Is X(3872) {\sl Really} a Molecular State?

Abstract

After taking into account both the pion and sigma meson exchange potential, we have performed a dynamical calculation of the $D^0{\bar{D}}^{\ast 0}$ system. The $\sigma$ meson exchange potential is repulsive from heavy quark symmetry and numerically important for a loosely bound system. Our analysis disfavors the interpretation of X(3872) as a loosely bound molecular state if we use the experimental $D^{\ast }D\pi$ coupling constant $g=0.59$ and a reasonable cutoff around 1 GeV, which is the typical hadronic scale. Bound state solutions with negative eigenvalues for the $D{\bar{D}}^{\ast }$ system exist only with either a very large coupling constant (two times of the experimental value) or a large cutoff ($\Lambda \sim 6$ GeV or $\beta \sim 6$ GeV${}^2$). In contrast, there probably exists a loosely bound S-wave $B{\bar{B}}^{\ast }$ molecular state. Once produced, such a molecular state would be rather stable since its dominant decay mode is the radiative decay through $B^{\ast }\to B\gamma$. Experimental search of these states will be very interesting.

11 pages, 7 figures, 9 tables. The version to appear in EPJC

References in corpus (12)

• Pion Interactions in the X(3872)
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Axial Resonances in the Open and Hidden Charm Sectors
• New Hadron States
• Is Z^+(4430) a loosely bound molecular state?
• $Z^{+}(4430)$ as a $D_1^{\prime }{D}^{\ast }$ ($D_1{D}^{\ast }$) molecular state
• Threshold effect and π^\pm ψ(2S) peak
• Isospin properties of the X state near the D {\bar D}^{*} threshold
• Weakly-bound Hadronic Molecule near a 3-body Threshold
• $X(3872)\to D\bar{D}\gamma$ decays and the structure of X(3872)
• Bottomed Analog of Z+(4433)
• Possible new resonance at the $D^{\ast }{\bar{D}}^{\ast }$ threshold in $e^{+}{e}^{-}$ annihilation

Cited by in corpus (13)

• X(3872) and Other Possible Heavy Molecular States
• Are Y(4260) and {\rm Z${}_2^{+}$(4250)} ${\mathrm{D}}_1\mathrm{D}$ or ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ Hadronic Molecules?
• Is X(3872) a molecule?
• Isospin breaking effects in the X(3872) resonance
• X(3872) as a hadronic molecule and its decays to charmonium states and pions
• QCD Sum Rules for the X(3872) as a mixed molecule-charmoniun state
• Dynamics of Hadronic Molecule in One-Boson Exchange Approach and Possible Heavy Flavor Molecules
• The bound state problem of S-wave heavy quark meson-aitimeson systems
• ${\rm Y}(4S,5S)\to {\rm Y}(1S)\eta$ transitions in the rescattering model and the new BaBar measurement
• X(3872) and the bound state problem of $D^0{\bar{D}}^{\ast 0}$ (${\bar{D}}^0{D}^{\ast 0}$) in a chiral quark model
• ${\mathrm{Z}}^{+}(4430)$ and Analogous Heavy Flavor States
• Tetraquarks with charm in coupled-channel formalism
• Low-lying exotic mesons in the coupled-channel formalism