Double ${\pi }^0$ Photoproduction on the Proton at GRAAL

The double ${\pi }^0$ photoproduction off the proton has been measured in the beam energy range of 0.65–1.5 GeV. The total and differential cross sections and the $\Sigma$ beam asymmetry were extracted. The total cross section measured for the first time in the third resonance region of the nucleon shows a prominent peak. The interpretation of these results by two independent theoretical models infers mostly the selective excitation of $P_{11}$- and $D_{13}$-nucleon resonances.

Figure 1

Total cross section of the reaction $\gamma p\to p{\pi }^0{\pi }^0$. GRAAL data together with previous data from MAMI, TAPS(1996) and TAPS(2000) and theoretical calculation from Oset and Laget models. The GRAAL data are shown with statistical error bars only and the systematical error is estimated to be 3%. In the lower part the partial contributions of the different diagrams of Laget model are given, labeled with numbers: label 1 associated with the dash-dotted line corresponds to $\gamma p\to P_{11}(1440)\to \Delta \pi$; label 2, dashed lines, $\gamma p\to D_{13}(1520),D_{13}(1700)\to \Delta \pi$; label 3, continuous line, $\gamma p\to P_{11}(1440),P_{11}(1710)\to \sigma p$; label 4, dotted line $\gamma p\to \sigma p$. The contribution of $D_{33}(1700)$ is too small to be seen. In the inset, the main contributions of the Oset calculation are given [6]: thick solid line, full calculation; lines (a), (b), and (c) for $D_{13}(1520)$, $\Delta$, and $P_{11}(1440)$ intermediate states, respectively.

Figure 2

Invariant mass spectra for the reaction $\gamma p\to p{\pi }^0{\pi }^0$ at four beam energies. See explanations in the text. At $E_{\gamma }=720\mathrm{M}\mathrm{e}\mathrm{V}$ the insets compare the Laget (solid line) and Oset [6] (dashed lines) models with the GRAAL data (dots).

Figure 3

The beam asymmetry $\Sigma$ for the reaction $\gamma p\to p{\pi }^0{\pi }^0$ at four beam energies: (a) 650–780 MeV, (b) 780–970 MeV, (c) 970–1200 MeV, and (d) 1200–1450 MeV. On the left, $\Sigma$ as a function of the IM of the system (${\pi }^0{\pi }^0$) and on the right, of the IM of the system ($p{\pi }^0$). The continuous line shows the Laget model results. The reaction plane used to define the $\varphi$ angle in order to extract $\Sigma$ was, on the left, the plane of the incident photon and the outgoing proton, and on the right, of the incident photon and any one of the two outgoing ${\pi }^0$’s .

Figure 4

The beam asymmetry $\Sigma$ for the reaction $\gamma p\to p{\pi }^0{\pi }^0$ at for bins of beam energy in terms of ${\Theta }_{CM}({\pi }^0{\pi }^0)$ (on the left) and of ${\Theta }_{CM}({\pi }^0)$ (on the right). The calculations of Laget (solid line) and the Valencia group (dashed line) are shown. Notations as in Fig. 3.