Study of $e^{+}{e}^{-}\to p\overline{p}$ using initial state radiation with BABAR

The $e^{+}{e}^{-}\to p\overline{p}$ cross section is determined over a range of $p\overline{p}$ masses, from threshold to $4.5\mathrm{GeV}/c^2$, by studying the $e^{+}{e}^{-}\to p\overline{p}\gamma$ process. The data set corresponds to an integrated luminosity of $232{\mathrm{fb}}^{-1}$, collected with the BABAR detector at the PEP-II storage ring, at an $e^{+}{e}^{-}$ center-of-mass energy of 10.6 GeV. The mass dependence of the ratio of electric and magnetic form factors, $|G_E/G_M|$, is measured for $p\overline{p}$ masses below $3\mathrm{GeV}/c^2$; its value is found to be significantly larger than 1 for masses up to $2.2\mathrm{GeV}/c^2$. We also measure $J/\psi \to p\overline{p}$ and $\psi (2S)\to p\overline{p}$ branching fractions and set an upper limit on $Y(4260)\to p\overline{p}$ production and decay.

Figure 1

The diagram for the $e^{+}{e}^{-}\to p\overline{p}\gamma$ process.

Figure 2

The ${\chi }_p^2$ distribution (left panel) for MC simulated $e^{+}{e}^{-}\to p\overline{p}\gamma$ (solid line) and $e^{+}{e}^{-}\to K^{+}{K}^{-}\gamma$ (dashed line) events, and the ${\chi }_K^2$ distribution (right panel) for MC simulated $e^{+}{e}^{-}\to K^{+}{K}^{-}\gamma$ (solid line) and $e^{+}{e}^{-}\to p\overline{p}\gamma$ (dashed line) events with ${\chi }_p^2<30$.

Figure 3

The $p\overline{p}$ invariant mass spectrum for $p\overline{p}\gamma$ candidates that satisfy all selection criteria.

Figure 4

The $M_{\pi \pi }$ spectrum for data events with ${\chi }_p^2<30$ and ${\chi }_K^2>30$, and one proton candidate (left plot; selection 2 in the text) or two proton candidates (right plot; selection 4 in the text). The histograms are the results of the fit described in the text.

Figure 5

The calculated $M_{p\overline{p}}$ spectra for $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ (dotted histogram), $e^{+}{e}^{-}\to K^{+}{K}^{-}\gamma$ (solid histogram), and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}\gamma$ (dashed histogram) background processes. The spectra are normalized to the number of events expected to pass the $p\overline{p}\gamma$ selection criteria for each process: $5.9\pm 2.5$ for pions and $2.5\pm 1.0$ for kaons. For the muon channel, the upper limit of 11 events is used for the normalization.

Figure 6

The $M_{p\overline{p}}$ spectrum (left panel) and the $\cos {\theta }_p$ distribution (right panel) for selected $e^{+}{e}^{-}\to p\overline{p}{\pi }^0$ candidates in data. The shaded histogram shows the background contribution estimated from $M_{\gamma \gamma }$ sidebands.

Figure 7

The expected $M_{p\overline{p}}$ spectrum for $e^{+}{e}^{-}\to p\overline{p}{\pi }^0$ events selected with the standard $p\overline{p}\gamma$ criteria. The spectrum is obtained by scaling the data distribution shown in Fig. 6 by the factor $K_{\mathrm{MC}}(M_{p\overline{p}})$ described in the text.

Figure 8

Left panel: the $p\overline{p}{\pi }^0$ mass spectrum for selected $e^{+}{e}^{-}\to p\overline{p}{\pi }^0\gamma$ candidates with ${\chi }^2<20$. The shaded histogram shows the background contribution estimated from the sideband with $30<{\chi }^2<50$. Right panel: the $p{\pi }^0$ ($\overline{p}{\pi }^0$) mass spectrum for $e^{+}{e}^{-}\to p\overline{p}{\pi }^0\gamma$ data events with $p\overline{p}{\pi }^0$ mass outside the $J/\psi$ peak.

Figure 9

The $\cos {\theta }_p$ distributions for different $p\overline{p}$ mass regions: (a) $1.877–1.950\mathrm{GeV}/c^2$, (b) $1.950–2.025\mathrm{GeV}/c^2$, (c) $2.025–2.100\mathrm{GeV}/c^2$, (d) $2.100–2.200\mathrm{GeV}/c^2$, (e) $2.200–2.400\mathrm{GeV}/c^2$, (f) $2.400–3.000\mathrm{GeV}/c^2$. The points with error bars show data distributions after background subtraction. The histograms are fit results: the dashed histograms show the contributions corresponding to the magnetic form factor; the dash-dotted histograms show the contributions from the electric form factor.

Figure 10

The angular dependence of the detection efficiency for simulated events with $M_{p\overline{p}}<2.5\mathrm{GeV}/c^2$ before (open squares) and after (filled circles) correction for data-simulation difference in detector response.

Figure 11

The measured $|G_E/G_M|$ mass dependence. Filled circles depict BABAR data; the curve is the fit result. Open circles show the data from PS170 [10].

Figure 12

The $\cos {\theta }_p$ distributions for $J/\psi \to p\overline{p}$ decay. The points with error bars correspond to the background-subtracted data distribution, the solid histogram is the fit result, and the dashed and dashed-dotted histograms show the fit contributions from the magnetic and electric form factors, respectively.

Figure 13

The ratio of data and simulated distributions of $\cos {\theta }_K$ for the $e^{+}{e}^{-}\to K^{+}{K}^{-}\gamma$ process.

Figure 14

The $p\overline{p}$ mass dependence of detection efficiency obtained from MC simulation. The line on the left plot is the fit to a third-order polynomial. The efficiency for $M_{p\overline{p}}>3\mathrm{GeV}/c^2$ is fit to a constant value.

Figure 15

The relative difference between detection efficiencies for a purely electric ($G_M=0$) and purely magnetic ($G_E=0$) transition in the $e^{+}{e}^{-}\to p\overline{p}\gamma$ reaction.

Figure 16

The $e^{+}{e}^{-}\to p\overline{p}$ cross section measured in this work and $e^{+}{e}^{-}$ experiments: FENICE [6], DM2 [5], DM1 [4], ADONE73 [7], BES [8], CLEO [9]. The contribution of $J/\psi \to p\overline{p}$ and $\psi (2S)\to p\overline{p}$ decays is subtracted.

Figure 17

The $e^{+}{e}^{-}\to p\overline{p}$ cross section near threshold measured in this work and $e^{+}{e}^{-}$ experiments: FENICE [6], DM2 [5], DM1 [4], ADONE73 [7], BES [8].

Figure 18

The proton effective form factor measured in this work and in $e^{+}{e}^{-}$ and $p\overline{p}$ experiments: FENICE [6], DM2 [5], DM1 [4], BES [8], CLEO [9], PS170 [10], E835 [12], E760 [11]. The upper plot shows the mass interval from the $p\overline{p}$ threshold to $3.01\mathrm{GeV}/c^2$. The lower plot presents data for $p\overline{p}$ masses from 2.58 to $4.50\mathrm{GeV}/c^2$.

Figure 19

The proton effective form factor measured in this work and in $e^{+}{e}^{-}$ and $p\overline{p}$ experiments, shown on a logarithmic scale: FENICE [6], DM2 [5], DM1 [4], BES [8], CLEO [9], PS170 [10], E835 [12], E760 [11]. The curve corresponds to the QCD fit described in the text.

Figure 20

The proton effective form factor near the $p\overline{p}$ threshold measured in this work and in $e^{+}{e}^{-}$ and $p\overline{p}$ experiments: FENICE [6], DM1 [4], PS170 [10].

Figure 21

The $p\overline{p}$ mass spectra in the mass regions near $J/\psi$ (left panel) and $\psi (2S)$ (right panel). The curves are the result of the fit described in the text.

Figure 22

The $p\overline{p}$ invariant mass spectrum for $p\overline{p}\gamma$ candidates in the $(3.9–4.5)\mathrm{GeV}/c^2$ mass range. The curves are the result of the fit described in the text.