Precision Measurement of the $p(e,e^{\prime }p){\pi }^0$ Reaction at Threshold

New results are reported from a measurement of ${\pi }^0$ electroproduction near threshold using the $p(e,e^{\prime }p){\pi }^0$ reaction. The experiment was designed to determine precisely the energy dependence of $s$- and $p$-wave electromagnetic multipoles as a stringent test of the predictions of chiral perturbation theory (ChPT). The data were taken with an electron beam energy of 1192 MeV using a two-spectrometer setup in Hall A at Jefferson Lab. For the first time, complete coverage of the ${\varphi }_{\pi }^{*}$ and ${\theta }_{\pi }^{*}$ angles in the $p{\pi }^0$ center of mass was obtained for invariant energies above threshold from 0.5 up to 15 MeV. The 4-momentum transfer $Q^2$ coverage ranges from 0.05 to $0.155(\mathrm{GeV}/c{)}^2$ in fine steps. A simple phenomenological analysis of our data shows strong disagreement with $p$-wave predictions from ChPT for $Q^2>0.07(\mathrm{GeV}/c{)}^2$, while the $s$-wave predictions are in reasonable agreement.

Figure 1

Left: Overlap between three BigBite Spectrometer proton laboratory angle settings (colored boxes) and $p{\pi }^0$ center-of-mass bins at $Q^2=0.135(\mathrm{GeV}/c{)}^2$ and $\mathrm{\Delta }W=9.5\mathrm{MeV}$. Radial and concentric lines separate bins of ${\varphi }_{\pi }^{*}$ and ${\theta }_{\pi }^{*}$, respectively. Only 5 out of 9 ${\theta }_{\pi }^{*}$ bins are shown. The blue line shows ${\varphi }_{\pi }^{*}=180$. Right: Radial and concentric lines separate bins of ${\theta }_{\pi }^{*}$ and $\mathrm{\Delta }W$, respectively, projected onto proton lab momentum $p_p$ and ${\theta }_p$. Bins to the (left, right) of the blue line correspond to (${\varphi }_{\pi }^{*}=180°$, ${\varphi }_{\pi }^{*}=0°$). The innermost circle represents $\mathrm{\Delta }W=0.5\mathrm{MeV}$.

Figure 2

Left: Coincidence timing between the LHRS and BigBite. Events belonging to the true coincidence peak were selected using cuts indicated by the vertical lines, while random coincidences were selected from the region highlighted in red. Right: Missing mass distribution at $Q^2=0.15(\mathrm{GeV}/c{)}^2$ for the invariant mass range $0<\mathrm{\Delta }W<10\mathrm{MeV}$. Background events from random coincidences (red) and target cell windows (blue) were subtracted from the raw distribution, leaving the ${\pi }^0$ missing mass peak shown in gray.

Figure 3

Differential cross sections for $p(e,e^{\prime }p){\pi }^0$ from this experiment at $Q^2=0.135(\mathrm{GeV}/c{)}^2$ and $\mathrm{\Delta }W=9.5\mathrm{MeV}$ binned in $p{\pi }^0$ center-of-mass angles ${\varphi }_{\pi }^{*}$ and cos ${\theta }_{\pi }^{*}$. See text for description of curves. Units are $\mu \mathrm{b}/\text{sr}$. Errors are statistical only.

Figure 4

Total cross section for $p(e,e^{\prime }p){\pi }^0$ as a function of $Q^2$ for different bins in $\mathrm{\Delta }W$ (invariant mass above threshold) for ($\square$) this experiment and ($\mathrm{\Delta }$) MAMI [13]. Units of $\mathrm{\Delta }W$ are MeV. Errors are statistical only.

Figure 5

The $Q^2$ dependence of $a_0$ (left) and $b$ (right) from the fits of Eq. (7) to the Legendre coefficient $A_0^{T+L}$. The theory curves are calculated for the beam energy of our experiment (1192 MeV). For the curve labeled REFIT the BKM96 LEC $b_P$ has been lowered from 13 to $9.3(\mathrm{GeV}{)}^{-3}$ (see text and Fig. 6). Errors are statistical only.

Figure 6

The $\mathrm{\Delta }W$ dependence of Legendre coefficients from fits to our data at $Q^2=0.135(\mathrm{GeV}/c{)}^2$. Note that the $\mathrm{\Delta }W=9.5\mathrm{MeV}$ bin corresponds to the Legendre fit shown in Fig. 3. Errors are statistical only.