ 0 (1385) excitation, Monte Carlo simulations were performed for backgrounds from non-resonant and resonant production. The first group of reactions includes processes such as pp → NK + πX(γ) and pp → NK + ππX(γ), with X A clear concentration of π 0 events is seen, though with a central value of the mass ∼ 8 MeV/c 2 too high, a deviation that is consistent with the resolution expected for a four-particle missing mass. The left shaded vertical box covers this π 0 region and the right one has M M (pK + pπ − ) > 190 MeV/c 2 originating, e.g., from π 0 γ and ππ.
representing any allowed Λ or Σ hyperon. The second group comprises Λ(1405) and Λ(1520) hyperon production. The simulations, based on the GEANT3 package, were performed in a similar manner to those in Ref. [18]. Events were generated according to phase space using relativistic Breit-Wigner parametrisations for the known hyperon resonances [2]. Their relative contributions were deduced by fitting the experimental data, giving the results shown by the histograms of Fig. 3. Also included is a small contribution from the Λ(1405) channel, arising from the tail of the missing-mass events in Fig. 2 leaking into the π 0 region. As expected, the Σ 0 (1385) peak dominates over a small and smooth background.
at p beam = 3.65 GeV/c. The systematic uncertainty in the fitting procedure and cross section evaluation was estimated by varying some of the event selection parameters, such as the width of the MM(pK + pπ − ) bands or the range for the Λ peak (see Fig. 1), or the non-resonant background in Fig. 3. The cross section is only a little lower than at 6 GeV/c, (7 ± 1) µb [19], whereas that for pp → pK + Λ increases by a factor of four over a similar change in excess energy [20].
Turning now to the Λ(1405), simulations show that the Σ 0 (1385) does not contaminate the missing-mass MM(pK + pπ − ) range above 190 MeV/c 2 . This point is crucial since it allows us to obtain a clean separation of the Σ 0 (1385) and Λ(1405). There is the possibility of some contamination from the pK + Λ(ππ) 0 channel but there is only a limited amount of the five-body phase space available near the maximum missing mass. Simulations also show that the ANKE acceptance varies only marginally in the mass range around 1400 MeV/c 2 . The corresponding experimental missing-mass MM(p F d K + ) spectrum is shown in Fig. 4a. The asymmetric distribution, which peaks around 1400 MeV/c 2 , has a long tail on the high missing-mass side that extends up to the kinematical limit.
as the Λ(1520). The resulting non-resonant background is indicated by the shaded histogram in Fig. 4a. When this is subtracted from the data we obtain the distribution shown as experimental points in Fig. 4b.
Our background-subtracted data exhibit a prominent structure around 1400 MeV/c 2 . There is no indication of a second near 1500 MeV/c 2 , which might result from the production of the Λ(1520) [11]. The excess of at most 20 events for MM(p F d K + ) > 1490 MeV/c 2 leads to an upper limit for the Λ(1520) production cross section of σ tot < 0.2 µb. The smallness of the signal in this case would be largely due to the low branching of only 9% into this channel. There is no evidence either for a significant contribution from the Y 0 * (1480) hyperon [18]. If this state were the same as the one-star Σ 0 (1480) of Ref. [2], the decay into Σ 0 π 0 would be forbidden. However, this state is also not seen in the K − p → π 0 π 0 Λ reaction [21].
We finally turn to the contribution from lower missing masses. From the number of events with 1320 < MM(p F d K + ) < 1440 MeV/c 2 , equal to 156 ± 23, we find a total production cross section of σ tot (pp → pK + Λ(1405)) = (4.5 ± 0.9 stat ± 1.8 syst ) µb at p beam = 3.65 GeV/c. The cumulative branching ratio for the Λ(1405) decay chain of reaction (2) of 21% and the acceptance of ∼ 4 × 10 −6 have been included, as well as the overall detection efficiency of ∼ 55%.
In Fig. 4b our experimental points are compared to the results of Thomas and Hemingway, which have been normalised by scaling their values down by factors of ∼3 and ∼7, respectively. The effect of theKN threshold is apparent in these published data, with the Λ(1405) mass distribution being distorted by the opening of this channel. Despite the very different production mechanisms, the three distributions have consistent shapes. A fit of one to either of the others leads to a χ 2 /ndf of the order of unity though, as pointed out in Ref. [6], for Σ + π − production [11] there is likely to be some residual distortion from I = 1 channels. The K − p → Λ(1405)π 0 → Σ 0 π 0 π 0 data yield a somewhat different distribution [22] but, as noted in this reference, the uncertainty as to which π 0 originated from the Λ(1405) "smears the resonance signal in the spectra". The situation is therefore very similar to that of the Hemingway Σ − π − π + π + data [11] and such results can only be interpreted within the context of a specific reaction model, such as that of Ref. [9].
Models based on unitary chiral perturbation theory find two poles in the neighborhood of the Λ(1405) which evolve from a singlet and an octet in the exact SU(3) limit [8,9]. One has a mass of 1390 MeV/c 2 and a width of 130 MeV/c 2 and couples preferentially to Σπ. The narrower one, located at 1425 MeV/c 2 , couples more strongly toKN, whose threshold lies at ∼ 1432 MeV/c 2 . Both states may contribute to the experimental distributions, and it is their relative population, which depends upon the production mechanism, that will determine the observed lineshape. Our experimental findings show that the properties (mass, width, and shape) of the Λ(1405) resonance are essentially identical for these three different production modes.
In summary, we have measured the excitation of the Σ 0 (1385) and Λ(1405) hyperon resonances in proton-proton collisions at a beam momentum of 3.65 GeV/c. We have succeeded in unambiguously separating the two states through their Λπ 0 and Σ 0 π 0 → Λγπ 0 decay modes. Cross sections of the order of a few µb have been deduced for both resonances. The Λ(1405), as measured through its Σ 0 π 0 decay, has a shape that is consistent with data on the charged decays [11,13], with a mass of ∼ 1400 MeV/c 2 and width of ∼ 60 MeV/c 2 . This might suggest that, if there are two states present in this region, then the reaction mechanisms in the three cases are preferentially populating the same one. However, by identifying particular reaction mechanisms, proponents of the two-state solution can describe the shape of the distribution that we have found [10].
The Σ 0 π 0 channel is by far the cleanest for the observation of the Λ(1405) since it is not contaminated by the Σ(1385) nor the confusion regarding the identification of the pion from its decay. However, although we have shown that the method works in practice, in view of our limited statistics, further data are clearly needed. The decay Λ(1405) → Σ 0 π 0 → Λγπ 0 can be detected directly in electromagnetic calorimeters. Corresponding measurements are under way in γp reactions (CB/TAPS at ELSA [23], SPring−8/LEPS [24]) and are also planned in pp interactions with WASA at COSY [25].