Deep sub-threshold Ξ − production in Ar+KCl reactions at 1.76A GeV
G. Agakishiev, A. Balanda, R. Bassini, D. Belver, A. V. Belyaev, A. Blanco, M. Böhmer, J. L. Boyard, P. Braun-Munzinger, P. Cabanelas, E. Castro, S. Chernenko, T. Christ, M. Destefanis, J. Díaz, F. Dohrmann, A. Dybczak, T. Eberl, L. Fabbietti, O. V. Fateev, P. Finocchiaro, P. Fonte, J. Friese, I. Fröhlich, T. Galatyuk, J. A. Garzón, R. Gernhäuser, A. Gil, C. Gilardi, M. Golubeva, D. González-Díaz, F. Guber, T. Hennino, R. Holzmann, I. Iori, A. Ivashkin, M. Jurkovic, B. Kämpfer, K. Kanaki, T. Karavicheva, D. Kirschner, I. Koenig, W. Koenig, B. W. Kolb, R. Kotte, F. Krizek, R. Krücken, W. Kühn, A. Kugler, A. Kurepin, S. Lang, J. S. Lange, K. Lapidus, T. Liu, L. Lopes, M. Lorenz, L. Maier, A. Mangiarotti, J. Markert, V. Metag, B. Michalska, J. Michel, D. Mishra, E. Morinière, J. Mousa, C. Müntz, L. Naumann, J. Otwinowski, Y. C. Pachmayer, M. Palka, Y. Parpottas, V. Pechenov, O. Pechenova, J. Pietraszko, W. Przygoda, B. Ramstein, A. Reshetin, M. Roy-Stephan, A. Rustamov, A. Sadovsky, B. Sailer, P. Salabura, A. Schmah, Yu. G. Sobolev, S. Spataro, B. Spruck, H. Ströbele, J. Stroth, C. Sturm, M. Sudol, A. Tarantola, K. Teilab, P. Tlusty, M. Traxler, R. Trebacz, H. Tsertos, V. Wagner, M. Weber, M. Wisniowski, T. Wojcik, et al. (4 additional authors not shown)
DDeep sub-threshold Ξ − production in Ar+KCl reactions at 1.76 A GeV
G. Agakishiev , A. Balanda , R. Bassini , D. Belver , A.V. Belyaev , A. Blanco , M. B¨ohmer , J. L. Boyard ,P. Braun-Munzinger , P. Cabanelas , E. Castro , S. Chernenko , T. Christ , M. Destefanis , J. D´ıaz , F. Dohrmann ,A. Dybczak , T. Eberl , L. Fabbietti ,d , O. V. Fateev , P. Finocchiaro , P. Fonte ,a , J. Friese , I. Fr¨ohlich ,T. Galatyuk , J. A. Garz´on , R. Gernh¨auser , A. Gil , C. Gilardi , M. Golubeva , D. Gonz´alez-D´ıaz ,F. Guber , T. Hennino , R. Holzmann , I. Iori ,c , A. Ivashkin , M. Jurkovic , B. K¨ampfer ,b , K. Kanaki ,T. Karavicheva , D. Kirschner , I. Koenig , W. Koenig , B. W. Kolb , R. Kotte , F. Krizek , R. Kr¨ucken ,W. K¨uhn , A. Kugler , A. Kurepin , S. Lang , J. S. Lange , K. Lapidus , T. Liu , L. Lopes , M. Lorenz ,L. Maier , A. Mangiarotti , J. Markert , V. Metag , B. Michalska , J. Michel , D. Mishra , E. Morini`ere ,J. Mousa , C. M¨untz , L. Naumann , J. Otwinowski , Y. C. Pachmayer , M. Palka , Y. Parpottas , V. Pechenov ,O. Pechenova , J. Pietraszko , W. Przygoda , B. Ramstein , A. Reshetin , M. Roy-Stephan , A. Rustamov ,A. Sadovsky , B. Sailer , P. Salabura , A. Schmah ,d , Yu. G. Sobolev , S. Spataro , B. Spruck , H. Str¨obele ,J. Stroth , , C. Sturm , M. Sudol , A. Tarantola , K. Teilab , P. Tlusty , M. Traxler , R. Trebacz , H. Tsertos ,V. Wagner , M. Weber , M. Wisniowski , T. Wojcik , J. W¨ustenfeld , S. Yurevich , Y. V. Zanevsky , P. Zhou (HADES collaboration) Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali del Sud, 95125 Catania, Italy LIP-Laborat´orio de Instrumentac¸ ˜ao e F´ısica Experimental de Part´ıculas , 3004-516 Coimbra, Portugal Smoluchowski Institute of Physics, Jagiellonian University of Cracow, 30-059 Krak´ow, Poland GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany Institut f¨ur Strahlenphysik, Forschungszentrum Dresden-Rossendorf, 01314 Dresden, Germany Joint Institute of Nuclear Research, 141980 Dubna, Russia Institut f¨ur Kernphysik, Johann Wolfgang Goethe-Universit¨at, 60438 Frankfurt, Germany II.Physikalisches Institut, Justus Liebig Universit¨at Giessen, 35392 Giessen, Germany Istituto Nazionale di Fisica Nucleare, Sezione di Milano, 20133 Milano, Italy Institute for Nuclear Research, Russian Academy of Science, 117312 Moscow, Russia Physik Department E12, Technische Universit¨at M¨unchen, 85748 M¨unchen, Germany Department of Physics, University of Cyprus, 1678 Nicosia, Cyprus Institut de Physique Nucl´eaire (UMR 8608), CNRS/IN2P3 - Universit´e Paris Sud, F-91406 Orsay Cedex, France Nuclear Physics Institute, Academy of Sciences of Czech Republic, 25068 Rez, Czech Republic Departamento de F´ısica de Part´ıculas, Univ. de Santiago de Compostela, 15706 Santiago de Compostela, Spain Instituto de F´ısica Corpuscular, Universidad de Valencia-CSIC, 46971 Valencia, Spain a also at ISEC Coimbra, Coimbra, Portugal b also at Technische Universit¨at Dresden, 01062 Dresden, Germany c also at Dipartimento di Fisica, Universit`a di Milano, 20133 Milano, Italy d also at Excellence Cluster Universe, Technische Universit¨at M¨unchen, 85748 Garching, Germany (Dated: October 25, 2018)We report first results on a deep sub-threshold production of the doubly strange hyperon Ξ − in a heavy-ion reaction. At a beam energy of 1.76 A GeV the reaction Ar+KCl was studied with the High AcceptanceDi-Electron Spectrometer (HADES) at SIS18/GSI. A high-statistics and high-purity Λ sample was collected,allowing for the investigation of the decay channel Ξ − → Λ π − . The deduced Ξ − / (Λ + Σ ) production ratioof (5 . ± . +1 . − . ) · − is significantly larger than available model predictions. PACS numbers: 25.75.-q, 25.75.Dw
The doubly strange Ξ − baryon (also known as cascadeparticle) has, in vacuum, a mass of 1321.3 MeV and de-cays ( c τ = 4 . cm) almost exclusively into the Λ - π − fi-nal state [1]. In elementary nucleon-nucleon (NN) collisionsnear threshold it must be co-produced with two kaons ensur-ing strangeness conservation. This requires a minimum beamenergy of E thr = 3 . GeV ( √ s thr = 3 . GeV). In heavy-ion collisions, the Ξ − yield was measured at various beamenergies covered by the RHIC [2], SPS [3, 4] and AGS [5]accelerators. Though cooperative processes in heavy-ion re-actions allow for particle production below NN threshold, no sub-threshold Ξ − production was observed so far. Predic-tions of sub-threshold cascade production at energies avail-able with the heavy-ion synchrotron SIS18 at GSI, Darm-stadt, were presented within a relativistic transport model[6]. The cross sections of the strangeness exchange reac-tions ¯KY → π Ξ ( Y = Λ , Σ ), which are essential for Ξ cre-ation below the nucleon-nucleon threshold, were taken from acoupled-channel approach based on a flavor SU(3)-invarianthadronic Lagrangian [7]. The Ξ − / Λ ratio was found toamount to a few times − , varying with system size andbeam energy, however, being fairly independent on centrality. a r X i v : . [ nu c l - e x ] J u l At SIS18 energies, also ¯K production, being a prerequisite ofthe above strangeness exchange reactions, proceeds below theNN threshold ( E thr = 2 . GeV). A similar strangeness ex-change reaction like that relevant for Ξ production is found tobe dominant in sub-threshold ¯K production in heavy-ion colli-sions [8], i.e. π Y → ¯KB ( B = N , ∆ ). Thus, medium effectson strange meson properties, like effective anti-kaon massesand hence reduced production thresholds, could strongly in-fluence the Ξ yield. However, the authors of [6] found the Ξ yield to be more sensitive to the magnitude of the cross sec-tions of strangeness-exchange reactions than to the mediumeffects due to modified kaon properties. Generally, the yieldof multi-strange particles, measured below their productionthreshold in NN collisions, is expected to be sensitive to theequation of state (EoS) of nuclear matter. In heavy-ion reac-tions, the necessary energy for the production of these par-ticles is accumulated via multiple collisions involving nucle-ons, produced particles and short-living resonances. The cor-responding number of such collisions increases with the den-sity inside the reaction zone the maximum of which in turndepends on the stiffness of the EoS.In this Letter we report on the first observation of sub-threshold Ξ − production in heavy-ion collisions. The exper-iment was performed with the H igh A cceptance D i- E lectron S pectrometer (HADES) at SIS18 [9]. HADES, primarily de-signed to measure di-electrons [10], offers excellent hadronidentification capabilities, too [11, 12, 13].A Ar beam of about particles/s with kinetic energyof 1.756 A GeV ( √ s NN = 2 . GeV) was incident on a four-fold segmented nat
KCl target with a total thickness of 5 mmcorresponding to . interaction probability. The beam en-ergy is known with a precision of about − . The energy lossof the beam particles in the target is estimated to be less than0.5 A MeV per target slice. The position resolution of the pri-mary (reaction) vertex amounts to 0.3 mm in both transversedirections while in beam direction it amounts to 1.5 mm as ex-pected from the finite thickness of the target slices. The datareadout was started by a first-level trigger (LVL1) decision, re-quiring a minimum charged-particle multiplicity ≥ in thetime-of-flight detectors. The integrated cross section selectedby this trigger comprises approximately the most central 35 %of the total reaction cross section. About 700 million LVL1events were processed for the present Ξ − investigation.In the present analysis we identified the Λ hyperons throughtheir decay Λ → p π − . Note that the reconstructed Λ yieldincludes the decay Λ ’s of the (slightly heavier) Σ baryondecaying exclusively into Λ and a photon [1] which cannotbe detected with HADES. Hence, the Λ yield has to be un-derstood as that of (Λ + Σ ) throughout the paper. To al-low for Λ selection various cuts on single-particle and two-particle quantities were applied. The most important onesact on geometrical distances, i.e. i) minimum values of thep, π − track distances to the primary vertex (p-VecToPrimVer, π -VecToPrimVer), ii) an upper threshold of the p- π − min-imum track distance (p- π -MinVecDist), and iii) a mini-mum value of the Λ vertex distance to the primary vertex ( Λ -VerToPrimVer). [MeV] inv M [ / ( . M e V )] i n v d N / d M – sigma) = 46528 – signal (mean significance = 195signal / bg = 4.6 FIG. 1: The p- π − invariant mass distribution. Hatched histogram:Scaled combinatorial background produced via event mixing. With these conditions we first analysed the invariant-massdistribution of proton- π − pairs (Fig. 1). A clear Λ signal couldbe separated from the combinatorial background (bg) as de-termined via the event mixing technique. The backgroundnormalization was performed over the given invariant-massrange, except a ± MeV interval around the Λ peak. For a ± σ mass cut around the Λ peak, the signal-to-backgroundratio and the significance, defined as signal / √ signal + bg ,amount to 4.6 and 195, respectively. The total Λ yield for thegiven cuts is N Λ = 46 , ± . Fitting a Gaussian functionto the signal, we obtain a mean value of (1114 . ± . MeVand a width ( σ ) of (2 . ± . MeV.Taking this high-statistics Λ sample, we started the Ξ − in-vestigation by combining - for each event containing a Λ can-didate - the Λ with those π − mesons not already contribut-ing to the Λ . The result was a structureless Λ - π − invariantmass distribution. Hence, additional conditions were neces-sary: iv) a lower limit on the 2nd π − (potential Ξ − daugh-ter) track distance to primary vertex ( π -VecToPrimVer), v)an upper limit of the distance of the Ξ − pointing vector w.r.t.the primary vertex ( Ξ -VecToPrimVer), vi) a maximum valueof the minimum track distance of the Λ and the 2nd π − ( π - Λ -MinVecDist), vii) a minimum value of the distance ofthe Ξ − vertex relative to the primary one ( Ξ -VerToPrimVer),and viii) a window of ± MeV around the Λ mass peak of thep- π − invariant mass distribution.The conditions on the geometrical quantities are summa-rized in Fig. 2, where the optimum cut values are indicated byarrows. We studied the stability of the signal if more strin-gent conditions were chosen. Because of the limited statis-tics all other cuts were kept fixed at the optimum values whenvarying a single cut quantity. The dependences on the variousgeometrical distances of experimental data and GEANT [14]simulations (see below) are found in good agreement.Figure 3 shows the invariant mass distribution of Λ - π − pairs after applying all conditions. Indeed, a narrow signalshows up on top of a smooth distribution. For an invariant-mass window of ± MeV (4 bins) around the peak center,we find N Ξ − = 141 ± ± entries to be attributed to Ξ − with the given statistical and systematic errors. The signal-to-background ratio and the significance amount to 0.17 and 4.6, FIG. 2: Relative Ξ − yields as a function of the cut value of various Λ and Ξ − geometrical distances (see text, units are mm). The full(open) dots display the experimental (simulation) data. The verticaland horizontal arrows indicate the chosen cut values and the regionof accepted distances, respectively. respectively. The given systematic error of the signal is dueto the signal variation for various histogram binnings, back-ground normalization regions and mass windows assigned tothe signal. These systematic variations are also reflected inthe significance of the signal of about − . The full line inthe bottom panel of Fig. 3 represents a Gaussian fit to the sig-nal. The mean value of (1320 ± MeV is well in agreementwith the PDG value of 1321.3 MeV [1]. Taking into accountthe bias due to the rather large bin size of 5 MeV to be usedfor statistical reasons, the peak width ( σ ) of (4 ± MeV is infair agreement with GEANT simulations which predict for Λ and Ξ − baryons almost equal values of about 2.5 MeV. In or-der to ensure that not a fake signal is selected, we performeda Λ -side-band analysis. No signal was found when choos-ing instead of condition viii) a window in the p- π − invariantmass of < | M p π − − (cid:104) M Λ (cid:105)| < MeV. Furthermore, whendividing randomly the data sample into two sub-samples, the Ξ − sub-yields were found - within errors - compatible withhalf of the above quoted total yield.Corrections for the finite acceptances and reconstructionefficiencies were deduced from simulations. Thermal Λ ’s( Ξ − ’s), characterized by the temperature parameter T Λ ( T Ξ − )were generated with the event generator Pluto [15]. The ex-perimental Λ rapidity distribution is found slightly broaderthan the thermal model distribution [11, 16]. Consequently,in Pluto we allowed also for anisotropic, i.e. longitudinallyelongated, phase-space distributions. For this purpose, an ad-ditional width parameter of Gaussian rapidity distributions, σ y , is taken into account. The Λ parameters are chosen suchthat the simulation reproduces both, the experimental val-ues of the effective inverse slope parameter at mid-rapidity, T eff, Λ = 95 MeV, and the rapidity width, σ y, Λ = 0 . [MeV] inv M [ / ( M e V )] i n v d N / d M – – signal (mean signal / bg = 0.17significance = 4.6 [MeV] inv M [ / ( M e V )] i n v d N / d M -20020406080 – Gauss fit: integral = 142 1) MeV – mean = (1320 1) MeV – sigma = (4 FIG. 3: Top: The same as Fig. 1, but for Λ - π − pairs. Bottom: Theinvariant mass distribution after background subtraction. The fullline represents a Gaussian fit to the Ξ − signal. [11, 12]. Since the phase-space distribution of the Ξ − isnot known, we investigated its geometrical acceptance for abroad range of the transverse and longitudinal shape param-eters, i.e. the inverse slope and rapidity width, T eff, Ξ − =(95 ± MeV and σ y, Ξ − = 0 . ± . , respectively.Here, the Λ inverse slope serves as a reference value. Thelower limit of T eff, Ξ − matches the measured inverse slopeparameter of K − mesons [12, 13] being essential for pro-ducing Ξ hyperons via strangeness-exchange processes (seeabove), while the upper limit is set by a similar interval abovethe Λ slope. We assumed the rapidity width of Ξ − ’s to belarger than the width of thermal Ξ − ’s with a temperature of95 MeV but smaller than that of Λ ’s. This choice is substan-tiated by two facts: Firstly, for a thermal rapidity distribution,the width approximately scales with the square root of mass( σ y = (cid:112) T /m c ), and secondly, the cascade particle maycarry less longitudinal momentum than the Λ hyperon, sinceit contains only one light quark which arises from projectilenucleons. With the given parameters and their ranges, we cal-culated the HADES acceptance (including the branching ratiofor the decay Λ → p π − ) for the Λ to (cid:15) acc , Λ = 0 . ± . ,and for the Ξ − to (cid:15) acc , Ξ − = (9 . +2 . − . ) · − . The simula-tion data are processed through GEANT modeling the detec-tor response. The GEANT data were embedded into real ex-perimental data and processed through the full analysis chain.Relating the outputs after cuts to the corresponding inputs,the Λ and Ξ − reconstruction efficiencies were estimated to (cid:15) eff , Λ = (6 . ± . · − and (cid:15) eff , Ξ − = (5 . ± . · − ,respectively. We proved our acceptance and efficiency correc-tions by extracting the lambda yield [11] which is found to bein agreement with existing data [16]. With the above correc-tion factors, the ratio of Ξ − and Λ production yields can bedetermined. Such a ratio, when derived from the same dataanalysis, has the advantage that systematic errors cancel to alarge extent. The ratio is calculated as P Ξ − P Λ+Σ = N Ξ − N Λ (cid:15) acc , Λ (cid:15) acc , Ξ − (cid:15) eff , Λ (cid:15) eff , Ξ − = (5 . ± . +1 . − . )10 − , (1)where statistical and systematic errors are given, resultingfrom adding the individual ones quadratically. The statisticalerror in (1) is dominated by the 20 % error of the Ξ − signalwhile the systematic error is governed by the stability of thesignal against cut and background variation and by the rangeof the parameters T Ξ − and σ y, Ξ − entering the simulation. FIG. 4: The yield ratio Ξ − / (Λ + Σ ) as a function of √ s NN or √ s NN − √ s thr (inset). The arrow gives the threshold in free NNcollisions. The open star, triangles and square represent data for cen-tral Au+Au and Pb+Pb collisions measured at RHIC [2], SPS [3, 4]and AGS [5], respectively. The filled circle shows the present ratio(1) for Ar+KCl reactions at 1.76 A GeV (statistical error within ticks,systematic error as bar). Full line: Statistical model for Au+Au [17].