Study of the $K_L^0\to {\pi }^0{\pi }^0\nu \overline{\nu }$ decay

The rare decay $K_L^0\to {\pi }^0{\pi }^0\nu \overline{\nu }$ was studied with the E391a detector at the KEK 12-GeV proton synchrotron. Based on $9.4\times {10}^9$ $K_L^0$ decays, an upper limit of $8.1\times {10}^{-7}$ was obtained for the branching fraction at 90% confidence level. We also set a limit on the $K_L^0\to {\pi }^0{\pi }^{0}X$ ($X\to \mathrm{\text{invisible particles}}$) process; the limit on the branching fraction varied from $7.0\times {10}^{-7}$ to $4.0\times {10}^{-5}$ for the mass of $X$ ranging from $50\mathrm{MeV}/c^2$ to $200\mathrm{MeV}/c^2$.

Figure 1

Schematic cross sectional view of the E391a detector. The entrance of the detector is at “0 m.”

Figure 2

$P_T$ vs effective mass ($M_{{\pi }^0{\pi }^0}$) plots of the ${\pi }^0{\pi }^0$ system from Run-III MC simulations for (a) $K_L^0\to {\pi }^0{\pi }^0\nu \overline{\nu }$, (b) $K_L^0\to {\pi }^0{\pi }^0$, (c) $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$, and (d) Run-III real data. The statistics of the MC events in (b) and (c) are normalized to those of the real data. The signal region is defined to be inside of the triangular area in the plots. A curved line in (a) indicates the kinematical limit for the $K_L^0\to {\pi }^0{\pi }^0\nu \overline{\nu }$ decay.

Figure 3

Kinematic boundaries of $P_T$ vs $M_{{\pi }^0{\pi }^0}$ for the bifurcation analysis.

Figure 4

Proper-time distribution of the ${\pi }^0{\pi }^0$ system for the events with $P_T\ge 0.1\mathrm{GeV}/c$ and $0.45\le M_{{\pi }^0{\pi }^0}\le 0.55\mathrm{GeV}/c^2$ with a loose requirement for $V_Z$ for the Run-II and Run-III, assuming the production point was on the downstream edge of CC02. The solid line is an expectation from the $K_S^0\to {\pi }^0{\pi }^0$ decay.

Figure 5

$P_T$ vs $M_{{\pi }^0{\pi }^0}$ distribution for Run-II and Run-III combined.