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

The first dedicated search for the rare neutral-kaon decay $K_L^0\to {\pi }^0\nu \overline{\nu }$ has been carried out in the E391a experiment at the KEK 12-GeV proton synchrotron. The final upper limit of $2.6\times {10}^{-8}$ at the 90% confidence level was set on the branching ratio for the decay.

Figure 1

Schematic view of the neutral beam line: (top) the arrangements of the components and (bottom) the collimation scheme. C1–C3, C5, and C6 were tungsten collimators, assembled as a stack of cylindrical blocks 5-cm thick with circular holes of different diameters. Each collimator approximated the cone-shaped aperture as indicated by the A-E lines in the bottom figure. The $Z=0$ coordinate is at the center of the production target.

Figure 2

Momentum spectrum of $K_L^0$ at the exit of C6, obtained from beam line simulations.

Figure 3

Beam profiles of neutrons and photons above 1 MeV at the exit of C6 collimator, obtained from beam line simulations.

Figure 4

Beam profile of $K_L^0$ at the exit of C6 collimator, obtained from beam line simulations. Filled and open circles show the case with and without the Be absorber, respectively.

Figure 5

Detection system.

Figure 6

Assembly of detector subsystems in the downstream end cap.

Figure 7

Cross-sectional end view of the MB (outer ring) and FB (inner ring).

Figure 8

Light yield and attenuation for a MB module.

Figure 9

BA used in Run-2 (top) and Run-3 (bottom).

Figure 10

Membrane used for the vacuum separation.

Figure 11

Segments of CsI blocks.

Figure 12

Cosmic-ray track used for calibration. The outer ring shows the MB.

Figure 13

Stability of the kinematic variables over the entire period of Run-3. The upper and lower graphs show the peak and width of the effective mass distribution of $3{\pi }^0$ from the $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ decay, respectively.

Figure 14

Time difference between two photons from the $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ decay, obtained by subtracting the timing of lower-energy photon from that of higher-energy photon.

Figure 15

Distribution of the number of crystals having the energy deposit greater than 5 MeV in a photon cluster, comparing the data and $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ MC. The top portion shows a comparison between the number of events in the data and MC, and the bottom portion shows the ratio between them. All analysis cuts for the $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ mode, as will be described in Sec. 5b, are imposed.

Figure 16

Difference of the reconstructed $x$ position of the photons on the calorimeter from the true value ($\Delta x$), obtained by $K_L^0\to {\pi }^0\nu \overline{\nu }$ MC simulation. The $x$ coordinate denotes the horizontal position at the face of the CsI. The resolution was improved after the energy and position corrections.

Figure 17

Schematic diagram of simulation.

Figure 18

Distributions of reconstructed mass (top left), vertex position (top right), momentum (bottom left), and transverse momentum (bottom right) obtained from the six-photon data samples, compared to the data and the $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ MC. In each plot, the top portion shows a comparison between the number of events in the data and MC, and the bottom portion shows the ratio between them. All the veto cuts and kinematic selections, except those for the respective abscissa variable for the $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ mode, are applied in these plots. Details of the cuts are described in Sec. 5b.

Figure 19

Reconstructed invariant-mass distribution of events with four photons in the calorimeter. The points show the data and the histograms indicate the contribution of $K_L^0\to {\pi }^0{\pi }^0$ and $K_L^0\to {\pi }^0{\pi }^0{\pi }^0$ decays (and their sum), as expected from the simulation, normalized by the number of events in the $K_L^0\to {\pi }^0{\pi }^0$ peak. All veto and kinematic cuts except for the cut on the $4\gamma$ invariant mass for the $K_L^0\to {\pi }^0{\pi }^0$ mode are applied. It includes the shower-leakage correction, but does not include the correction for photo-nuclear interactions.

Figure 20

Schematic layout of the Al plate run.

Figure 21

Reconstructed invariant-mass distribution of the two-photon event in the Al plate run with all the veto cuts imposed. The points represent data and the solid line is from FLUKA simulations. The peaks at $0.14\mathrm{GeV}/c^2$ $0.55\mathrm{GeV}/c^2$ correspond to ${\pi }^0$ and $\eta$ particles, respectively.

Figure 22

Reconstructed $Z_{\mathrm{VTX}}$ distribution of two-photon events in the Al plate run. The points represent the real data and the solid (dashed) line is obtained from the FLUKA MC simulation with (without) the effects of photo-nuclear interaction. In both cases, the shower-leakage correction was applied.

Figure 23

Energy deposition in a single crystal hit versus the distance from the nearest photon cluster of the two-photon events from the $K_L^0\to {\pi }^0\nu \overline{\nu }$ (top) and $K_L^0\to {\pi }^0{\pi }^0$ (bottom) simulations. Events above the solid line were rejected.

Figure 24

Distributions of the output values obtained by two neural-network selections for the signal mode (hollow) and the background events (hatched). The top figure shows the fusion neural-network selection, in which the background is CV ${\pi }^0$. The bottom figure shows the CV-$\eta$ neural-network selection, in which the background is CV $\eta$. In both plots, all analysis cuts except for the respective neural-network cut are imposed for the signal mode. Several cuts are loosened for the background case in order to enhance the events.

Figure 25

Scatter plot of $P_T$ vs the reconstructed $Z$ position after applying all cuts to the MC samples for background simulation, including halo neutron and $K_L^0\to {\pi }^0{\pi }^0$ backgrounds. The region bounded by the solid line shows the signal box. Events around $Z_{\mathrm{VTX}}=275\mathrm{cm}$ are halo neutron events reconstructed at the position of CC02, and those around $Z_{\mathrm{VTX}}=560\mathrm{cm}$ are events reconstructed at the CV. The numbers of events in each region are listed in Table 4.

Figure 26

Density plot of $P_T$ vs the reconstructed $Z$ position for the $K_L^0\to {\pi }^0\nu \overline{\nu }$ Monte Carlo events after imposing all of the analysis cuts. The box indicates the signal region for $K_L^0\to {\pi }^0\nu \overline{\nu }$.

Figure 27

Scatter plot of $P_T$ vs the reconstructed $Z$ position for the events with all of the selection cuts imposed. The box indicates the signal region for $K_L^0\to {\pi }^0\nu \overline{\nu }$.