Invariant mass spectra from MC

Invariant mass distributions are formed for the events where 3 and 5 clusters have been reconstructed in the LGD, and passed through a mass filter to identify $\pi ^0\gamma$, $\eta \gamma$, and $\pi ^0\pi ^0\gamma$ events. Current sample sizes are too small to allow the study of $\pi^0\eta\gamma$ in the case of $5\gamma$ events. The requirements for selecting events of interest are as follows.

1

- $E(clusters) > E_{\mbox{thresh}}$

2

- $N_{\mbox{pixel}} = 1$

The following additional cuts define the $\pi ^0\gamma$ selection.

3

- exactly 3 clusters reconstructed in the LGD

4

- the lightest pair has to have invariant mass within the $\pi^0$ window (0.1-0.18 GeV).

For $\eta \gamma$ the additional cuts were as follows.

3

- exactly 3 clusters reconstructed in the LGD

4

- the lightest pair has to have invariant mass greater than 0.18 GeV.

5

- at least one pair has to have a mass within the $\eta$ window (0.45-0.65 GeV).

For $\pi ^0\pi ^0\gamma$ the additional cuts were as follows.

3

- exactly 5 clusters reconstructed in the LGD

4

- the lightest pair has to have invariant mass within the $\pi^0$ window (0.1-0.18 GeV)

5

- the lightest pair from the remaining three clusters must also fall within the $\pi^0$ window (0.1-0.18 GeV).

In Fig. 1 are shown invariant mass distributions for two values of the energy threshold: $E_{\mbox{thresh}}>3.0$ GeV (first row) and $E_{\mbox{thresh}}>4.0$ GeV (second row). The black curves in Fig. 1 represent sum from all reactions from the list [1], while the colored curves show contributions from the most prominent meson channels for the given selection criteria. For example, one can see two peaks from reactions when $\omega$ is reconstructed in the $\pi ^0\gamma$ sample with $E_{\mbox{thresh}}>3.0$ GeV. One of them represents the fully reconstructed $\omega$ from $\omega \rightarrow \pi^0\gamma$ decays, while the one near 0.3 GeV is an artifact of false reconstruction. It is possible to have $\gamma p \rightarrow \omega(\pi^+\pi^-\pi^0) p$ where one charged $\pi$ converts to $\pi^0$ in the LGD, which is then reconstructed as a single photon. The same feature is visible in the case of $5\gamma$ events where we see two peaks in $b_1$ reactions, one when the $\omega$ decays to $\pi^+\pi^-\pi^0$ and one when $\omega$ goes to $\pi ^0\gamma$. This kind of background is suppressed when the energy threshold in the LGD is increased. Thus increasing the value of $E_{\mbox{thresh}}$ makes the $\omega$ and $\phi$ peaks more prominent in the case of $3\gamma$ decays. This same effect was observed in the analysis of experimental data [3]. In the case of $5\gamma$ events, requiring more energy in the LGD produces a similar reduction in the charged particle background, although in this case a single prominent peak does not emerge in the one-dimensional mass plot after charged reactions are suppressed. In Fig. 2 are shown particular contributions from neutral and charged $\phi$ and $b_1$ channels to the total invariant mass in the $\eta \gamma$ event sample for a 4.0 GeV energy threshold. It can be seen that our "$\phi$ peak" contains a real $\phi$ contribution as well as a contribution from false reconstructions of the $b_1$. It is clear that missed reconstructions of the $b_1 \rightarrow \omega(\pi^0\gamma)\pi^0$ decay is going to enhance the apparent $\phi$ signal in $\eta \gamma$. Note that the $b_1$ background in $\eta \gamma$ comes primarily from the $\pi ^0\gamma$ decay of the $\omega$ even though its rate is an order of magnitude smaller than $b_1 \rightarrow \omega(\pi^+\pi^-\pi^0)\pi^0$ channel. The ratio of $\phi$/($b_1 + \phi$) under the peak is $\approx 0.3$. This can explain why we see $\approx 3$ times more $\phi$ relative to $\omega$ in our experimental data [3] than we expected based upon the known $\gamma p \rightarrow \phi p$ and $\gamma p \rightarrow \omega p$ cross sections.

Figure: Invariant mass distributions for two energy cuts in the LGD, $E_{\mbox{thresh}}>3.0$ GeV (the first row) and $E_{\mbox{thresh}}>4.0$ GeV (the second row) and three classes of events: $\pi ^0\gamma$, $\eta \gamma$, $\pi ^0\pi ^0\gamma$ (the first, second and third column respectively).

Figure: Contribution of particular reactions to invariant mass for $E_{\mbox{thresh}}>4.0$ GeV.