Measurement of the $\gamma \gamma *\to {\eta }_c$ transition form factor

We study the reaction $e^{+}{e}^{-}\to e^{+}{e}^{-}{\eta }_c$, ${\eta }_c\to K_S{K}^{\pm }{\pi }^{\mp }$ and obtain ${\eta }_c$ mass and width values $2982.2\pm 0.4\pm 1.6\mathrm{MeV}/c^2$ and $31.7\pm 1.2\pm 0.8\mathrm{MeV}$, respectively. We find $\Gamma ({\eta }_c\to \gamma \gamma )\mathcal{B}({\eta }_c\to K\overline{K}\pi )=0.374\pm 0.009\pm 0.031\mathrm{keV}$, and measure the $\gamma {\gamma }^{*}\to {\eta }_c$ transition form factor in the momentum transfer range from 2 to $50{\mathrm{GeV}}^2$. The analysis is based on $469{\mathrm{fb}}^{-1}$ of integrated luminosity collected at PEP-II with the BABAR detector at $e^{+}{e}^{-}$ center-of-mass energies near 10.6 GeV.

Figure 1

The Feynman diagram for the $e^{+}{e}^{-}\to e^{+}{e}^{-}{\eta }_c$ two-photon production process.

Figure 2

The Feynman diagrams for the background processes (a) $e^{+}{e}^{-}\to J/\psi \gamma$, and (b) $e^{+}{e}^{-}\to e^{+}{e}^{-}J/\psi$.

Figure 3

The $M_{2\pi }$ distribution for $K_S$ candidates in the no-tag data sample. The shaded histogram shows events rejected by the requirement $\cos {\psi }_{K_S}>0.95$. The arrows indicate the region used to select event candidates.

Figure 4

The distribution of the invariant mass of ${\eta }_c$ candidates in the no-tag data sample. The shaded histogram shows events rejected by the requirement $p_{\perp }^{*}<0.25\mathrm{GeV}/c$.

Figure 5

The transverse momentum distribution for $e{\eta }_c$ data candidates. The shaded histogram is for simulated signal events. Data candidates for which $p_{\perp }^{*}<0.25\mathrm{GeV}/c$ (indicated by the arrow) are retained.

Figure 6

The distribution of $r$ defined in Eq. (3) for data (points with error bars) and simulated signal events (shaded histogram). The arrows indicate the region used to select candidate events ($-0.02<r<0.03$).

Figure 7

The invariant mass distribution for single-tag ${\eta }_c$ candidates. The shaded histogram is for events with the wrong sign of the $e{\eta }_c$ momentum $z$-component.

Figure 8

The $K_S{K}^{\pm }{\pi }^{\mp }$ invariant mass spectrum for no-tag data events satisfying (dashed histogram) and not satisfying (solid histogram) the condition for ISR event selection [Eq. (4)].

Figure 9

The distribution of the difference ($\delta m$) between measured and true $K_S{K}^{\pm }{\pi }^{\mp }$ mass for simulated events (a) for the two-photon process $e^{+}{e}^{-}\to e^{+}{e}^{-}{\eta }_c$, and (b) for the ISR process $e^{+}{e}^{-}\to J/\psi \gamma$. The curves correspond to fits defined in the text.

Figure 10

The $K_S{K}^{\pm }{\pi }^{\mp }$ invariant mass distribution and fitted curve for no-tag data events that (a) fail Eq. (4), and (b) satisfy Eq. (4) for ISR event selection.

Figure 11

The Dalitz plots for data events from (a) the ${\eta }_c$ signal region $2.94<M_{K\overline{K}\pi }<3.02\mathrm{GeV}/c^2$, and (b) the combined sideband regions, $2.90<M_{K\overline{K}\pi }<2.94\mathrm{GeV}/c^2$ and $3.02<M_{K\overline{K}\pi }<3.06\mathrm{GeV}/c^2$.

Figure 12

The projections of the Dalitz plots of Fig. 11; the solid and dashed histograms correspond to the ${\eta }_c$ signal and sideband $M_{K\overline{K}\pi }$ regions, respectively.

Figure 13

The $\cos {\theta }_K$ distribution for events from the ${\eta }_c$ signal region after background subtraction (points with error bars), and for events from the sidebands after subtraction of the ${\eta }_c$ contribution (solid histogram). The dashed histogram represents the signal MC simulation.

Figure 14

The $K_S{K}^{\pm }{\pi }^{\mp }$ mass spectrum for single-tag data events with $2<Q^2<50{\mathrm{GeV}}^2$. The solid curve is the fit result. The dashed curve represents nonpeaking background.

Figure 15

The $K_S{K}^{\pm }{\pi }^{\mp }$ mass spectra for single-tag data events from three representative $Q^2$ intervals. In each figure the solid curve represents the fit result, and the dashed curve indicates nonpeaking background.

Figure 16

The distribution of the ${\eta }_c$ candidate transverse momentum for no-tag data events containing an ${\eta }_c$ (points with error bars), and for simulated signal events (histogram).

Figure 17

The ${\pi }^0$ candidate mass spectrum for the selected $e^{+}{e}^{-}\to e^{+}{e}^{-}{K}_S{K}^{\pm }{\pi }^{\mp }{\pi }^0$ data events in no-tag mode.

Figure 18

The $K_S{K}^{\pm }{\pi }^{\mp }$ mass spectrum for $e^{+}{e}^{-}\to e^{+}{e}^{-}{K}_S{K}^{\pm }{\pi }^{\mp }{\pi }^0$ candidate events in no-tag mode with $0.11<M_{\gamma \gamma }<0.15\mathrm{GeV}/c^2$. The solid curve is the fit result. The dashed curve represents nonpeaking background.

Figure 19

The detection efficiency as a function of momentum transfer squared for events with a tagged electron (squares), a tagged positron (triangles), and their sum (circles).

Figure 20

The $Q^2$ dependence of the relative difference between detection efficiencies determined from MC simulation with and without Dalitz-plot reweighting.

Figure 21

The $Q^2$ dependence of the data-MC double ratio for events with and without the polar angle restriction $0.387<\theta <2.400$ rad for all four charged-particle tracks from the ${\eta }_c$ decay.

Figure 22

The correction to the MC-estimated kaon identification efficiency as a function of $Q^2$.

Figure 23

The correction to the MC-estimated electron identification efficiency as a function of $Q^2$.

Figure 24

The $Q^2$ dependence of the radiative correction factor.

Figure 25

The $e^{+}{e}^{-}\to e^{+}{e}^{-}{\eta }_c$ differential cross section multiplied by the ${\eta }_c\to K\overline{K}\pi$ branching fraction; the statistical and $Q^2$-dependent systematic errors of Table  have been combined in quadrature.

Figure 26

The $\gamma {\gamma }^{*}\to {\eta }_c$ transition form factor normalized to $F(0)$ (points with error bars). The solid curve shows the fit to Eq. (22). The dotted curve shows the leading order pQCD prediction from Ref. 3.