Shedding New Light on Kaon-Nucleon/Nuclei Interaction and Its Astrophysical Implications with the AMADEUS Experiment at DAFNE
A. Scordo, M. Bazzi, G. Bellotti, C. Berucci, D. Bosnar, A.M. Bragadireanu, A. Clozza, M. Cargnelli, C. Curceanu, A. Dawood Butt, R. Del Grande, L. Fabbietti, C. Fiorini, F. Ghio, C. Guaraldo, M. Iliescu, P. Levi Sandri, J. Marton, D. Pietreanu, K. Piscicchia, H. Shi, D. Sirghi, F. Sirghi, I. Tucakovic, O. Vazquez Doce, W. Wiedmann, J. Zmeskal
SShedding New Light on Kaon-Nucleon / Nuclei Interactionand Its Astrophysical Implications with the AMADEUSExperiment at DA Φ NE A. Scordo , M. Bazzi , G. Bellotti , C. Berucci , D. Bosnar ,A.M. Bragadireanu , A. Clozza , M. Cargnelli , C. Curceanu , A. Dawood Butt ,R. Del Grande , L. Fabbietti , C. Fiorini , F. Ghio , C. Guaraldo , M. Iliescu ,P. Levi Sandri , J. Marton , D. Pietreanu , K. Piscicchia , H. Shi , D. Sirghi ,F. Sirghi , I. Tucakovic , O. Vazquez Doce , W. Wiedmann and J. Zmeskal INFN Laboratori Nazionali di Frascati, Frascati (Roma), Italy. Politecnico di Milano, Dipartimento di Elettronica, Informazione e Bioingegneria and INFN Sezione di Milano,Milano, Italy. Stefan-Meyer-Institut für subatomare Physik, Vienna, Austria. Physics Department, University of Zagreb, Zagreb, Croatia. Horia Hulubei National Institute of Physics and Nuclear Engineering (IFIN-HH), Magurele, Romania. Excellence Cluster Universe, Technische Universität München, Garching, Germany. Museo Storico della Fisica e Centro Studi e Ricerche "Enrico Fermi", Roma, Italy. Ru ¯der Bo˘skovi´c Institute, Bijeni˘cka cesta 54, Zagreb, Croatia. a) Corresponding author: [email protected]
Abstract.
The AMADEUS experiment deals with the investigation of the low-energy kaon-nuclei hadronic interaction at theDA Φ NE collider at LNF-INFN, which is fundamental to respond longstanding questions in the non-perturbative QCD strangenesssector. The antikaon-nucleon potential is investigated searching for signals from possible bound kaonic clusters, which would openthe possibility for the formation of cold dense baryonic matter. The confirmation of this scenario may imply a fundamental role ofstrangeness in astrophysics. AMADEUS step 0 consisted in the reanalysis of 2004 / K − absorptionsin H, He , Be and C in the setup materials. In this paper, together with a review on the multi-nucleon K − absorption and theparticle identification procedure, the first results on the Σ p channel will be presented including a statistical analysis on the possibleaccomodation of a deeply bound state. INTRODUCTION
The AMADEUS experiment [1, 2] deals with the study of the low-energy interactions of the negatively chargedkaons with light nuclei. Such type of physics, extremely important for the understanding of the non-perturbativeQCD in the strangeness sector, has important consequences, going from hadron and nuclear physics to astrophysics.In this context, useful information can be obtained from the strength of the K − binding in nuclei. The investigationof the absorptions of K − inside the KLOE Drift Chamber (DC) was originally motivated by the prediction of theformation of deeply bound kaonic nuclear states [3, 4]. Their binding energies and widths could be determined bystudying their decays into hyperons and nucleons. Also intimately connected with the kaon-nucleon potential is the Λ (1405) resonance, of which the still puzzling nature can be investigated within AMADEUS [5]. The study of the KNinteraction at low energies is of interest not only for quantifying the meson-baryon potential with strange content, butalso because of its impact on models describing the structure of neutron stars (NS) [6]. The KN potential is attractive,as theory predicts [7] and kaonic atoms confirm [8], and this fact leads to the formulation of hypotheses about antikaonrole inside the dense interior of neutron stars; one or more nucleons could be kept together by the strong attractive a r X i v : . [ nu c l - e x ] D ec nteraction between antikaons and nucleons and the so-called kaonic bound states, as ppK − or ppnK − , might beformed. The observation of such states and the measurements of their binding energies and widths, would provide aquantitative measurement of the KN interaction in vacuum, representing an important reference for the investigationof the in-medium properties of kaons. From the experimental point of view, two main approaches have been usedfor studying the K − pp cluster: p - p and heavy ion collisions [9] [10], and in-flight or stopped K − interactions in lightnuclei. For the second, results have been published by the FINUDA [11] and KEK-PS E549 collaborations [12]. Theinterpretation of both results is far from being conclusive, and it requires an accurate description of the single andmulti-nucleon absorption processes that a K − would undergo when interacting with light nuclei. From the analysis ofthe KLOE 2004-2005, information on both the strength of the K − binding in nuclei and the in-medium modificationof the Σ ∗ and Λ ∗ resonances properties can be extracted by analysing, respectively, the Λ / Σ − p , d , t channels and atthe resonances decay channels Λ / Σ − π . In this paper we focus, in particular, on the analysis of the Σ p final stateproduced in absorption processes of K − on two or more nucleons, occurring in the KLOE DC entrance wall, and onthe search for a signature of the ppK − → Σ + p kaonic bound state. A more detailed description of the analysisprocedures can be found in [13]. The DA Φ NE collider and the KLOE detector DA Φ NE [14] (Double Anular Φ -factory for Nice Experiments) is a double ring e + e − collider, designed to work atthe center of mass energy of the φ particle m φ = (1019 . ± . MeV / c . The φ meson decay produces chargedkaons (with BR( K + K − ) = . ± . ∼ MeV / c ) which is ideal either to stop them, or toexplore the products of the low-energy nuclear absorptions of K − s. The KLOE detector [15] is centered around theinteraction region of DA Φ NE and is characterised by a ∼ π geometry and an acceptance of ∼ µ m of carbon fibre and 150 µ m of aluminium foil. Dedicated GEANT MonteCarlo simulations of the KLOE apparatus were performed to estimatethe percentages of K − absorptions in the materials of the DC entrance wall (the K − absorption physics were treatedby the GEISHA package). Out of the total number of kaons interacting in the DC entrance wall, about 81% results tobe absorbed in the carbon fibre component and the residual 19% in the aluminium foil. The KLOE DC is filled witha mixture of helium and isobutane (90% in volume He and 10% in volume C H ). The chamber is characterisedby excellent position and momentum resolutions. Tracks are reconstructed with a resolution in the transverse R − φ plane of σ R φ ∼ µ m and a resolution along the z-axis of σ z ∼ mm . The transverse momentum resolution for lowmomentum tracks ((50 < p < MeV / c ) is σ pT p T ∼ . / fibres / glue = ffi ciency for photons in the range (20-300) MeV / c . The position of thecluster along the fibres can be obtained with a resolution σ (cid:107) ∼ . cm / √ E ( GeV ). The resolution in the orthogonaldirection is σ ⊥ ∼ . cm . The energy and time resolutions for photon clusters are given by σ E E γ = . √ E γ ( GeV ) and σ t = ps √ E γ ( GeV ) ⊕ ps . As a step 0 of AMADEUS, we analysed the 2004-2005 KLOE collected data, for whichthe dE / dx information of the reconstructed tracks is available ( dE / dx represents the truncated mean of the ADCcollected counts due to the ionisation in the DC gas). An important contribution of in-flight K − nuclear captures, indi ff erent nuclear targets from the KLOE materials, was evidenced and characterised, enabling to perform invariantmass spectroscopy of in-flight K − nuclear captures [18]. Preliminary results of the data analyses
The investigation of the negatively charged kaons interactions in nuclear matter is performed through the reconstruc-tion of hyperon-pion and hyperon-nucleon / nucleus correlated pairs productions, following the K − absorptions in H, He, Be and C. The investigation of the K − multi-nucleon absorptions and the properties of possible antikaonmulti-nucleon bound states proceeds through the analyses of the Λ / Σ − p , d , t , correlations; this last channel is, inparticular, extremely promising for the search and characterisation in di ff erent nuclear targets of the extremely rarefour nucleon absorption process. The search for the Λ (1405) is performed through its decay into Σ π (purely isospinI =
0) and Σ + π − (also the analysis of the Σ − π + decay channel started recently with a characterisation of neutron clustersn the KLOE calorimeter). The line shapes of the three combinations ( Σ π ) were recently obtained, for the first time,in a photoproduction experiment [19]; as the line-shapes of the three invariant mass spectra were found to be di ff erent,a comparative study with K − N production is of extreme interest. Moreover, a precise measurement of the Σ + π − Σ − π + pro-duction ratio in di ff erent targets can unveil the nature of the Λ ∗ state, by observing modifications of its parameters asa function of the density [20, 21]. To conclude, given the excellent resolution for the Λ π − invariant mass, the analysisof the Λ π − (isospin I =
1) production, both from direct formation process and from internal conversion of a primaryproduced Σ hyperon ( Σ N → Λ N (cid:48) ) is presently ongoing. Our aim is to measure, for the first time, the module of thenon-resonant transition amplitude (compared with the resonant Σ ∗− ) below threshold. The Λ (1116) selection The presence of a hyperon always represents the signature of a K − hadronic interaction inside the KLOE setup mate-rials. Most of the analyses introduced in the previous section then start with the identification of a Λ (1116), throughthe reconstruction of the Λ → p + π − (BR = ± . dE / dx versus momentumscatterplot for the finally selected protons is shown, where the function used for the selection of protons is displayedin red. The typical signature of pions in dE / dx versus momentum can be also seen in figure 1 left illustrating thee ffi cient rejection of π + contamination in a broad range of momentum. A minimum track length of 30 cm is required,and a common vertex is searched for all the p − π − pairs in each event. When found, the common vertex positionis added as an additional constraint for the track refitting. The module of the momentum and the vector cosines areredefined for both tracks, taking into account for the energy loss in the gas and the various crossed materials (signaland field wires, DC wall, beam pipe) when tracks are extrapolated back through the detector. As a final step for theidentification of Λ decays, the vertices are cross checked with quality cuts using the minimum distance between tracks(minimum distance < m p π − , calculated under the p and π − mass hypothesis, is shown in figure 1 right. The Gaussian fit gives a mass of 1115.723 ± MeV / c andan excellent resolution ( σ ) of 0.3 MeV / c , confirming the unique performances of KLOE for charged particles (thesystematics, depending on the momentum calibration of the KLOE setup, are presently under evaluation). FIGURE 1.
Left: dE / dx (in ADC counts) vs. momentum for the selected proton (up) and pion (down) tracks in the final selection.The proton selection functions is displayed in red. Right: m p π − invariant mass spectrum for the selected pion-proton pairs. This is the common procedure for all the analysed channels starting with the initial search of a Λ as a signature forthe hadronic interaction of the K − . Cuts on the radial position ( ρ Λ ) of the Λ decay vertex were optimised in orderto separate the two samples of K − absorption events occurring in the DC wall and the DC gas: ρ Λ = ± . ρ Λ >
33 cm, respectively. The ρ Λ limits were set based on MC simulations and a study of the Λ decay path. Inarticular, the ρ Λ = ± . K − interactions in gas as lowas (5 . + . − . %). Σ p analysis After the Λ search, a common vertex between the Λ candidate and an additional proton track is searched for. Theobtained resolution on the radial coordinate for the Λ p vertex is 12 mm, while its invariant mass resolution is found tobe, from MC studies, equal to 1 . MeV / c . The Σ candidates are identified through their decay into Λ γ pairs. Afterthe reconstruction of a Λ p pair, the photon selection is carried out via its identidication in the EMC. Photon candidatesare selected by applying a cut on the di ff erence between the EMC time measurement and the expected time of arrivalof the photon within − . < ∆ t < . ns . Then, the Σ p invariant mass, opening angle, and the individual Σ andproton momenta distributions are considered simultaneously in a global fit to extract the contributions of the variousabsorption processes. The processes that are taken into account in the fit of the experimental data are: • K − A → Σ − ( π ) p spec ( A (cid:48) ) • K − pp → Σ − p (2 NA ) • K − ppn → Σ − p − n (3 NA ) • K − ppnn → Σ − p − n − n (4 NA )where A is the atomic number of the target nucleus, p spec is the spectator proton, A’ is the atomic number of the residualnucleus and 2 / / / / K − absorption on two nucleons withand without final state interaction (FSI) for the Σ p state and processes involving more than two nucleons in the initialstate. These contributions are either extracted from experimental data samples or modelled via simulations. Two kindsof background contribute to the analysed Σ p final state: the machine background and the events with Λ π p in thefinal state. Both are quantified using experimental data [13]. The obtained fit is shown in figure 2 and the results aresummarised in table 1. TABLE 1.
Production probability of the Σ p final state for di ff erent in-termediate processes normalised to the number of stopped K − in the DCwall. The statistical and systematic errors are shown as well [13]. Process yield / K − stop × − σ stat × − σ syst × − . ± . + . − . . ± . + . − . Tot 2NA 0 . ± . + . − . . ± . + . − . Tot 3 body 0 . ± . + . − . + bkg. 0 . ± . + . − . The final fit results deliver the contributions of the di ff erent channels to the analysed Σ p final state. The best fit deliversa χ of 0.85. The emission rates extracted from the fit are normalised to the total number of stopped antikaons. Thefit results lead to the first measurements of the genuine 2NA-QF for the final state Σ p in reactions of stopped K − on targets of C and Al . This contribution is found to be only 12% of the total absorption cross-section. The laststep of the analysis consists in the search of the ppK − bound state produced in K − interaction with nuclear targets,decaying into a Σ p pair. The ppK − are simulated similarly to the 2NA-QF process but sampling the mass of the ppK − state with a Breit-Wigner distribution, rather than the Fermi momenta of the two nucleons in the initial state.The event kinematic is obtained by imposing the momentum conservation of the ppK − residual nucleus system.Di ff erent values for the binding energy and width varying within 15 − MeV / c and 30 − MeV / c in steps of15 and 20 MeV / c , respectively, are tested. This range has been selected according to several theoretical predictionspresent in literature and taking into account the experimental resolution. The global fit is repeated adding the ppK − .The best fit ( χ / nd f = . ppK − candidate with a binding energy of 45 MeV / c and a width of30 MeV / c , respectively. Figure 3 shows the results of the best fit for the Σ p invariant mass and proton momentumdistributions where the ppK − bound state contribution is shown in green.The resulting yield normalised to the number of stopped K − is ppK − / K − stop = (0 . ± . stat + . − . syst ) × − . IGURE 2.
Experimental distributions of the Σ p invariant mass, cos ( θ Σ p ) , Σ and proton momentum together with the results ofthe global fit. The experimental data after the subtraction of the machine background are shown by the black circles, the systematicerrors are represented by the boxes and the coloured histograms correspond to the fitted signal distributions where the light-coloured bands show the fit errors and the darker bands represent the symmetrised systematic errors. The gray line show the totalfit distributions (see [13] for details). FIGURE 3. Σ p invariant mass and proton momentum distributions together with the results of the global fit including the ppK − .The di ff erent contributions are labeled as in figure 2 and the green histograms represent the ppK − signal he F-test conducted to compare the simulation models with and without the ppK − signal gave a significance of theresult of only 1 σ for the ppK − yield result [13]. This shows that although the measured spectra are compatible withthe hypothesis of a contribution of a deeply bound state, the significance of the result is not su ffi cient to claim thediscovery of this state. Conclusions and perspectives
The broad experimental program of AMADEUS, dealing with the non-perturbative QCD in the strangeness sector, issupported by the quest for high precision and statistics measurements, able to set more stringent constraints on theexisting theoretical models. We demonstrated the capabilities of the KLOE detector to perform high quality physics(taking advantage of the unique features of the DA Φ NE factory) in the open sector of strangeness nuclear physics. Ourinvestigations, presently spread on a wide spectrum of physical processes, represent the most ambitious and systematice ff ort in this field. In particular, in this report we have presented the analysis of the K − absorption processes leadingto the Σ p state measured with the KLOE detector. It was shown that the full kinematics of this final state can bereconstructed and a global fit of the kinematic variables allows to pin down quantitatively the various contributingprocesses. Also, the possibility to accomodate a signal from a ppK − bound state has been investigated. We proved thepossibility to deliver very accurate and valuable results in the stangeness sector, in particular for what concerns thecomprehension of the KN potential, by studying all the possible channels following a K − absorption on one or severalnucleons, for very low momentum kaons. For the future, a dedicated AMADEUS setup, with dedicated gaseous andsolid targets, where to enhance the fraction of stopped kaons, is under study. ACKNOWLEDGMENTS
We thank all the KLOE Collaboration and the DA Φ NE sta ff for the fruitful collaboration.We acknowledge the Croatian Science Foundation under Project No. 1680.Part of this work was supported by the European Community-Research Infrastructure Integrating Activity “Study ofStrongly Interacting Matter” (HadronPhysics2, Grant Agreement No. 227431, and HadronPhysics3 (HP3) ContractNo. 283286) under the EU Seventh Framework Programme. REFERENCES [1] AMADEUS Letter of Intent, http: // / esperimenti / siddharta / LOI_AMDEUS_March2006.pdf[2] The AMADEUS collaboration, LNF preprint, LNF / / / //