We use QCD sum rules to test the nature of the meson Xð3872Þ, assumed to be a mixture between charmonium and exotic molecular ½c "q½q " c states with J PC ¼ 1 þþ . We find that there is only a small range for the values of the mixing angle that can provide simultaneously good agreement with the experimental value of the mass and the decay width, and this range is 5 0 13 0 . In this range we get m X ¼ ð3:77 AE 0:18Þ GeV and ÀðX ! J=c þ À Þ ¼ ð9:3 AE 6:9Þ MeV, which are compatible, within the errors, with the experimental values. We, therefore, conclude that the Xð3872Þ is approximately 97% a charmonium state with 3% admixture of $88% D 0 D Ã0 molecule and $12% D þ D ÃÀ molecule.

We identify the recently observed charmoniumlike structure Z AE c ð3900Þ as the charged partner of the Xð3872Þ state. Using standard techniques of QCD sum rules, we evaluate the three-point function and extract the coupling constants of the Z þ c J=c þ , Z þ c c þ and Z þ c D þ " D Ã0 vertices and the corresponding decay widths in these channels. The good agreement with the experimental data gives support to the tetraquark picture of this state.

In the past decade, due to the experimental observation of many charmonium-like states, there has been a revival of hadron spectroscopy. In particular, the experimental observation of charged charmonium-like, Z c states, and bottomonium-like, Z b states, represents a challenge since they can not be accommodated within the naive quark model. These charged states are good candidates of either tetraquark or molecular states and their observation motivated a vigorous theoretical activity. This is a rapidly evolving field with enormous amount of new experimental information. In this work, we review the current experimental progress and investigate various theoretical interpretations of these candidates of the multiquark states. The present review is written from the perspective of the QCD sum rules approach, where we present the main steps of concrete calculations and compare the results with other approaches and with experimental data.

We use QCD sum rules to calculate the width of the radiative decay of the meson X(3872), assumed to be a mixture between charmonium and exotic molecular [cq][qc] states with J P C = 1 ++ . We find that in a small range for the values of the mixing angle, 5 0 ≤ θ ≤ 13 0 , we get the branching ratio Γ(X → J/ψγ)/Γ(X → J/ψπ + π − ) = 0.19 ± 0.13, which is in agreement, with the experimental value. This result is compatible with the analysis of the mass and decay width of the mode J/ψ(nπ) performed in the same approach.

Using the QCD sum rule approach we investigate the possible four-quark structure for the new observed B 0 s π ± narrow structure (D0). We use a diquak-antidiquark scalar current and work to the order of ms in full QCD, without relying on 1/mQ expansion. Our study indicates that although it is possible to obtain a stable mass in agreement with the state found by the D0 collaboration, a more constraint analysis (simultaneous requirement of the OPE convergence and the dominance of the pole on the phenomenological side) leads to a higher mass. We also predict the masses of the bottom scalar tetraquark resonances with zero and two strange quarks.PACS numbers: 11.55. Hx, 12.38.Lg , Recently the D0 Collaboration reported the observation of a narrow structure, called X(5568), in the de-. This is the first observation of a hadronic state with two quarks and two antiquarks of four different flavors and, therefore, can only be explained as a tetraquark or molecular state. The mass and width of the observed state were reported to be: m = 5567.8 ± 2.9(sta) +0.9 −1.9 (syst) MeV/c 2 and Γ = 21.9 ± 6.4(sta)2 . As pointed out in Ref.[1], considering the large mass difference between the mass of the X(5568) and the sum of the B 0 and K ± masses, it can be difficult to explain the X(5568) as a molecular state. Therefore, the X (5568) [19][20][21][22] or a mixture between two-meson and four-quark states [23]. In this paper we use the QCD sum rule (QCDSR) approach [24][25][26][27][28] to investigate the possible four-quark structure for the X(5568) and, therefore, to test if the X(5568) could be the isovector bottom partner of the D + s0 (2317). The QCDSR for scalar mesons are constructed from the two-point correlation function written in terms of a scalar current j S :The key idea of the QCDSR method is to consider that this correlation function is of dual nature and it depends on the value of the momentum q. For large momentum, i.e., short distances, the correlation function can be calculated using perturbative QCD. In this case, the current j S is written in terms of the quark content of the studied mesons. However, since we are interested in studying the properties of hadrons, the relevant energies are lower and contributions from quark condensates, gluon condensates, etc., need to be included in the evaluation of Eq. (1). This can be done by using the Wilson operator product expansion (OPE) of the correlation function. In this case, Eq. (1) is expanded in terms of local condensates and a series of coefficients. The local operators incorporate nonperturbative long-distance effects, while the coefficients, by construction, include only the shortdistance domain and can be determined perturbatively. This way of evaluating the correlation function is customarily named as the calculation on the "OPE side".At large distances, or, equivalently, small momentum, the currents j † S and j S of Eq. (1) can be interpreted as operators of creation and annihilation of the scalar mesons. In this case, the correlation function is obtained by ins...