Observation of the $h_c(1P)$ Using $e^{+}{e}^{-}$ Collisions above the $D\overline{D}$ Threshold

Using $586{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collision data at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$, produced at the Cornell Electron Storage Ring collider and collected with the CLEO-c detector, we observe the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c(1P)$. We measure its cross section to be $15.6\pm 2.3\pm 1.9\pm 3.0\mathrm{pb}$, where the third error is due to the external uncertainty on the branching fraction of $\psi (2S)\to {\pi }^0{h}_c(1P)$, which we use for normalization. We also find evidence for $e^{+}{e}^{-}\to \eta h_c(1P)$ at 4170 MeV at the $3\sigma$ level and see hints of a rise in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c(1P)$ cross section at 4260 MeV.

Figure 1

The recoil mass of the ${\pi }^{+}{\pi }^{-}$ system versus the recoil mass of the $\gamma {\pi }^{+}{\pi }^{-}$ system for candidate $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$; $h_c\to \gamma {\eta }_c$ events at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$. The signal appears at the intersection of the $h_c$ and ${\eta }_c$ masses. The vertical lines indicate the region used to select the ${\eta }_c$. The horizontal lines mark $\pm 10\mathrm{MeV}/c^2$ around the $h_c$ mass.

Figure 2

Fits to determine the yields of $h_c$ events from (a) $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$; (b) $e^{+}{e}^{-}\to \eta h_c$ at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$; (c) $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ at $E_{\mathrm{c}.\mathrm{m}.}=4260\mathrm{MeV}$; and (d) the normalizing mode $\psi (2S)\to {\pi }^0{h}_c$.

Figure 3

Cross sections as a function of center-of-mass energy. The triangle shows the cross section for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$; the closed circles are for the same process at other center-of-mass energies. For reference, the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}J/\psi$ cross section [1] is indicated by open circles. The inner error bars are the statistical errors; the outer error bars are the quadratic sum of the statistical and systematic errors.

Figure 4

The (a) ${\pi }^{+}{\pi }^{-}$ and (b) $h_c{\pi }^{\pm }$ mass distributions from $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{h}_c$ at $E_{\mathrm{c}.\mathrm{m}.}=4170\mathrm{MeV}$. The points are obtained by fitting for the $h_c$ yields in bins of ${\pi }^{+}{\pi }^{-}$ or ${\pi }^{\pm }{h}_c$ mass. The histograms are from Monte Carlo simulations, generated according to phase space and scaled by the total $h_c$ yield.