Abstract
We calculate the cross section for $e^+ e^-$ annihilation into $D^{*0} \bar D^0 +\gamma$ at center-of-mass energies near the $D^{*0} \bar D^{*0}$ threshold under the assumption that $X(3872)$ is a weakly bound charm meson molecule. The Dalitz plot has a $\bar D^{*0}$ resonance band in the squared invariant mass $t$ of $\bar D^0 \gamma$. In the limit as the decay width of the $D^{*0}$ goes to 0, the Dalitz plot also has a narrow band in the squared invariant mass $u$ of $D^{*0} \bar D^0$ from a charm-meson triangle singularity. At the physical value of the $D^{*0}$ width, the narrow band reduces to a shoulder. Thus the triangle singularity cannot be observed directly as a peak in a differential cross section as a function of $u$. It may however be observed indirectly as a local minimum in the $t$ distribution for events with $u$ below the triangle singularity. The minimum is produced by the Schmid cancellation between triangle loop diagrams and a tree diagram. The observation of this minimum would support the identification of $X(3872)$ as a weakly bound charm meson molecule.
Highlights
The Xð3872Þ meson, discovered in 2003 [1], was the first of the dozens of exotic hadrons whose constituents include a heavy quark and its antiquark that have been discovered in high-energy physics experiments [2,3,4,5,6]
If Xð3872Þ is a weakly bound charm-meson molecule, a charm-meson triangle singularity produces a narrow peak in the cross section for eþe− annihilation into X þ γ just above the DÃ0D Ã0 threshold [22]
The pepakffiffi appears near a value of the center-of-mass energy s given by sΔ inpffiEffi q. (13)
Summary
The Xð3872Þ meson, discovered in 2003 [1], was the first of the dozens of exotic hadrons whose constituents include a heavy quark and its antiquark that have been discovered in high-energy physics experiments [2,3,4,5,6]. Recent studies have revealed that a charm-meson triangle singularity produces a narrow peak in the production rate of X accompanied by a pion or photon with invariant mass near a DÃD Ã threshold [14,15,16]. S-wave channel will produce a narrow peak in the invariant mass distribution of Xπ0, Xπ−, or Xπþ near the appropriate DÃD Ã threshold [14,15] Such a narrow peak arises in the production of Xπ in decays of B mesons into K þ Xπ [14] and at hadron colliders [15]. Guo pointed out that any high-energy process that can create DÃ0D Ã0 at short distances in an S-wave channel will produce a narrow peak in the invariant mass distribution of X þ γ near the DÃ0D Ã0 threshold due to a charm-meson triangle singularity [16]. The loop integral that produces the triangle singularity is calculated in terms of Lorentz-invariant variables in Appendix B
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call