Abstract
If the $X(3872)$ is a weakly bound charm-meson molecule, it can be produced in $e^+ e^-$ annihilation by the creation of $D^{*0} \bar D^{*0}$ from a virtual photon followed by the rescattering of the P-wave charm-meson pair into the $X$ and a photon. A triangle singularity produces a narrow peak in the cross section for $e^+ e^- \to X \gamma$ 2.2 MeV above the $D^{*0} \bar{D}^{*0}$ threshold. We predict the normalized cross section in the region of the peak. We show that the absorptive contribution to the cross section for $e^+ e^- \to D^{*0} \bar D^{*0} \to X \gamma$, which was calculated previously by Dubynskiy and Voloshin, does not give a good approximation to the peak from the triangle singularity.
Highlights
Since early in this century, a large number of exotic hadrons whose constituents include a heavy quark and its antiquark have been discovered in high energy physics experiments [1,2,3,4,5,6,7,8,9,10]
We presented details of the calculation of the cross section for Xð3872Þγ from eþe− annihilation
A pair of P-wave spin-1 neutral charm mesons is created by the virtual photon from eþe− annihilation, and the charm mesons rescatter into Xγ
Summary
Since early in this century, a large number of exotic hadrons whose constituents include a heavy quark and its antiquark have been discovered in high energy physics experiments [1,2,3,4,5,6,7,8,9,10]. Because of the charm-meson triangle singularity, a high-energy process that can create an S-wave DÃD Ã pair at short distances can produce Xπ with a narrow peak near the DÃD Ã threshold. The cross section was not measured at energies near the DÃ0D Ã0 threshold at 4.014 GeV, which is where the narrow peak from the charm-meson triangle singularity is predicted to appear. VI, we calculate the absorptive contribution to the cross section for eþe− → Xγ from intermediate charm mesons DÃ0D Ã0 that are on their mass shells We show that it does not provide a good approximation to the peak in the cross section from the triangle singularity. We present a prescription for calculating the cross section for producing the X resonance feature in cases where the X is not a narrow bound state
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