Search for the decay $K_L^0\to 3\gamma$

We performed a search for the decay $K_L^0\to 3\gamma$ with the E391a detector at KEK. In the data accumulated in 2005, no event was observed in the signal region. Based on the assumption of $K_L^0\to 3\gamma$ proceeding via parity-violation, we obtained the single event sensitivity to be $(3.23\pm 0.14)\times {10}^{-8}$, and set an upper limit on the branching ratio to be $7.4\times {10}^{-8}$ at the 90% confidence level. This is a factor of 3.2 improvement compared to the previous results. The results of $K_L^0\to 3\gamma$ proceeding via parity-conservation were also presented in this paper.

Figure 1

Schematic cross-sectional view of the E391a detector. “0m” in the scale corresponds to the entrance of the front barrel detector. $K_L^0$’s entered from the left side.

Figure 2

Distributions of $f_E$ and $f_E^w$ (subfigure) in the region of $x^{\prime }>0$. The red histogram shows the distribution of single-photon clusters and the black histogram shows the distribution of fusion clusters. A significant difference between the distributions in the region of $y^{\prime }>0$ was also observed. By requiring $|f_E^w-0.5|>0.15$ in this region and similar requirements on $f_E$ or $f_E^w$ in other regions, the fusion-related $K_L^0\to 3{\pi }^0$ events, which missed by NN fusion cut, were completely rejected.

Figure 3

Distribution of $m_{13}$–$m_{23}$ of the MC events with three clusters in the CsI calorimeter. The contour shows the $K_L^0\to 3\gamma$ parity-violating results, and the dots show the $K_L^0\to {\pi }^0{\pi }^0$ results. The events inside the cross region were rejected.

Figure 4

Distribution of Cluster radial position vs cluster energy of the MC events and the distributions of the NN output (subfigure). The banded contour shows the $K_L^0\to 3\gamma$ parity-violating results, and the line contour shows the $K_L^0\to 3{\pi }^0$ results. The significant differences in the distributions were also observed in the other two clusters.

Figure 5

Distributions of $m_{13}$ of the events in the normalization region ($0.13\mathrm{GeV}/c^2<m_{23}<0.17\mathrm{GeV}/c^2$). The points with error bars show the data, the star sign shows the only survived $K_L^0\to 3{\pi }^0$ MC event, and the shaded histograms show the $K_L^0\to \gamma \gamma$ MC events. The hollow solid histogram is the sum of the $K_L^0\to 3{\pi }^0$, $K_L^0\to {\pi }^0{\pi }^0$ and $K_L^0\to \gamma \gamma$ MC results.

Figure 6

Distribution of $m_{13}$–$m_{23}$ of the data with all selection cuts imposed. No event was observed in the signal region.