DN interaction from the Juelich meson-exchange model
aa r X i v : . [ h e p - ph ] A ug DN interaction from the Jülich meson-exchange model
L Tolos ∗ , J. Haidenbauer † and G. Krein ∗∗ ∗ Institut de Ciències de l’ Espai (IEEC/CSIC), Campus Universitat Autònoma de Barcelona, Facultat deCiències, Torre C5, E-08193 Bellaterra (Barcelona), Spain † Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany ∗∗ Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento Teobaldo Ferraz, 271 - 01140-070São Paulo, SP, Brazil
Abstract.
The DN interaction is studied in close analogy to the meson-exchange ¯ KN potential of the Jülich group usingSU(4) symmetry constraints. The model generates the L c (2595) resonance dynamically as a DN quasi-bound state. Resultsfor DN scattering lengths and cross sections are presented and compared with predictions based on the Weinberg-Tomozawaterm. Some features of the L c (2595) resonance are also discussed emphasizing the role of the near-by p S c threshold. Keywords:
DN interaction, meson-exchange model, L c ( ) resonance PACS:
INTRODUCTION
The study of the interaction of open charm D -mesons with nucleons is challenging for several reasons. From theexperimental side, reliable models are crucial for guiding planned experiments by the ¯PANDA and CBM experimentsof the future FAIR facility at Darmstadt [1]. From the theoretical point of view, the physics motivations are several.Amongst the most exciting ones is the possibility of studying chiral symmetry in matter. Also, studies of J / y dissociation in matter [2] require a good knowledge of the interaction of D -mesons with ordinary hadrons. Anotherexciting perspective is the possibility of the formation of D -mesic nuclei [3, 4] and of exotic nuclear bound states like J / y binding to nuclei [5, 6, 7].To this end, coupled-channel meson-baryon models in the charm sector have been developed [8, 9, 10, 11, 12,13, 14]. In those approaches the strong attraction is provided by vector-meson exchange [10, 14], by the Weinberg-Tomazawa (WT) term [9, 8, 11, 12, 15], or by an extension of the WT interaction to an SU(8) spin-flavor scheme[13, 16]. All of them obtained dynamically the L c (2595) resonance. This resonance was reported by the CLEOcollaboration [17] and subsequently confirmed by several other experiments [18, 19, 20].In this paper, the DN interaction is derived in close analogy to the meson-exchange ¯ KN model of the Jülich group[21]. Results for DN scattering observables are obtained and compared to the outcome of the leading-order SU(4) WTcontact term [11, 15] and to a SU(8) WT scheme [13, 16]. We also analyze the L c (2595) resonance and focus on theconsequences of the fact that this resonance coincides practically with the p S c threshold. DN MODEL IN THE MESON-EXCHANGE FRAMEWORK
The DN interaction is derived in close analogy to the meson-exchange ¯ KN model of the Jülich group [21], usingas a working hypothesis SU(4) symmetry constraints, and by exploiting also the close connection between the DN and ¯ DN systems due to G-parity conservation. More specifically, we use the latter constraint to fix the contributionsto the direct DN interaction potential while the former one provides the transitions to channels that can couple tothe DN system. The main ingredients of the DN → DN interaction are provided by vector meson ( r , w ) exchangeand higher-order box diagrams involving D ∗ N , D D , and D ∗ D intermediate states. As far as the coupling to otherchannels is concerned, we follow here Ref. [21] and take into account only the channels p L c ( ) and p S c ( ) .Furthermore, we restrict ourselves to vector-meson exchange and we do not consider any higher-order diagramsin those channels. Pole diagrams due to the L c ( ) and S c ( ) intermediate states are, however, consistentlyincluded in all channels. We refer the reader to Ref. [22] for details. The resulting interaction potential V i j ( i , j = DN , p L c , p S c ) is then used to calculated the corresponding reaction amplitudes T i j by solving a coupled-channel
25 50 75 100 125 150 s -m N -m D (MeV) s t o t ( m b ) I=0 s -m N -m D (MeV) s t o t ( m b ) I=1 s (MeV) | T | q ( a . u . ) p - S ++ p S + p + S pS c -> pS c FIGURE 1.
Left and middle plots: DN cross sections for the isospin I = I = e = √ s − m N − m D .Results for the Jülich model [22] (solid lines), the SU(4) WT model [11] (dashed lines) and SU(8) WT scheme [13] (dashed-double-dotted lines) are displayed. Right plot: p S c invariant mass spectrum predicted by the Jülich DN meson-exchange model. We showalso data for the p + p − L + c invariant mass distribution taken from [19] (squares) and [20] (circles). Lippmann-Schwinger-type scattering equation: T i j = V i j + (cid:229) k V ik G k T k j , (1)from which we calculate the observables in the standard way [23]. DN SCATTERING OBSERVABLES AND THE L c ( ) RESONANCE
The SU(4) extension of the Jülich ¯ KN model to the DN interaction [22] generates narrow states in the S and S partial waves which we identify with the experimentally observed L c ( ) and S c ( ) resonances, respectively.Not surprisingly, we find an additional pole in the S partial wave, located close to the other one with a larger width,similarly to the ¯ KN sector. Our model also generates a further state, namely in the P partial wave at 2804 MeV,i.e. just below the DN threshold. We are tempted to identify this state with the L c ( ) resonance, whose quantumnumbers are not yet established [24].These results can be compared to previous works on the DN interaction. The SU(4) WT model of Ref. [11] obtainsthree S and two S states up to 2900 MeV [13]. Among them, there is a S state at 2694 MeV with a width of G =
153 MeV that strongly couples to the DN channel, with similar effects as the S resonance of our model. On theother hand, the SU(8) DN WT model [13] predicts even more states in this energy region.Those resonant states will have a determinant role in some DN scattering observables close to the DN threshold,such as scattering lengths and cross sections. Within the Jülich model we obtain the following scattering lengths fordifferent isospin ( I ): a I = = − i a I = = − i a I = is due to our S resonant state. The S -wave scattering lengths predicted by our model and by the SU(4) WT approachturn out to be very similar qualitatively for the I = I = DN cross sections for I = I = DN model [22] based on the parameter set that reproduces the positions of the L c ( ) and S c ( ) of the Particle Data Group (solid lines). The DN cross sections of the SU(4) WT model of Ref. [11] (dashed lines)and of the SU(8) WT model of Ref. [13] (dash-double-dotted lines) are also displayed. The DN cross sections of theU(4) WT approach of Ref. [11] show a similar behaviour as the one of the Jülich model for the I = S partial wave. In case of the I = S -wave contributionswhile the results of the Jülich model are dominated by the P -wave. Overall larger differences are seen in comparisonto the results for the SU(8) WT model.Finally, we would like to discuss the L ( ) resonance and the role of the near-by p S c threshold. The excitedcharmed baryon L c (2595) was first observed by the CLEO collaboration [17] and later confirmed by E687 [18] andARGUS [19], appearing as a pronounced peak in the invariant mass distribution of the p + p − L + c channel.In Fig. 1 (right plot) we present results for the p S c invariant mass spectrum in the particle basis for p S c → p S c which illustrate the subtle effects of the slightly different thresholds of the p + S c , p S + c , and p − S ++ c channels on thevarious invariant mass distributions. Similar invariant mass distributions are obtained for DN → p S c channel [22].The p S + c → p S + c channel resembles very much the measured signal and one can imagine that smearing out ourresults by the width of the S + c , which is roughly 4 MeV [20, 24], would yield a fairly good fit to the data. However,experimentally it was found that the L c (2595) decays predominantly into the p + S c and p − S ++ c channels with abranching fraction in the range of 66% [19] to close to 100% [20]. Smearing out the corresponding results with thesignificantly smaller and better known widths of the S c and S ++ c , of just 2 MeV [24], would still leave many of theevents found below the nominal p + S c and p − S ++ c threshold unexplained, especially for the CLEO experiment [20].Of course, the presence of the pp L + c channel should be incorporated in our model. But, in any case, it would beimportant to confirm the new CLEO data by independent measurements of the pp L + c and p S c mass spectra in theregion of the L c ( ) . ACKNOWLEDGMENTS
This work is partially supported by the Helmholtz Association through funds provided to the virtual institute “Spin andstrong QCD” (VH-VI-231), by the EU Integrated Infrastructure Initiative HadronPhysics2 Project (WP4 QCDnet),by BMBF (06BN9006), by DFG (SFB/TR 16, “Subnuclear Structure of Matter”) and FPA2010-16963 from DGIfunds. G.K. acknowledges financial support from CAPES, CNPq and FAPESP (Brazilian agencies). L.T. acknowledgessupport from the Ramon y Cajal Research Programme (Ministerio de Ciencia e Innovación)
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