Low-energy K (cid:0) Hadronic Interactions with Light Nuclei by AMADEUS

The AMADEUS collaboration aims to provide new experimental constraints to the K (cid:0) N strong interaction in the regime of non-perturbative QCD, exploiting low-energy K (cid:0) hadronic interactions with light nuclei (e.g. H, 4 He, 9 Be and 12 C). The low-momentum kaons ( p K (cid:24) 127 MeV / c) produced at the DA (cid:8) NE collider are ideal to explore both stopped and in-ﬂight K (cid:0) nuclear captures. The KLOE detector is used as an active target, allowing to achieve excellent acceptance and resolutions for the data. In this work the results obtained from the study of (cid:3) (cid:25) (cid:0) and (cid:3) p correlated production in the ﬁnal state are presented.


Introduction
The theoretical investigation of the low-energy K − N interaction predicts, in the energy region below the K − N threshold, a sufficiently attractive interaction to form a bound state in the isospin I=0 channel [1,2]. In [3][4][5][6][7] the I=0 Λ(1405) is interpreted as a pureKN bound state, this leads to the 1 prediction of deeply bound kaonic nuclear states. According to Chiral models [8][9][10][11][12] the Λ(1405) emerges as a superposition of two states, as a consequence of the K − N interaction is much less attractive, which implies the prediction of only slightly bound kaonic nuclear states.
The experimental investigation of the K − pp bound state properties in K − induced reactions is strongly biased by the competing K − -multi-nucleon absorption processes leading to the same final states (see e. g. [13,14]). In Ref. [15,16] a complete characterization of the K − two-, three-and fournucleon absorptions (2NA, 3NA and 4NA) was performed for the first time in the Λp and Σ 0 p final states exploiting low-energy K − captures on a 12 C target. In particular, in Ref. [15] the corresponding low-energy cross sections are measured, these represent a crucial ingredient for the determination of the in-medium K − optical potential [17,18]. In Section 2 a brief summary of the analysis [15] is given.
The experimental investigation of the Λ(1405) properties is also challenging. The resonance lineshape is found to depend on both the production mechanism and the observed decay channel. Moreover in K − induced reactions the non-resonant contribution to the final state Σπ production has to be also taken into account. In Section 3 a brief summary of the results obtained in [19] is given, which could give important information on the underlyingKN interaction models.
The described analyses refer to a sample of 1.74 fb −1 integrated luminosity collected by the KLOE collaboration [20] during the 2004/2005 data campaign. Low-energy K − s are produced at the DAΦNE collider [21], from the Φ-meson decay nearly at-rest, with a momentum of about 127 MeV/c. The K − captures, at-rest and in-flight, on the materials of the KLOE detector, used as an active target, are investigated.
In summer 2012 a high purity carbon target (graphite) was realized and installed inside the KLOE detector, between the beam pipe and the DC inner wall.
2. K − multi-nucleon absorption cross sections and branching ratios in Λp and Σ 0 p final states The possible existence of the K − pp bound state can be investigated in low-energy K − induced reactions by reconstructing the decays to Λ(Σ 0 )p.
Recently, Λ(Σ 0 )p decay modes were investigated by the AMADEUS collaboration in K −12 C absorption [15]. These studies allowed to perform the first comprehensive measurements of two, three and four nucleon absorption branching ratios (BRs) and cross sections for low-momentum kaons in Λp and Σ 0 p channels. The BR of the Σ 0 p direct production in K − 2NA quasi free interaction is found to be greater than the corresponding Λp production, contrary to what is expected by comparing the pure phase spaces. This gives important indications on the underlying three-body interaction. The Λp spectra are entirely interpreted in terms of K − multi-nucleon absorption processes, an eventual contribution due to the intermediate formation of a K − pp bound state completely overlaps with the K − 2NA in this channel, hence the corresponding yield is not extracted.

Resonant and non-resonant Yπ transition amplitudes below theKN threshold
In the investigation of the Λ(1405) properties, produced through the K − p mechanism in light nuclear targets, two biases have to be taken into account. The first bias is the energy threshold imposed by the absorbing nucleon binding energy (for K − capture at rest on 4 He the Σπ invariant mass threshold is about 1412 MeV, while for 12 C it is about 1416 MeV). In order to access theKN subthreshold region corresponding to the Λ(1405) high-mass predicted pole (about 1420 MeV), K − N absorption in-flight has to be exploited. For a mean kaon momentum of 100 MeV/c, the Σπ invariant mass threshold is shifted upwards by about 10 MeV.
Among the three (Σπ) 0 charge combinations Σ 0 π 0 represents the best signature for the Λ(1405) resonance, since it is free from the isospin I=0 background. In Fig. 1 the Σ 0 π 0 invariant mass spectrum from K − captures in 12 C nuclei for two data samples is shown [22]. The black distribution corresponds to the 2004/2005 data campaign, which include both K − captures at-rest and in flight. The blue distribution is obtained from 2012 data which include K − captures at-rest. The blue and the black distributions are normalized to unity. A red line indicates the energy threshold corresponding to K − absorption in 12 C at-rest. A rich sample of in-flight K −12 C captures can be easily identified above the red line. The Λ(1405) shape can be now extracted after subtracting the Σ 0 π 0 non-resonant contribution. The second bias is related to the non-resonant K − N → Σπ contribution that has to be subtracted in order to extract the Λ(1405) shape. The K − n → Λπ − non-resonant transition amplitude modulus below theKN threshold was obtained for the first time in [19] exploiting K − absorptions on 4 He target nuclei.
In this work the measured Λπ − invariant mass, momentum and angular distributions were simultaneously fitted by means of dedicated Monte Carlo simulations based on the phenomenological K − -nucleus absorption model described in Ref. [23] (the fit is shown in Fig. 2). All the resonant and non-resonant contributing reactions were taken into account together with the background process due to ΣN → ΛN ′ conversion reactions, and the contamination of K −12 C. The non-resonant transition amplitude modulus is found to be |A K − n→Λπ − | = (0.334 ± 0.018 stat +0.034 −0.058 syst) fm at (33±6) MeV below theKN threshold. This result can serve as a reference for the corresponding chiral predictions (See. Ref. [18,[24][25][26][27][28]). Moreover it can be used to get information on the isospin I=0 non-resonant counterpoint contributing to the Σ 0 π 0 invariant mass shape shown in Fig. 1.  Fig. 2. Panels a-f: p Λπ (Λπ momentum), cos(θ Λπ ) (cosine of angle between Λ and π), m Λπ (Λπ invariant mass), T Λπ , p Λ (Λ momentum) and p π (π momentum) distributions [19]. The experimental data and the corresponding statistical errors are represented by the black crosses, the systematic errors are light blue boxes. The different contributions included in the fit are shown by the colored histograms: non-resonant at-rest (red), resonant at-rest (blue), non-resonant in-flight (brown), resonant in-flight (cyan), ΣN → ΛN' internal conversion (magenta), K − absorptions in Carbon (green). The light and dark bands correspond to systematic and statistical errors, respectively. The gray band shows the total fit with the corresponding statistical error.