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

Abstract

It was recently proposed that the $X(3872)$ binding energy, the difference between the $D^0{\bar{D}}^{\ast 0}$ threshold and the $X(3872)$ mass, can be precisely determined by measuring the $\gamma X(3872)$ line shape from a short-distance $D^{\ast 0}{\bar{D}}^{\ast 0}$ source produced at high-energy experiments. Here, we investigate the feasibility of such a proposal by estimating the cross sections for the $e^{+}{e}^{-}\to {\pi }^0\gamma X(3872)$ and $p\bar{p}\to \gamma X(3872)$ processes considering the $D^{\ast 0}{\bar{D}}^{\ast 0}{D}^0/{\bar{D}}^{\ast 0}{D}^{\ast 0}{\bar{D}}^0$ triangle loops. These loops can produce a triangle singularity slightly above the $D^{\ast 0}{\bar{D}}^{\ast 0}$ threshold. It is found that the peak structures originating from the $D^{\ast 0}{\bar{D}}^{\ast 0}$ threshold cusp and the triangle singularity are not altered much by the energy dependence introduced by the $e^{+}{e}^{-}\to {\pi }^0{D}^{\ast 0}{\bar{D}}^{\ast 0}$ and $p\bar{p}\to {\bar{D}}^{\ast 0}{D}^{\ast 0}$ production parts or by considering a finite width for the $X(3872)$. We find that $\sigma (e^{+}{e}^{-}\to {\pi }^0\gamma X(3872))\times \mathrm{Br}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )$ is $\mathcal{O}(0.1\mathrm{fb})$ with the $\gamma X(3872)$ invariant mass integrated from 4.01 to 4.02 GeV and the c.m. energy of the $e^{+}{e}^{-}$ pair fixed at 4.23 GeV. The cross section $\sigma (p\bar{p}\to \gamma X(3872))\times \mathrm{Br}(X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi )$ is estimated to be of $\mathcal{O}(10\mathrm{pb})$. Our results suggest that a precise measurement of the $X(3872)$ binding energy can be done at PANDA.

29 pages, 11 figures

References in corpus (25)

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• Pion Interactions in the X(3872)
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• Estimate for the X(3872) to gamma J/psi decay width
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Cited by in corpus (8)

• $T_{cc}^{+}$ decays: Differential spectra and two-body final states
• Triangle Singularity in the Production of $T_{cc}^{+}$(3875) and a Soft Pion
• Galilean-Invariant XEFT at Next-to-Leading Order
• $D^{\pm }{D}^{\ast \mp }$ Hadronic Atom as a Key to Revealing the $X(3872)$ Mystery
• $D^{+}{D}^{-}$ hadronic atom and its production in $pp$ and $p\bar{p}$ collisions
• 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
• Study of $e^{+}{e}^{-}\to {\pi }^{0}X(3872)\gamma$ and search for $Z_c(4020{)}^0\to X(3872)\gamma$
• Photoproduction of the $X(3872)$ beyond vector meson dominance: the open-charm coupled-channel mechanism