Baryon bound states of three hadrons with charm and hidden charm
aa r X i v : . [ h e p - ph ] J u l Baryon bound states of three hadronswith charm and hidden charm
Chu-Wen Xiao a , Melahat Bayar a , b and Eulogio Oset aa Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC,Institutos de Investigación de Paterna, Aptdo. 22085, 46071 Valencia,Spain b Department of Physics, Kocaeli University, 41380 Izmit, Turkey
In this talk, we show our recent theoretical results for three-body systems in the charm sectorwhich are made of three hadrons and contain one nucleon, one D meson and in additionanother meson, D , K or K . While the three baryon system has been a subject of intense theoretical study, it has onlybeen recently that attention was brought to systems with two mesons and one baryon. Thelow lying excited J P = + Λ and Σ states were described in [1], and N ∗ states in [2],combining Faddeev equations and chiral dynamics. A N ∗ state around 1920 MeV waspredicted in [3] as a molecule of NKK , corroborated in [4] and [5] by Faddeev equations.For three mesons systems, the X(2175) (now φ ( ) ) was explained as a resonant KK φ system in [6]. Similarly the K ( ) is explained as a KKK state in [7].In a recent work we study the three body systems in the charm sector, and use the FixedCenter Approximation to the Faddeev equations (FCA), which has been proved to be re-liable in [8, 9] and has been applied to the study of the
NKK system [10] and the resultscompare favorably with those of the Faddeev approach in [4] and those of the variationalapproach in [3]. There are some well known two body states in this sector, such as Λ c ( ) in DN with its coupled channels interaction [11, 12], D ∗ s ( ) in KD interaction [13–15],and the hypothetical X ( ) generated in isospin I=0 DD interaction [13]. These statesare the clusters in the FCA in our study. Following [9, 10, 16], we will apply the FCA to study the charm sector. The FCA approxi-mation to Faddeev equations is depicted in Figure 1. chuwen.xiao@ific.uv.es IV International Conference on Hadron Spectroscopy (hadron2011), 13-17 June 2011, Munich, Germany a ) ( b ) ( c ) ( d )31 2( e ) 31 2( f )+ + 31 2( g ) 321 ( h )+ + ... + ... + Figure 1:
Diagrammatic representation of the FCA to Faddeev equations.
With this meaning of the FCA, the equations can be written by two partition functions T , T which sum all diagrams of the series of Fig. 1, T = t + t G T ,(1) T = t + t G T ,(2) T = T + T ,(3)where T is the total three-body scattering amplitude. The amplitudes t and t representthe unitary scattering amplitudes respectively. And G is the propagator of particle 3. In this part we show the results of our investigation in that systems
KDN , NDK and
NDD .In Figure 2 (left) we show the results of | T | for the K Λ c ( ) scattering in the KDN system. We find a peak around 3150 MeV, slightly above the threshold of the Λ c ( ) + K mass (3088 MeV) and below the threshold of the KDN system (3298 MeV), of which thewidth is about 50 MeV. For the system
KDN , its quantum numbers are C = + S = − J P = + since we only consider the interaction among the components in L = NDK system, we obtain | T | for the ND ∗ s ( ) scattering shown in Fig. 2 (right).We found a peak around 3050 MeV which is about 200 MeV below the N + D ∗ s ( ) threshold and the width less than 10 MeV. We also do not find a counterpart in the PDGand the quantum numbers, with positive strangeness, correspond to an exotic state.Finally we obtain the T matrix, for the NDD interaction by means Eq. (3), and show theresults of | T | in Figure 3. From this figure we can see that there is a clear peak of | T | around 4400 MeV and the width is very small, less than 10 MeV. The peak appears belowthe NDD and NX ( ) thresholds and corresponds to a bound state of NX ( ) . This2 IV International Conference on Hadron Spectroscopy (hadron2011), 13-17 June 2011, Munich, Germany | T | [ M e V - ] s [MeV] | T | [ M e V - ] s [MeV] Figure 2:
Modulus squared of the scattering amplitude for K Λ c ( ) (left) and ND ∗ s ( ) (right). would be a hidden charm baryon state of J P = + which appears in the same region ofenergies as other hidden charm states of J P = − obtained in [17, 18]. | T | [ M e V - ] s [MeV] Figure 3:
Modulus squared of the the NX ( ) scattering amplitude. In all cases we find bound or quasibound states, relatively narrow, with energies 3150MeV, 3050 MeV and 4400 MeV, respectively. All these states have J P = + and isospin I = S = − C = S = C = S = C =
0, respectively. We hope that the work stimulates other theory calculations andfuture experiments in Facilities of FAIR or BELLE upgrade to prove our findings.3
IV International Conference on Hadron Spectroscopy (hadron2011), 13-17 June 2011, Munich, Germany
Acknowledgements
This work is partly supported by DGICYT contract FIS2006-03438, the Generalitat Valen-ciana in the program Prometeo and the EU Integrated Infrastructure Initiative HadronPhysics Project under Grant Agreement n.227431. M. Bayar acknowledges support of theScientific and Technical Research Council (TUBITAK) BIDEP-2219 grant.
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