Improved upper limit on the decay $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$

Based on results of a search for the lepton-family-number-violating decay $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$ with data collected by experiment E865 at the Alternating Gradient Synchrotron of Brookhaven National Laboratory, we place an upper limit on the branching ratio at $2.1\times {10}^{-11}$ (90% C.L.). Combining the results with earlier E865 data and those of a previous experiment, E777, an upper limit on the branching ratio of $1.3\times {10}^{-11}$ (90% C.L.) is obtained.

Figure 1

Left: Feynman diagram for extended technicolor mechanism for $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$ decay; right: Feynman diagram for $K^{+}\to {\pi }^0{\mu }^{+}\nu$ decay. (${\theta }_c$ is the Cabibbo angle; $g_H$ and $g$ are the ETC and weak coupling constants.)

Figure 2

Overall view of the detector with a simulated $K_{\pi \mu e}$ event (horizontal cross section at beam height). C1, C2: gas Čerenkov counters; P1, P2, P3, P4: proportional chambers; D5, D6: dipole magnets; A, B, C, D: scintillation counter trigger hodoscopes.

Figure 3

Target likelihood, $L_{\mathrm{target}}$, distributions for the reconstructed $K^{+}\to {\pi }^{+}{\pi }^{+}{\pi }^{-}$ (upper) and $K^{+}\to {\pi }^0{\pi }^{+}$ with a ${\pi }^0\to e^{+}{e}^{-}\gamma$ (lower) events. Poor target likelihood for the $K^{+}\to {\pi }^0{\pi }^{+}$ events is caused by the photon, which is not included in the kinematic reconstruction of the kaon momentum vector at the vertex causing it to fall out of the acceptable phase space of the kaon beam. For signal events, $L_{\mathrm{target}}>-20$ was required, corresponding to an efficiency of 92%.

Figure 4

Left: $M_{\pi \mu e}$ mass distribution for $e^{+}{\mu }^{+}{e}^{-}$ events measured with the EEPS monitor trigger ($K_{\mathrm{Dal}}$ background). Vertical lines mark the $M_{\pi \mu e}$ mass signal region; center: $M_{ee}$ invariant-mass spectrum for measured $K_{\mathrm{Dal}}$ events. The cut on $M_{ee}>0.055\mathrm{GeV}$ removes 94% of the $K_{\mathrm{Dal}}$ events; right: $M_{\pi \mu e}$ mass spectrum for the ${\pi }^{+}{\mu }^{+}{\pi }^{-}$ events measured with the TAU monitor trigger ($K_{\tau }$ background). Vertical lines mark the $M_{\pi \mu e}$ mass signal region.

Figure 5

Scatter plot of differences between track times: $t_{{\pi }^{-}(1)}-t_{{\pi }^{+}(2)}$ versus $t_{{\pi }^{-}(1)}-t_{{\pi }^{+}(3)}$ for the high momentum accidental events [(a)] and measured $K_{\tau }$ events [(b)]; scatter plot of ${\pi }^{+}$ track angle at the vertex ($\theta$) versus ${\pi }^{+}$ momentum ($P_{\pi }$) for the simulated $K^{+}\to {\pi }^0{\pi }^{+}$ [(c)] and $K^{+}\to {\pi }^{+}{\mu }^{+}{e}^{-}$ [(d)] events.

Figure 6

The reconstructed $M_{\pi \mu e}$ mass distribution for the (a) estimated $K_{\tau }$ background; (b) estimated $K_{\mathrm{Dal}}$ background; (c) estimated accidental background. (d) Comparison of the $M_{\pi \mu e}$ mass distribution for the $K_{\pi \mu e}$ data (markers with error bars) and total estimated background (histogram).

Figure 7

Comparison of the general likelihood distributions for measured (markers with error bars) and simulated directly from the PDF events for the $K_{\pi \mu e}$ (top) and the accidental background (bottom). The $K_{\pi \mu e}$ likelihood was calculated from the measured $K_{\tau }$ event sample (see text for details).

Figure 8

Scatter plot of $K_{\pi \mu e}$ data (bold dots) and simulated signal (top) and background (bottom). The abscissa is the log likelihood of the reconstructed events; the ordinate is the invariant mass ($M_{\pi \mu e}$) of the detected particles. The horizontal lines mark the $3\sigma$ mass region.

Figure 9

Distributions of target likelihood ($L_{\mathrm{target}}$), reconstructed kaon mass $M_{\pi \mu e}$, vertex quality $S_{\mathrm{norm}}$, minimum time difference between extra clumps in the calorimeter and closest in-time track pair ($T_{\mathrm{extra}}$), sum of track’s ${\chi }^2$, and $T_{\max }$ for the $K_{\pi \mu e}$ data. For reference purposes, corresponding PDFs are shown for signal (dotted line) and background (solid line) hypotheses.

Figure 10

Comparison of the Monte Carlo simulations of $K_{\tau }$ decays (histogram) with data (markers with error bars). Left: distance of closest approach $S_{\mathrm{norm}}$ to the common vertex for the three charged tracks; center: distribution of decay vertices along the beam direction $Z$ ($Z=0$ at the entrance of the first dipole magnet); right: reconstructed $K^{+}$ momentum.