Semihadronic and hadronic decays of ${\rho }^0$ and $\omega$ mesons coherently photoproduced in isoscalar nuclei

The interference of ${\rho }^0$ and $\omega$ mesons has been studied in the hadronic and leptonic decay channels, i.e., dipion and dilepton decay channels respectively, but this interference has not been studied yet in the semihadronic or semileptonic decay channel, e.g., $V\to {\pi }^0\gamma$. $V$ denotes either a ${\rho }^0$ or $\omega$ meson. To look for this interference in the ${\pi }^0\gamma$ decay channel as well as the contribution of the $\rho$ meson to the cross section, the correlated ${\pi }^0\gamma$ invariant mass distribution spectra are calculated in the photonuclear reaction in the multi-GeV region. It is assumed that these bosons arise in the final state due to the decay of ${\rho }^0$ and $\omega$ mesons which are photoproduced coherently in the isoscalar nucleus. The elementary reaction in the nucleus is considered to proceed as $\gamma N\to VN$, $V\to {\pi }^0\gamma$. The forward propagation of the $\rho$ and $\omega$ mesons and the near forward emission of pions are considered, so that they can be described by the eikonal form. The meson-nucleus interactions are evaluated using the $t\varrho$ approximation. Replacing the decay vertex $V\to {\pi }^0\gamma$ by $V\to {\pi }^{+}{\pi }^{-}$ in the above formalism, it is also used to study the $\rho -\omega$ interference in the ${\pi }^{+}{\pi }^{-}$ decay channel.

Figure 1

The ${\pi }^0\gamma$ invariant mass $m$ distribution spectra in the coherent $(\gamma ,V)$ reaction on the ${}^{12}\mathrm{C}$ nucleus. The enhancement in the cross section due to the ${\rho }^0$ meson is distinctly visible beyond the peak region. See the text for an explanation of various curves appearing in the figure.

Figure 2

The same as in Fig. 1 but for the beam energy 5 GeV.

Figure 3

The same as in Fig. 2 but for the ${}^{40}\mathrm{Ca}$ nucleus.

Figure 4

The calculated ${\pi }^{+}{\pi }^{-}$ invariant mass $m$ distribution spectra in the coherent $(\gamma ,V)$ reaction on the ${}^{12}\mathrm{C}$ nucleus. The data along with the background curves are taken from Ref. [10]. As mentioned there, the background curves are due to the interference with nonresonant $\pi \pi$ emission (dot-dashed curve), the nonresonant $\pi \pi$ emission (dot-dot-dashed curve), and other background (long-dashed curve). The calculated results (added with the backgrounds) are compared with the data. The solid curve arises because of the contribution of the $\omega$ meson being coherently added to that of the ${\rho }^0$ meson (short-dashed curve).

Figure 5

The calculated ${\pi }^{+}{\pi }^{-}$ invariant mass $m$ distribution spectra originating due to the decay of ${\rho }^0$ and $\omega$ mesons photoproduced coherently in the ${}^{12}\mathrm{C}$ nucleus. The various curves are explained in the text.