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In this letter, we propose interpolating currents for the X(3872) resonance, and show that, in the Heavy Quark limit of QCD, the X(3872) state should have degenerate partners, independent of its internal structure. Magnitudes of possible I=0 and I=1 components of the X(3872) are also discussed.
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In this work, an Effective Field Theory (EFT) incorporating light SU(3)-flavour and heavy quark spin symmetry is used to describe charmed meson-antimeson bound states. At Lowest Order (LO), this means that only contact range interactions among the heavy meson and antimeson fields are involved. Besides, the isospin violating decays of the X(3872) will be used to constrain the interaction between the $D$ and a $bar{D}^*$ mesons in the isovector channel. Finally, assuming that the X(3915) and Y(4140) resonances are $D^*bar{D}^*$ and $D_s^*bar{D}_s^*$ molecular states, we can determine the four Low Energy Constants (LECs) of the EFT that appear at LO and, therefore, the full spectrum of molecular states with isospin I=0, 1/2 and 1.
Since the discovery of the $X(3872)$ the study of heavy meson molecules has been the subject of many investigations. On the experimental side different experiments have looked for its spin partners and the bottom analogs. On the theoretical side different approaches have been used to understand this state. Some of them are EFT that impose HQSS and so they make predictions for the partners of the $X(3872)$, suggesting the existence of a $J^{PC}=2^{++}$ partner in the charm sector or $J^{PC}=1^{++}$ or $2^{++}$ analogs in the bottom. In our work, in order to understand the $X(3872)$, we use a Chiral quark model in which, due to the proximity to the $DD^*$ threshold, we include $cbar c$ states coupled to $DD^*$ molecular components. In this coupled channel model the relative position of the bare $cbar c$ states with two meson thresholds are very important. We have looked for the $X(3872)$ partners and we dont find a bound state in the $D^*D^*$ $J^{PC}=2^{++}$. In the bottom sector we find the opposite situation where the $B^*B^*$ with $J^{PC}=2^{++}$ is bounded while the $J^{PC}=1^{++}$ is not bounded. These results shows how the coupling with $cbar c$ states can induced different results than those expected by HQSS. The reason is that this symmetry is worse in the open heavy meson sector than in the hidden heavy meson sector.
Following the procedure and motivations developed by Richardson, Buchmuller and Tye, we derive the potential of static quarks consistent with both the three-loop running of QCD coupling constant under the two-loop perturbative matching of V and MS-bar schemes and the confinement regime at long distances. Implications for the heavy quark masses as well as the quarkonium spectra and leptonic widths are discussed.
Inspired by the observation of the $P_{cs} (4459)$ state by LHCb recently, we reexamine the results of the interaction of the $J/psi Lambda$ channel with its coupled channels, exploiting the coupled channel unitary approach combined with heavy quark spin and local hidden gauge symmetries. By tuning the only free parameter, we find a pole of $(4459.07+i6.89)$ MeV below the $bar D^* Xi_c$ threshold, which was consistent well with the mass and width of the $P_{cs} (4459)$ state. Thus, we assume the $P_{cs} (4459)$ state to be a $bar D^* Xi_c$ bound state with the uncertainties on its degeneracy with $J^P = frac{1}{2}^-$ and $J^P = frac{3}{2}^-$. For the degeneracy, it would have two-poles structure, like $P_c (4450)$ before. There is another pole in the $J^P = frac{1}{2}^-$ sector, $(4310.53+i8.23)$ MeV, corresponding to a deep bound state of $bar D Xi_c$. Furthermore, the previously predicted loose bound states of $bar D Xi_c$, $bar D^* Xi_c$, $bar D^* Xi^*_c$ with $J=1/2,~I=0$ and $bar D^* Xi_c$, $bar D Xi^*_c$, $bar D^* Xi_c^*$ with $J=3/2,~I=0$ may exist as either bound states or unbound virtual states. We hope that future experiments can search for the $bar D^{(*)} Xi_c$ molecular states in their dominant decay channels of $bar D^{(*)}_s Lambda_c$, also in the $J/psi Lambda$ and $eta_c Lambda$ channels to reveal their different nature.
The $D^{(ast)}Xi_{cc}^{(ast)}$ system and $bar{Xi}_{cc}^{(ast)}Xi_{cc}^{(ast)}$ system can be related to the $D^{(ast)}bar{D}^{(ast)}$ system via heavy anti-quark di-quark symmetry (HADS). In this work, we employ a contact-range effective field theory to systematically investigate the likely existence of molecules in these systems in terms of the hypothesis that X(3872) is a $1^{++}$~$Dbar{D}^{ast}$ bound state in the isospin symmetry limit, with some of the unknown low energy constants estimated using the light-meson saturation approximation. In the meson-meson system, a $J^{PC}=2^{++}$~$bar{D}^{ast}D^{ast}$ molecule commonly referred to as $X(4013)$ is reproduced, which is the heavy quark spin partner of $X(3872)$. In the meson-baryon system, we predict two triply charmed pentaquark molecules, $J^{P}=1/2^{-}$~$D^{ast}Xi_{cc}$ and $J^{P}=5/2^{-}$~$D^{ast}Xi_{cc}^{ast}$. In the baryon-baryon system, there exist seven di-baryon molecules, $J^{PC}=0^{-+}$~$bar{Xi}_{cc}Xi_{cc}$, $J^{PC}=1^{--}$~$bar{Xi}_{cc}Xi_{cc}$, $J^{PC}=1^{-+}$~$bar{Xi}_{cc}Xi_{cc}^{ast}$, $J^{PC}=1^{--}$~$bar{Xi}_{cc}Xi_{cc}^{ast}$, $J^{PC}=2^{-+}$~$bar{Xi}_{cc}Xi_{cc}^{ast}$, $J^{PC}=2^{-+}$~$bar{Xi}_{cc}^{ast}Xi_{cc}^{ast}$ and $J^{PC}=3^{--}$~$bar{Xi}_{cc}^{ast}Xi_{cc}^{ast}$. Among them, the $J^{PC}=0^{-+}$~$bar{Xi}_{cc}Xi_{cc}$ and/or $J^{PC}=1^{--}$~$bar{Xi}_{cc}Xi_{cc}$ molecules may contribute to the $X(7200)$ state recently observed by the LHCb Collaboration, which implies that $X(7200)$ can be related to $X(3872)$ via HADS. As a byproduct, with the heavy quark flavor symmetry we also study likely existence of molecular states in the $B^{(ast)}bar{B}^{(ast)}$, $bar{B}^{(ast)}Xi_{bb}^{(ast)}$, and $bar{Xi}_{bb}^{(ast)}Xi_{bb}^{(ast)}$ systems.
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