Process $e^{+}{e}^{-}\to \pi \pi X(3823)$ in the soft pion limit

The production of the resonance $X(3823)$, identified as the charmonium ${}^3{D}_2$ state, in the process $e^{+}{e}^{-}\to \pi \pi X(3823)$ has been recently reported by BESIII. Here it is pointed out that this process is fully described, up to one overall coupling constant, in the soft pion limit. An interpretation of the available and possible future data within the discussed theoretical framework may reveal new features of the charmoniumlike states. In particular, the observed relative yield for this process at different energies strongly suggests a very significant enhancement of the amplitude at the charmoniumlike peak near 4.36 GeV.

Figure 1

The contribution of the production of the $S$-wave (dashed) and the $D$-wave (dot-dashed) $\pi \pi$ system to the rate of the process $e^{+}{e}^{-}\to \pi \pi X(3823)$ at $\sqrt{s}=4.42\mathrm{GeV}$. Also shown is the distribution of the total rate (solid).

Figure 2

The dependence of the phase space integral $\mathrm{\Phi }$ on the total c.m. energy.