Revisiting $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in XEFT

Abstract

The calculation of the decay $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ in effective field theory is revisited to include final state ${\pi }^0{D}^0$, ${\pi }^0{\bar{D}}^0$and $D^0{\bar{D}}^0$ rescattering diagrams. These introduce significant uncertainty into the prediction for the partial width as a function of the binding energy. The differential distribution in the pion energy is also studied for the first time. The normalization of the distribution is again quite uncertain due to higher order effects but the shape of the distribution is unaffected by higher order corrections. Furthermore the shape of the distribution and the location of the peak are sensitive to the binding energy of $X(3872)$. The shape is strongly impacted by the presence of virtual $D^{\ast 0}$ graphs which highlights the molecular nature of the $X(3872)$. Measurement of the pion energy distribution in the decay $X(3872)\to D^0{\bar{D}}^0{\pi }^0$ can reveal interesting information about the binding nature of the $X(3872)$.

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Cited by in corpus (14)

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• $T_{cc}^{+}$ decays: Differential spectra and two-body final states
• Subleading contributions to the decay width of the $T_{cc}^{+}$ tetraquark
• Strong decays of $T_{cc}^{+}$ at NLO in an effective field theory
• Galilean-Invariant XEFT at Next-to-Leading Order
• Hadronic decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Possible precise measurements of the $X(3872)$ mass with the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ reactions
• Triangle singularity in $B^0\to {\pi }^{-}{K}^{+}X(3872)$ via the $D_{s1}\bar{D}{D}^{\ast }$ loop and possible precise measurement of the $X(3872)$ mass
• Radiative decays of the heavy-quark-spin molecular partner of $T_{cc}^{+}$
• Evasion of HSR in the charmless decays of excited $P$-wave charmonia
• Hadronic molecules and multiquark states
• Low-energy $N\varphi$ scattering from a pole-enhanced triangle diagram
• Low-energy $DD$ scattering in lattice QCD