Measurement of ${\pi }^0$ photoproduction on the proton at MAMI C

Differential cross sections for the $\gamma p\to {\pi }^{0}p$ reaction have been measured with the A2 tagged-photon facilities at the Mainz Microtron, MAMI C, up to the center-of-mass energy $W=1.9\mathrm{GeV}$. The new results, obtained with a fine energy and angular binning, increase the existing quantity of ${\pi }^0$ photoproduction data by $\sim 47\%$. Owing to the unprecedented statistical accuracy and the full angular coverage, the results are sensitive to high partial-wave amplitudes. This is demonstrated by the decomposition of the differential cross sections in terms of Legendre polynomials and by further comparison to model predictions. A new solution of the SAID partial-wave analysis obtained after adding the new data into the fit is presented.

Figure 1

$cos\theta$ distributions for $\gamma p\to {\pi }^{0}p$, with $\theta$ being the angle between the directions of the outgoing ${\pi }^0$ and the incident photon in the c.m. frame, obtained for $E_{\gamma }=318$ MeV ($W=1215$ MeV): (a) experimental data after subtraction of the empty-target background and the random background; (b) angular acceptance obtained from the MC simulation of $\gamma p\to {\pi }^{0}p$; (c) results for the $\gamma p\to {\pi }^{0}p$ differential cross section compared to the prediction by SAID [23] with its CM12 [24] solution. The error bars on all data points represent statistical uncertainties only.

Figure 2

Same as Fig. 1, but for $E_{\gamma }=1202$ MeV ($W=1771$ MeV).

Figure 3

Same as Fig. 1, but for $E_{\gamma }=1512$ MeV ($W=1928$ MeV).

Figure 4

Comparison of the $\gamma p\to {\pi }^{0}p$ differential cross sections obtained by the A2 Collaboration in different experiments: (a) results for $E_{\gamma }=218$ MeV from Run-I (black points) and from the experiment [25] with MAMI energy of 855 MeV (green points); (b) same as (a) but for $E_{\gamma }=331$ MeV; (c) results for $E_{\gamma }=1434$ MeV from Run-I (black points) and Run-II (red points); (d) same as (c) but for $E_{\gamma }=1443$ and 1441 MeV of Run-I and Run-II, respectively; The error bars on all data points represent statistical uncertainties only.

Figure 5

Comparison of the $\gamma p\to {\pi }^{0}p$ differential cross sections from the present work (black points) with most recent results from other experimental setups at MAMI [26] (blue points) and other facilities: GRAAL [7] (red points), CLAS [27] (green points), CB-ELSA [28] (magenta points), and CBELSA/TAPS [29] (cyan points). Values of $E_{\gamma }$ in each panel indicate the photon-beam energies for the results of this work. All data from other experiments are shown for nearby energies. The error bars on the data points from this work represent statistical uncertainties only. The uncertainties of some previous results also include angular-dependent systematic uncertainties.

Figure 6

Total cross sections for $\gamma p\to {\pi }^{0}p$ from this work (black points) as a function of the c.m. energy $W$ compared with earlier A2 results [25] (red points), with results from Refs. [26] (blue points) and [28] (green points), and with the SAID solution CM12 [24] shown in (b) by a magenta dashed line. For a better comparison, the energy range is divided in two intervals: (a) $W<1340$ MeV and (b) $W>1340$ MeV. The error bars on the experimental data points represent their total uncertainties.

Figure 7

Selected results of this work (black points) for the $\gamma p\to {\pi }^{0}p$ differential cross sections compared to existing PWA solutions from SAID CM12 [24] (blue dashed line), MAID2007 [30] (magenta long-dashed line), and Bonn-Gatchina BG2014-02 [31] (green dash-dotted line) and to a new SAID PR15 solution (red solid line) obtained after adding the present data points into the fit. The error bars on all data points represent statistical uncertainties only.

Figure 8

Comparison of the previous SAID solution DU13 [5] (blue open triangles) applied to the present data and the new SAID PR15 solution (red full circles) obtained after adding the present data into the fit for: (a) ${\chi }^2/\mathrm{dp}$ values averaged only within each energy bin $E_{\gamma }$, where the horizontal lines (blue dashed for DU13 and red solid for PR15) show the corresponding ${\chi }^2/\mathrm{dp}$ values from Table 1; (b) results for the normalization parameter $X$ as a function of $E_{\gamma }$, where the horizontal solid lines show the deviations (from the dashed line at $X=1$) equal to the magnitude of the overall systematic uncertainties, which are 4% and 5% for the data from Run-I and Run-II, respectively.

Figure 9

Present results for the $\gamma p\to {\pi }^{0}p$ excitation function as a function of the c.m. energy $W$, shown for ten of 30 measured $cos\theta$ bins (where $\theta$ is the ${\pi }^0$ production angle), are compared to previous PWA solutions from SAID CM12 [24] (blue dashed line), MAID2007 [30] (magenta long-dashed line), and BG2014-02 [31] (green dash-dotted line) and to a new SAID PR15 solution (red solid line). The error bars on all data points (black points for Run-I and cyan points for Run-II) represent statistical uncertainties only. For a better comparison, all distributions are also plotted after rescaling by a factor of 5.

Figure 10

(a) present results for the $\gamma p\to {\pi }^{0}p$ differential cross section (blue full circles) at $E_{\gamma }=546$ MeV ($W=1380$ MeV) fitted with Legendre polynomials (red dashed line); (b) the new SAID PR15 solution (blue solid line) for ${\pi }^0$ production angle $\theta ={180}^{\circ }\left(cos\theta =-1\right)$ as a function of the c.m. energy $W$, compared with a similar ${\pi }^{-}p\to {\pi }^{0}n$ prediction (rescaled by a factor ${10}^{-3}$) from SAID WI08 [33] (red dashed line) and a $\gamma p\to {\pi }^{+}n$ prediction (rescaled by a factor 0.3) from SAID PR15 (black dashed line).

Figure 11

Energy dependence of the reduced ${\chi }^2$ values for Legendre fits of the present $\gamma p\to {\pi }^{0}p$ differential cross sections with $j_{\max }=6$ (black triangles down), 8 (blue circles), and 10 (red triangles up), where the angular-dependent systematic uncertainties were not taken into account.

Figure 12

Coefficients $A_j$ (in $\mu \mathrm{b}/\mathrm{sr}$ units) obtained from fitting the present $\gamma p\to {\pi }^{0}p$ differential cross sections with Legendre polynomials up to order six (cyan points) and ten (green points), compared to the results of the Legendre-polynomial fits ($j_{\max }=10$) made to the predictions generated from SAID CM12 [24] (blue solid line), MAID2007 [30] (red solid line), BG2014-02 [31] (black solid line), and SAID PR15 (blue dashed line). The error bars on all points represent $A_j$ uncertainties from the fits with using only the statistical uncertainties. A black histogram at the bottom of each plot shows the systematic uncertainty in $A_j$ caused by the angular-dependent systematics in the differential cross sections.