Role of $\omega$-meson exchange in scaling of the $\gamma p\to {\pi }^{0}p$ process from a Regge-type model with resonances

The scaling of photoproduction $\gamma p\to {\pi }^{0}p$ is investigated in the Reggeized model with $N^{*}$ and $\mathrm{\Delta }$ resonances included to describe resonance peaks up to photon energy $E_{\gamma }=3\mathrm{GeV}$. Given the $t$-channel exchanges $\rho \left(770\right)+\omega \left(780\right)+b_1\left(1235\right)+h_1\left(1170\right)$ Reggeized for the background contribution, the resonances of the Breit-Wigner form are introduced to agree with cross sections for total, differential, and beam asymmetry in the low energy region. The scaled differential cross sections $s^{7}d\sigma /dt$ are reproduced to agree with the recent JLab data, revealing the production mechanism of the big bump structure around $W\approx 2.2$ GeV by the deep-dip pattern of the $\omega$ exchange that originates from the zeros of the trajectory ${\alpha }_{\omega }\left(t\right)=0$ in the canonical phase, $\frac{1}{2}(-1+e^{-i\pi {\alpha }_{\omega }\left(t\right)})$.

Figure 1

Total cross section for $\gamma p\to {\pi }^{0}p$ from threshold to $E_{\gamma }=3\mathrm{GeV}$. Red dashed line is the background from $\rho +\omega +b_1+h_1$ Regge pole exchanges. Black solid line results from the background plus the resonances. Four resonances $\mathrm{\Delta }\left(1232\right)$ (dashed), $N\left(1520\right)$ (dotted), $N\left(1680\right)$ (dash-dotted), and $\mathrm{\Delta }\left(1950\right)$ (dash-dot-dotted) are illustrated to represent the sequential peaks. Data are taken from Refs. [3, 14].

Figure 2

Differential cross sections for $\gamma p\to {\pi }^{0}p$ in four energy bins $E_{\gamma }=362.5$ ($W=1249.2$), $762.5\left(1520.3\right),1037.5\left(1681.5\right)$, and $1475\left(1910\right)$ MeV. Data are taken from Ref. [3]. Notations for the curves are the same as in Fig. 1.

Figure 3

Angular distribution of beam asymmetry $\mathrm{\Sigma }$ for $\gamma p\to {\pi }^{0}p$ in four energy bins $E_{\gamma }=350$ ($W=1240$), $769\left(1524\right),1023\left(1673\right)$, and $1475\left(1910\right)$ MeV. Data are taken from Refs. [15, 16]. Notations for the curves are the same as in Fig. 1.

Figure 4

Scaled cross sections $s^7\frac{d\sigma }{dt}({10}^7{\text{GeV}}^{14}\text{nb}/{\text{GeV}}^2)$ for $\gamma p\to {\pi }^{0}p$ at $\theta ={90}^{\circ },\theta ={70}^{\circ }$, and $\theta ={50}^{\circ }$ as a function of total energy $W$. The scaled cross section agrees with data (green triangle-up) up to $W\approx 3$ GeV. $N^{*}$ contributions vanish at $\theta ={50}^{\circ }$. For the given angle $\theta$ the red dotted vertical line indicates the point of $W$ corresponding to the upper limit of $t=-2{\mathrm{GeV}}^2$ maximally allowed before saturation in Eq. (15). Data are taken from Refs. [2, 3, 15, 17, 18, 19].

Figure 5

Saturation of the trajectory $\alpha \left(t\right)={\alpha }_0+{\alpha }^{\prime }t$. The maximum ranges of $t$ limited by ${\alpha }_i\left(t\right)>-1$ are $t>-1.94$ for $\rho ,t>-1.6$ for $\omega ,t>-1.34$ for $b_1$, and $t>-1.49{\mathrm{GeV}}^2$ for $h_1$, respectively.