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Register a new userDecay widths of the spin-2 partners of the X(3872)
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We consider the $X(3872)$ resonance as a $J^{PC}=1^{++}$ $Dbar D^*$ hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers $2^{++}$, $X_{2}$, which would be a $D^*bar D^*$ loosely bound state. The $X_{2}$ is expected to decay dominantly into $Dbar D$, $Dbar D^*$ and $bar D D^*$ in $d$-wave. In this work, we calculate the decay widths of the $X_{2}$ resonance into the above channels, as well as those of its bottom partner, $X_{b2}$, the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the $X_{2}$ and $X_{b2}$ of the order of a few MeV. Finally, we also study the radiative $X_2to Dbar D^{*}gamma$ and $X_{b2} to bar B B^{*}gamma$ decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the $Dbar D^{*}$ or $Bbar B^{*}$ final state interaction.
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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.
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.
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.
In a previous work we have studied the isospin 1/2 lowest positive and negative parity states of the pentaquark $uudcoverline{c}$, in a constituent quark model with a linear confinement and an SU(4) flavor-spin hyperfine interaction and we compared the results with the $P^+_c(4312)$, $P^+_c(4440)$ and $P^+_c(4457)$ pentaquarks observed at LHCb in 2019. Here we extend the previous work by calculating ratios of decay rates of the $P_c$ pentaquarks to $J/Psi$ and $eta_c$ and similarly the ratio of decay rates to $Lambda_c {bar D}^*$ and $Lambda_c bar D$. Our predictions are based on the SU(4)$times$SU(2) structure of compact pentaquarks.
It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state $chi_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the $chi_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the $chi_{c2}(3930)$ is a $D^*bar D^*$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the $chi_{c2}(3930)$, residing about 100 MeV below the $D^*bar D^*$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.
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