$\omega$ yield

The $\omega$ sample is selected by requiring that at least one pair of photons have invariant mass within the (0.08, 0.2) GeV window. This corresponds to the case of selecting the $\pi ^0$ as opposed to rejecting the $\pi ^0$ for $\phi$ selection. In the case of $\omega$, no $\eta$ veto is needed. The $\pi ^0$ mass is small compared to the $\omega$ and in order to form $\omega$, the third photon should have a large separation so that invariant mass formed with one of the remaining photons will often be in the $\eta$ region. Thus cutting on the $\eta$ significantly decreases our $\omega$ signal.

Invariant mass distributions, obtained with the above criteria, for 4 total energy thresholds are shown in Fig. 2. They are fitted by the sum of two Gaussians, with the one corresponding to the background represented by the dashed line. Similar to the $\phi$ case, the signal to background ratio is enlarged when the energy threshold in the LGD is increased. The $\omega$ mass, width and yield for the corresponding energy cut are given in Table 2. In order to show the influence of $\pi ^0$ selection on our $\omega$ sample, by dotted lines in Fig. 2 are shown invariant mass distributions obtained with a narrower window around the $\pi ^0$ (0.1 $GeV/c_2 < M_{2\gamma} <$ 0.18 $GeV/c^2$). It seems that the signal to background ratio is not affected by narrowing the $\pi ^0$ window since the reduced events are almost uniformly distributed over the mass range, especially for the higher energy cuts.