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Register a new userHeavy Quark Spin Symmetry and SU(3)-Flavour Partners of the X(3872)
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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.
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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.
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.
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.
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.
Heavy ion collisions provide a unique opportunity to study the nature of X(3872) compared with electron-positron and proton-proton (antiproton) collisions. With the abundant charm pairs produced in heavy-ion collisions, the production of multicharm hadrons and molecules can be enhanced by the combination of charm and anticharm quarks in the medium. We investigate the centrality and momentum dependence of X(3872) in heavy-ion collisions via the Langevin equation and instant coalescence model (LICM). When X(3872) is treated as a compact tetraquark state, the tetraquarks are produced via the coalescence of heavy and light quarks near the quantum chromodynamic (QCD) phase transition due to the restoration of the heavy quark potential at $Trightarrow T_c$. In the molecular scenario, loosely bound X(3872) is produced via the coalescence of $D^0$-$bar D^{*0}$ mesons in a hadronic medium after kinetic freeze-out. The phase space distributions of the charm quarks and D mesons in a bulk medium are studied with the Langevin equation, while the coalescence probability between constituent particles is controlled by the Wigner function, which encodes the internal structure of the formed particle. First, we employ the LICM to explain both $D^0$ and $J/psi$ production as a benchmark. Then, we give predictions regarding X(3872) production. We find that the total yield of tetraquark is several times larger than the molecular production in Pb-Pb collisions. Although the geometric size of the molecule is huge, the coalescence probability is small due to strict constraints on the relative momentum between $D^0$ and $bar D^{*0}$ in the molecular Wigner function, which significantly suppresses the molecular yield.
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