X(3872) presents many surprises after its discovery more than ten years ago. Understanding its properties is crucial to understand the spectrum of possible exotic mesons. In this work, X(3872) meson and its heavy quark spin symmetry (HQSS) partners (including the mesons in the bottom sector) are studied within the QCD Sum Rules approach using a current motivated by the molecular picture of X(3872). We predict four heavy partners to X(3872) and bottomonium with the masses and J P C quantum numbers. Obtained results are in good agreement with the previous studies and available experimental data within errors.
I. INTRODUCTIONDuring the last decade experimental data from Belle, BaBar, BESIII, CDF, D0, LHCb and other collaborations have put some puzzles about the conventional hadron spectrum, i.e., quark-antiquark and three-quarks picture of hadrons. New states (called exotic states) were observed from these experiments and they opened a new era of hadron spectroscopy.The milestone of these exotic states is X(3872). The X(3872) was first observed by Belle Collaboration in 2003 and the production mode was B + → X(3872)K + → J/ψπ + π − K + [1]. It has been also confirmed by the CDF [2], D0 [3], and BaBar [4] collaborations. The current average mass of X(3872) is 3871.69 ± 0.17 MeV and it is only 0.16 MeV below the D 0D * 0 threshold with a less then 1.2 MeV full width [5]. Its quantum numbers were determined by the LHCb Collaboration to be J P C = 1 ++ in 2013 [6]. Its unusual properties presents a puzzle in the meson spectroscopy and up to now there is no consensus about its structure.The natural attempt to investigate X(3872) is using quark model as a cc state. According to quark model, X(3872) is a 2P charmonium state. The mass of this state was obtained as 3947 MeV in [7,8] and 3906 MeV in [9]. In [10] they studied X(3872) resonance as cc = χ c1 (2P ) which sits on the D * 0D0 threshold and has a mass of m(D * 0D0 ) = 3871.81 ± 0.36 MeV. They also suggest a program for experimental research in order to verify their assumption. The other quark model candidates with J P C = 1 ++ are 2 3 P 1 (3925) and 3 3 P 1 (3853) [11,12]. Lattice QCD calculations give 2 3 P 1 (4010) [13] and 2 3 P 1 (4067) [14]. As can be seen, the masses of 2 3 P 1 charmonium state are bigger than the observed state.The other inconsistency with quark model is the J/ψπ + π − and J/ψπ + π − π 0 decays. The combined result for ratio of the decay fractions of X(3872) into J/ψπ + π − and J/ψπ + π − π 0 is [15]In these decays, the pions are produced through the decay of intermediate ρ or ω mesons, respectively. If one considers the differences in phase space between ρ and ω mesons, the production amplitude ratio can be found as [16] | A(J/ψρ) A(J/ψω) | = 0.26 ± 0.007.(2)