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)

Cited by in corpus (11)

• Pentaquark and Tetraquark states
• Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$
• Heavy molecules and one-$\sigma /\omega$-exchange model
• The Spin-orbit force, recoil corrections and possible $B{\bar{B}}^{\ast }$ and $D{\bar{D}}^{\ast }$ molecular states
• Hidden-Charm Tetraquarks and Charged Zc States
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• Strong decays of the $XYZ$ states
• Is the newly reported $X(5568)$ a $B\bar{K}$ molecular state?
• Angular momentum coefficients for meson strong decay and unquenched quark models
• Searches for isospin-violating transitions ${\chi }_{c0,2}\to {\pi }^0{\eta }_c$
• On the origin of the narrow peak and the isospin symmetry breaking of the $X$(3872)