Measurement of $e^{+}{e}^{-}\to D_s^{(*)+}{D}_s^{(*)-}$ cross sections near threshold using initial-state radiation

We report a measurement of exclusive $e^{+}{e}^{-}\to D_s^{(*)+}{D}_s^{(*)-}$ cross sections as a function of center-of-mass energy near the $D_s^{(*)+}{D}_s^{(*)-}$ threshold with initial-state radiation. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of $967{\mathrm{fb}}^{-1}$.

Figure 1

(a) The distribution of $M_{\mathrm{recoil}}^2(D_s^{+}{D}_s^{-})$ for $M_{D_s^{+}{D}_s^{-}}<5.0\mathrm{GeV}/c^2$ after all the requirements are applied. (b) The polar angle distribution of the $D_s^{+}{D}_s^{-}$ combinations. (c) The mass spectrum of the $D_s^{+}{D}_s^{-}{\gamma }_{\mathrm{ISR}}$ combinations after subtraction of $E_{\mathrm{c}.\mathrm{m}.}$ energy in case (2). (d) The $M_{D_s^{+}{D}_s^{-}}$ spectrum after all the requirements applied. Crosshatched histograms show the normalized $M_{D_s^{+}}$ and $M_{D_s^{-}}$ sideband contributions. Feed down from the $D_s^{+}{D}_s^{*-}$ final state is shown by the open histograms. The signal windows are shown by vertical dashed lines.

Figure 2

(a) The distribution of the $M_{\mathrm{recoil}}^2(D_s^{+}{D}_s^{*-})$ for $M_{D_s^{+}{D}_s^{*-}}<5.0\mathrm{GeV}/c^2$ after all the requirements are applied. (b) The polar angle distribution of the $D_s^{+}{D}_s^{*-}$ combinations. (c) The mass spectrum of the $D_s^{+}{D}_s^{*-}{\gamma }_{\mathrm{ISR}}$ combinations after subtraction of $E_{\mathrm{c}.\mathrm{m}.}$ in case (2). (d) The obtained $M_{D_s^{+}{D}_s^{*-}}$ spectrum. Crosshatched histograms show the normalized $M_{D_s^{+}}$ and $M_{D_s^{*-}}$ sideband contributions. The small contamination from the $D_s^{*+}{D}_s^{*-}$ final state is shown by the open histograms. The signal windows are shown by vertical dashed lines.

Figure 3

(a) The distributions of the $M_{\mathrm{recoil}}^2(D_s^{*+}{D}_s^{*-})$ for $M_{D_s^{*+}{D}_s^{*-}}<5.0\mathrm{GeV}/c^2$ after all the requirements are applied. (b) The polar angle distribution of the $D_s^{*+}{D}_s^{*-}$ combinations. (c) The mass spectrum of the $D_s^{*+}{D}_s^{*-}{\gamma }_{\mathrm{ISR}}$ combinations after subtraction of $E_{\mathrm{c}.\mathrm{m}.}$ in case (2). (d) The $M_{D_s^{*+}{D}_s^{*-}}$ spectrum after all the requirements are applied. Crosshatched histograms show the normalized $M_{D_s^{*+}}$ and $M_{D_s^{*-}}$ sideband contributions. The signal windows are shown by vertical dashed lines.

Figure 4

The cross section averaged over the bin width for (a) the $e^{+}{e}^{-}\to D_s^{+}{D}_s^{-}$ process, (b) the $e^{+}{e}^{-}\to D_s^{+}{D}_s^{*-}+\mathrm{c}.\mathrm{c}.$ process, and (c) the $e^{+}{e}^{-}\to D_s^{*+}{D}_s^{*-}$ process. Error bars show statistical uncertainties only. There is a common systematic uncertainty for all measurements, 11% for $D_s^{+}{D}_s^{-}$, 17% for $D_s^{+}{D}_s^{*-}$, and 31% for $D_s^{*+}{D}_s^{*-}$. This uncertainty is described in the text. The dotted lines show masses of the $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ states [18].

Figure 5

The R ratio for the sum of the $D_s^{+}{D}_s^{-}$, $D_s^{+}{D}_s^{*-}$, and $D_s^{*+}{D}_s^{*-}$ final states. The vertical dotted lines show the masses of the $\psi (4040)$, $\psi (4160)$, and $\psi (4415)$ states [18]. Error bars show statistical uncertainties only.