Evidence for a Parity Doublet $\Delta (1920)P_{33}$ and $\Delta (1940)D_{33}$ from $\gamma p\to p{\pi }^0\eta$

Evidence is reported for the existence of a parity doublet of $\Delta$ resonances with total angular momentum $J=3/2$ from photoproduction of the $p{\pi }^0\eta$ final state. The two parity partners $\Delta (1920)P_{33}$ and $\Delta (1940)D_{33}$ make significant contributions to the reaction. Cascades of resonances into $\Delta (1232)\eta$, $N(1535)\pi$, and $N{a}_0(980)$ are clearly observed.

Figure 1

The $\gamma \gamma$ invariant mass distribution after a kinematic fit to $\gamma p\to p{\pi }^0\gamma \gamma$ (with C.L. $>10\%$) and a cut rejecting $\gamma p\to p{\pi }^0{\pi }^0$ events (with C.L. $>1\%$).

Figure 2

Total cross sections for $\gamma p\to p{\pi }^0\eta$. ●, this work; (a) black squares, Ref. [15]; (b) open circles, Ref. [16]. The solid curve represents a PWA fit. (a) Excitation functions. (1) shows the contribution from the $\Delta (1232)\eta$ intermediate state, (2) the $N(1535)\pi$, and (3) the $N{a}_0(980)$ contribution. (b) Contributions of the $D_{33}$ (4) and $P_{33}$ (5) partial waves.

Figure 3

Dalitz plot for the reaction $\gamma p\to p{\pi }^0\eta$ for (a) $E_{\gamma }<1.9\mathrm{GeV}$ and (b) $E_{\gamma }>1.9\mathrm{GeV}$. $\Delta (1232)$ is seen in both Dalitz plots; $N(1535)$ is visible only for high photon energies even though the $N(1535)\pi$ production threshold ($\sim 1.0\mathrm{GeV}$) is lower than the $\Delta (1232)\eta$ production threshold ($\sim 1.2\mathrm{GeV}$). (c)–(f) Selected distributions showing the deterioration of the fit (solid curve) when (c),(d) $\Delta (1920)P_{33}$ or (e),(f) $\Delta (1940)D_{33}$ is removed, compared to the best fit (dashed curve). Crosses represent data. For these figures (a)–(f), no acceptance correction was applied.

Figure 4

Differential cross sections $d\sigma /dM$ for (a)–(c) $E_{\gamma }<1.9\mathrm{GeV}$ and (d)–(f) $E_{\gamma }>2.1\mathrm{GeV}$. The distributions are not corrected undetected decay modes. The solid curves show the PWA result. The dashed lines represent the $\Delta (1232)\eta$ intermediate state, the dashed-dotted lines $N(1535)\pi$, and the dotted lines $p{a}_0(980)$.