Dispersive analysis of the isospin breaking in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^0{\pi }^{-}$ decays

Abstract

We analyze the latest LHCb data on the ${\pi }^{+}{\pi }^{-}$ spectrum in the isospin-violating $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ decay, based on dispersion theory to deal with the $\pi \pi$ final state interactions. Additionally, the isospin breaking effects are properly introduced, allowing for a reliable and accurate extraction of the ratio, $R_X$, between the $X(3872)$ couplings to the $J/\psi \rho$ and $J/\psi \omega$ channels from the data. We find very good agreement with the LHCb data for the whole range of the ${\pi }^{+}{\pi }^{-}$ invariant mass, and $R_X$ is determined to be {$0.26\pm 0.03$}. Using this value, we make predictions for the ${\pi }^{+}{\pi }^0{\pi }^{-}$ mass distribution in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^0{\pi }^{-}$ process, which is currently accessible by the BESIII Collaboration, and update a prediction for the pole positions of the isovector partner states of the $X(3872)$, $W_{c1}$, with $I(J^{PC})=1(1^{++})$.

9 pages, 1 table and 2 figures. Version to be published in Phys. Rev. D; results updated with a mistake on the rho-omega mixing corrected and a new appendix explaining how the mixing was obtained

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• Multiquark Resonances
• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Reconciling the X(3872) with the near-threshold enhancement in the D^0\bar{D}^{*0} final state
• Isospin breaking effects in the X(3872) resonance
• Study of the lineshape of the ${\chi }_{c1}(3872)$ state
• A Theory of X and Z Multiquark Resonances
• Isospin breaking, coupled-channel effects, and X(3872)
• Study of $e^{+}{e}^{-}\to \gamma \omega J/\psi$ and Observation of $X(3872)\to \omega J/\psi$
• Anomalous decay and scattering processes of the eta meson
• Measurements of $\psi (2S)$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ production in $pp$ collisions at $\sqrt{s}=8$ TeV with the ATLAS detector
• Evidence for X(3872) in PbPb collisions and studies of its prompt production at $\sqrt{s_{\mathrm{NN}}}=$ 5.02 TeV
• Study of the ${\psi }_2(3823)$ and ${\chi }_{c1}(3872)$ states in $B^{+}\to \left(J\psi {\pi }^{+}{\pi }^{-}\right)K^{+}$ decays
• Observation of the decay $X(3872)\to {\pi }^0{\chi }_{c1}(1P)$
• A Phenomenological analysis on isospin-violating decay of $X(3872)$
• Establishing the heavy quark spin and light flavor molecular multiplets of the $X(3872)$, $Z_c(3900)$ and $X(3960)$
• Revisit the isospin violating decays of $X(3872)$
• Observation of sizeable $\omega$ contribution to ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays
• A dispersive analysis of ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}\gamma$ and ${\eta }^{\prime }\to {\ell }^{+}{\ell }^{-}\gamma$
• Predicting isovector charmonium-like states from X(3872) properties
• Decipher the width of the $X(3872)$ via the QCD sum rules
• The X(3872) tetraquarks in B and B_s decays
• Observation of a New $X(3872)$ Production Process $e^{+}{e}^{-}\to \omega X(3872)$

Cited by in corpus (7)

• $P$-wave charmonium contribution to hidden-charm states from reanalysis of lattice QCD data
• Role of the short-range dynamics in the formation of $D^{(\ast )}{\bar{D}}^{(\ast )}/B^{(\ast )}{\bar{B}}^{(\ast )}$ hadronic molecules
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays
• Two nearby states in the $X(3872)$ region: Resolving the radiative-decay ratio tension with ${\eta }_{c2}$
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• Understanding large localized CP violation in $B^{\pm }\to K^{\pm }{\pi }^{+}{\pi }^{-}$ using dispersive methods