Isospin breaking, coupled-channel effects, and X(3872)

Abstract

We re-investigate the possibility of X(3872) as a $D{\bar{D}}^{\ast }$ molecule with $J^{PC}=1^{++}$ within the framework of both the one-pion-exchange (OPE) model and the one-boson-exchange (OBE) model. After careful treatment of the S-D wave mixing, the mass difference between the neutral and charged $D(D^{\ast })$ mesons and the coupling of the $D(D^{\ast })$ pair to $D^{\ast }{\bar{D}}^{\ast }$, a loosely bound molecular state X(3872) emerges quite naturally with large isospin violation in its flavor wave function. For example, the isovector component is 26.24% if the binding energy is 0.30 MeV, where the isospin breaking effect is amplified by the tiny binding energy. After taking into account the phase space difference and assuming the $3\pi$ and $2\pi$ come from a virtual omega and rho meson respectively, we obtain the ratio of these two hidden-charm decay modes: $\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi )/\mathcal{B}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )=0.42$ for the binding energy being 0.3 MeV, which is consistent with the experimental value.

published in Phys. Rev. D

References in corpus (12)

• Can the X(3872) be a 1^{++} four-quark state?
• 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) {\sl Really} a Molecular State?
• Is X(3872) a molecule?
• Isospin breaking effects in the X(3872) resonance
• QCD Sum Rules for the X(3872) as a mixed molecule-charmoniun state
• $Z^{+}(4430)$ as a $D_1^{\prime }{D}^{\ast }$ ($D_1{D}^{\ast }$) molecular state
• The Effects of Charged Charm Mesons on the Line Shapes of the X(3872)
• X(3872) in lattice QCD with exact chiral symmetry
• 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
• On the Spin of the X(3872)