$\phi$ yield

From the 3$\gamma$ data sample, $\phi$ events are selected by requiring that there is no $\pi ^0$ in the event and that $\eta$ candidates from 2$\gamma$ pairs are constrained to $\pm10\%$ of the $\eta$ mass (0.5 $GeV/c_2 < M_{2\gamma} <$ 0.6 $GeV/c^2$). We do not require just the presence of the $\eta$ because $\pi ^0$ production is 50 times larger than $\eta$. Without cutting on the $\pi ^0$, the $\eta$ signal competes with the $\pi ^0$ combinatoric background. The invariant mass distribution of 3$\gamma$ is then formed for different minimum total energy in the LGD. These distributions for 4 different energy thresholds are shown in Fig. 1, where one can see how the $\phi$ peak becomes more prominent when the total energy threshold is increased.

The number of $\phi$ is found from the fit of these distributions to 3 Gaussians: one corresponding to the residual $\omega$ peak, one broad corresponding to the background (BG) and the third one for the $\phi$. To keep the number of parameters small, the position of the background Gaussian is set to be equal to the position of the $\omega$ peak, while the width of the BG is fixed to the $\omega$ width by $\sigma_{BG} = a \sigma_{\omega}$. In addition, the width of $\phi$ is kept constant during fitting, $\sigma_{\phi} = b$. Constants a and b are adjusted until good fits with reasonable looking background is found. Obtained $\phi$ mass, width and yield for different energy cuts are given in the Table 1.

Table 1: $\phi$ mass, width and yield as a function of minimum deposited energy in the LGD.

	$E_{TOT} > [Gev]$		$M_{\phi} [Gev/c^2]$		$\sigma_{\phi} [Gev/c^2]$		$N_{\phi}$
	3.5		0.931		0.065		555513.0
	4.0		0.943		0.065		460076.0
	4.5		0.954		0.070		228128.0
	5.0		0.967		0.075		87140.4

Figure 1: Three Gaussian fit in the limited interval of 3$\gamma$ invariant mass given by solid line. Dashed line is the sum of background and $\omega$ Gaussians.