We suggest that the recently observed charmed scalar mesons D 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 scalar mesons could be four-quark bound states is not new [20] and, therefore, it is natural to consider analogous states in the charm sector.We propose that the resonances observed by BELLE [6] and FOCUS [7] Collaborations be considered as two different resonances. In this work we use the method of QCD sum rules (QCDSR) [21] to study the two-point functions of the scalar mesons, D sJ (2317), D 0 (2308) and D 0 (2405) considered as four-quark states. The use of the QCD sum rules to study the charmed scalar mesons was already done in refs. [8,11,12], but in these calculations they were interpreted as two-quark states.In a recent calculation [22] some of us have considered that the lowest lying scalar mesons are S-wave bound states of a diquark-antidiquark pair. As suggested in ref.[23] the diquark was taken to be a spin zero colour anti-triplet. We extend this prescription to the charm sector and, therefore, the corresponding interpolating fields containing zero, one and two strange quarks are:where a, b, c, ... are colour indices, C is the charge conjugation matrix and q represents the quark u or d according to the charge of the meson. Since D sJ has ones quark, we choose the j s current to have the same quantum numbers of D sJ , which is supposed to be an isoscalar. However, since we are working in the SU(2) limit, the isoscalar and isovector states are mass degenerate and, therefore, this particular choice has no relevance here. The QCDSR for the charmed scalar mesons are constructed from the two-point correlation functionThe coupling of the scalar meson, S, to the scalar current, j S , can be parametrized in terms of the meson decay constant f S as [22]: 0|j S |S = √ 2f S m 4 S , therefore, the phenomenological side of Eq. (2) can be written aswhere the dots denote higher resonance contributions that will be parametrized, as usual, through the introduction of the continuum threshold parameter s 0 [24].In the OPE side we work at leading order and consider condensates up to dimension six. We deal with the strange quark as a light one and consider the diagrams up to order m s . To keep the charm quark mass finite, we use the momentum-space expression for the charm quark propagator. We follow ref. [25] and calculate the light
We calculate the coupling constants of D * D s K and D * s DK vertices using the QCD sum rules technique. We compare our results with results obtained in the limit of SU(4) symmetry and we found that the symmetry is broken at the order of 40%.Keywords: Coupling constants; Form Factors; QCD Sum RuleThe knowledge of coupling constants in hadronic vertices is crucial to estimate cross sections when hadronic degrees of freedom are used. The kaon is one of the commovers light mesons that can annihilate the charmonium in a nuclear medium, given as result D and D s mesons. Therefore, the absorption of charmonium by kaons in a nuclear medium can be used to study the J/ψ suppression in heavy-ion collisions, which is one of the signatures of the formation of the quark gluon plasma (QGP) [1]. The processes of absorption of J/Ψ by kaons can be visualized in the Figure 1.To evaluate theoretically the cross section for these processes, one can use the approach based on effective SU(4) Lagrangians [2,4]. The effective Lagrangians that describe the processes represented in Fig
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
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