The $\eta'$ production estimate

The estimate is based on $0.2 \mu b$ cross section for $\eta'$ production on proton target. Total luminosity for the 2000 run is $L = 2.69$ $10^7 \mu b^{-1}$, corresponding to $5$ $10^7 s^{-1}$ event rate and the total live time $t = 432 h$. For $B_e$ target

$$L_p = 4L = 1.077*10^8 \mu b^{-1}$$ (1)

$$L_n = 5L = 1.347*10^8 \mu b^{-1}$$ (2)

Total number of produced particles $N = \sigma L$ in a given channel is governed by the decay rate $R$. The total number of reconstructed particles depends also on the acceptance

$$N = \sigma L R A$$ (3)

Rate of interest:

$$\eta' \to \gamma \gamma = 2.12 \%$$ (4)

$$\eta' \to \omega \gamma = 3.03 \%$$ (5)

$$\omega \to \pi^0 \gamma = 9.09 \%$$ (6)

$$\eta' \to \eta \pi^0 \pi^0 = 20.9 \%$$ (7)

$$\eta \to \gamma \gamma = 39.43 \%$$ (8)