Diquark-Antidiquark with open charm in QCD sum rules

Abstract

Using the QCD sum rule approach we investigate the possible four-quark structure of the recently observed charmed scalar mesons D 0 0 (2308) (BELLE) and D 0,+ 0 (2405) (FOCUS) and also of the very narrow D + sJ (2317), firstly observed by BABAR. We use diquak-antidiquark currents and work to the order of ms in full QCD, without relying on 1/mc expansion. Our results indicate that a fourquark structure is acceptable for the resonances observed by BELLE and BABAR: D 0 0 (2308) and D + sJ (2317) respectively, but not for the resonances observed by FOCUS: D 0,+ 0 (2405).In general, the classification of mesons containing a single heavy quark is interpreted with the help of heavyquark symmetry, i.e., the symmetry valid for the infinitely heavy mass of charm quark. Under this symmetry, the strong interaction conserves total angular momentum of the light quark, j. In the meanwhile, total angular momentum of the light-heavy system, J, should be still regarded as a good quantum number of the system, even if the heavy-quark symmetry breaks down. In this way, the classification of the charmed mesons can be explained in terms of the quantum numbers (L, S, J, j), where L and S denote the orbital angular momentum between the light and heavy quarks and total spin of the system, respectively. The doublets with j = 1/2 and L = 0 have been observed over the past two decades (∼ 1975 − 1994) The spectroscopy of cq and cs pseudoscalar, vector and scalar mesons is drawn in Fig. 1, where the theoretical predictions of ref.[5] are represented as solid lines for the cs and dashed lines for the cq, and the experimental data are represented as triangles for the cs and circles for the cq. Due to its low mass, the structure of the meson D + sJ (2317) has been extensively debated. It has been interpreted as a cs state [8,9,10,11,12], two-meson molecular state [13,14], D − K-mixing [15], four-quark states [16,17,18] or a mixture between two-meson and four-quark states [19]. The same analyses would also apply to the meson D 0 0 (2308). In the light sector the idea that the light scalar mesons (the isoscalars σ(500), f 0 (980), the isodublet κ(800) [20] and the isovector a 0 (980)) could be four-quark bound states is not new [21,22]. Indeed, in a four-quark scenario, the mass degeneracy of f 0 (980) and a 0 (980) is natural, the mass hierarchy pattern of the nonet is understandable, and it is easy to explain why σ and κ are broader than f 0 (980) and a 0 (980). The decays σ → ππ, κ → Kπ and f 0 , a 0 → KK are OZI superallowed without the need of any gluon exchange, while f 0 → ππ and a 0 → ηπ are OZI allowed as it is mediated by one gluon exchange. Since f 0 (980) and a 0 (980) are very close to thē KK threshold, the f 0 (980) is dominated by the ππ state

Coupling constants of D*DsK and Ds*DK processes

“…We have been working on the problem of computing coupling constants for others processes and have a consistent method for this [6][7][8][9][10][11][12][13][14]. Following the QCDSR formalism described in our previous works [6][7][8][9][10][11][12][13][14], we write the three-point correlation function associated with the D * D s K vertex, which is given by…”

“…Following the QCDSR formalism described in our previous works [6][7][8][9][10][11][12][13][14], we write the three-point correlation function associated with the D * D s K vertex, which is given by…”

Modifications on the Properties of \(D^*_{s0}\)(2317) as Four-quark State in Thermal Medium

“…where a and b are color indices. Also, the D * s0 (2317) state can be regarded as diquark-antidiquark and the current J(x) can be defined by the following expression [29]:…”

“…This situation has opened a discussion of their inner structures. The uncertainty with conventional cs interpretation motivates many authors to hypothesize that the D * s0 (2317) state might be a molecule [15,27] or a diquark-antidiquark state [28,29]. Further, the existence of a DK pole at this energy has been recently confirmed with Lattice calculations of scattering amplitudes.…”

Future prospects for hadron physics at P ¯ ANDA

“…Since the new resonances do not fit well into the quark model, they triggered a whole series of theoretical interpretations. Those range from models that predict the mass splitting of states due to chiral symmetry [57,58] to those proposing tetraquark states [59,60,61,62,63,64,65,66] or DK molecules [67].…”