Angular analysis of the $e^{+}{e}^{-}\to D^{(*)\pm }{D}^{*\mp }$ process near the open charm threshold using initial-state radiation

We report a new measurement of the exclusive $e^{+}{e}^{-}\to D^{(*)\pm }{D}^{*\mp }$ cross sections as a function of the center-of-mass energy from the $D^{(*)\pm }{D}^{*\mp }$ threshold through $\sqrt{s}=6.0\mathrm{GeV}$, using the initial-state radiation technique. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of $951{\mathrm{fb}}^{-1}$. The accuracy of the cross section measurement is increased by a factor of 2 over the first Belle study. We perform the first angular analysis of the $e^{+}{e}^{-}\to D^{*\pm }{D}^{*\mp }$ process and decompose this exclusive cross section into three components corresponding to the $D^{*}$ helicities.

Figure 1

MC simulation $M_{\mathrm{rec}}(D^{(*)+}{\gamma }_{\mathrm{ISR}})$ spectra for $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ (histogram) and $e^{+}{e}^{-}\to D^{+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ (hatched histogram). The signal window is shown by vertical lines.

Figure 2

The $\mathrm{\Delta }{M}_{\mathrm{rec}}$ distributions before (histogram) and after (points with errors) the refit procedure for the MC events of $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$. The signal window lies between vertical lines.

Figure 3

The $D^{*+}{D}^{*-}$ mass resolution after the refit procedure as a function of $M(D^{*+}{D}^{*-})$ for the process $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$.

Figure 4

The $M(D^{*+}{D}^{*-})$ spectrum in the data after applying all selection criteria (points with error bars). The sum of backgrounds (1)–(3) is shown as the hatched histogram. The inset shows the zoomed spectrum near the threshold with a finer (half-size) bin width of $10\mathrm{MeV}/c^2$.

Figure 5

The scatter plot of $M(D^{*+})$ vs $\mathrm{\Delta }{M}_{\mathrm{rec}}^{\mathrm{fit}}$ in the data.

Figure 6

Distributions of (a) $M(D^{*+})$ and (b) $\mathrm{\Delta }{M}_{\mathrm{rec}}^{\mathrm{fit}}$. The solid line represents the result of the fit described in the text. The background contributions are shown as dotted curves. The signal and sideband regions are indicated by vertical lines.

Figure 7

The $M(D^{*0}{D}^{*-})$ spectrum after applying all requirements (a) before and (b) after combinatorial background subtraction. The solid histogram corresponds to the total contribution of the combinatorial background.

Figure 8

The $M(D^{*+}{D}^{*-})$ spectrum after the combinatorial background (1)–(3) subtraction. The contribution from the process $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\pi }_{\mathrm{miss}}^0{\gamma }_{\mathrm{ISR}}$ is shown as open circles with error bars. The inset shows the spectrum near the threshold with finer bins.

Figure 9

The $M(D^{+}{D}^{*-})$ spectrum in the data after applying all selection criteria (points with error bars). The sum of backgrounds (1)–(3) is shown as the hatched histogram. The inset shows the spectrum near the threshold with finer bins.

Figure 10

The $M(D^{+})$ vs $\mathrm{\Delta }{M}_{\mathrm{rec}}^{\mathrm{fit}}$ scatter plot in the data.

Figure 11

Distributions of the (a) $M(D^{+})$ and (b) $\mathrm{\Delta }{M}_{\mathrm{rec}}^{\mathrm{fit}}$. The solid line represents the result of the fit described in the text. The combinatorial background contribution is shown as the dotted curve. The dashed curve corresponds to background (4). The signal and sidebands regions are indicated by vertical lines.

Figure 12

The $M(D^0{D}^{*-})$ spectrum (a) before and (b) after subtraction of combinatorial background.

Figure 13

The $M(D^{+}{D}^{*-})$ spectrum after subtraction of combinatorial background. Contribution from the $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ is shown as open circles with error bars.

Figure 14

(a) The $M_{\mathrm{rec}}(D^{+}{\gamma }_{\mathrm{ISR}})$ spectrum after subtraction of the combinatorial background and the contribution from the process $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ for $e^{+}{e}^{-}\to D^{+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$. (b) The $M_{\mathrm{rec}}(D^{*+}{\gamma }_{\mathrm{ISR}})$ spectrum after combinatorial-background subtraction for $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$. Points with error bars show the data after ${\gamma }_{\mathrm{ISR}}$ energy correction; the hatched histogram corresponds to the MC simulation. The signal window lies between the vertical lines.

Figure 15

The total efficiency, including the branching fractions, as a function of $M(D^{(*)+}{D}^{*-})$ for (a) $e^{+}{e}^{-}\to D^{+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ and (b) $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$.

Figure 16

The exclusive cross sections as functions of $\sqrt{s}$ for (a) $e^{+}{e}^{-}\to D^{+}{D}^{*-}$ and (b) $e^{+}{e}^{-}\to D^{*+}{D}^{*-}$.

Figure 17

The distribution of $\cos \theta$ before (top panels) and after (bottom panels) background subtraction for different mass range: (a) $M(D^{+}{D}^{*-})<4.05\mathrm{GeV}/c^2$, (b) $4.05\mathrm{GeV}/c^2<M(D^{+}{D}^{*-})<4.3\mathrm{GeV}/c^2$, (c) $4.3\mathrm{GeV}/c^2<M(D^{+}{D}^{*-})<4.8\mathrm{GeV}/c^2$, (d) $M(D^{+}{D}^{*-})>4.8\mathrm{GeV}/c^2$. The contribution from the combinatorial background only is shown as the hatched histogram. The total contribution from the background sources is shown as the open histogram.

Figure 18

The components of the $e^{+}{e}^{-}\to D^{+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ cross section corresponding to the different $D^{*-}$ helicity: top is transverse; bottom is longitudinal.

Figure 19

Two-dimensional distribution of $\cos {\theta }_f$ vs $\cos {\theta }_p$ for different mass ranges: (a) $4.0\mathrm{GeV}/c^2<M(D^{*+}{D}^{*-})<4.1\mathrm{GeV}/c^2$, (b) $4.1\mathrm{GeV}/c^2<M(D^{*+}{D}^{*-})<4.25\mathrm{GeV}/c^2$, (c) $4.25\mathrm{GeV}/c^2<M(D^{*+}{D}^{*-})<4.6\mathrm{GeV}/c^2$, (d) $M(D^{*+}{D}^{*-})>4.6\mathrm{GeV}/c^2$.

Figure 20

The $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ process: (a) reconstruction efficiency as a function $c_1$ and $c_2$ and (b) total combinatorial background distribution.

Figure 21

The components of the $e^{+}{e}^{-}\to D^{*+}{D}^{*-}{\gamma }_{\mathrm{ISR}}$ cross section corresponding to the different $D^{*\pm }$’s helicities.