Measurement of the $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }\gamma$ branching ratio

A measurement of the decay $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }\gamma$ has been performed with the E787 detector at Brookhaven National Laboratory. Forty events were observed in the signal region with the background expectation of ($16.5\pm 2.7$) events. The branching ratio was measured to be $(1.58\pm 0.46(\mathrm{stat}.)\pm 0.08(\mathrm{syst}.))\times {10}^{-5}$ in the kinematic region $E_{\gamma }>30\mathrm{MeV}$ and ${\theta }_{\mu \gamma }>20°$, where $E_{\gamma }$ is the energy of the emitted photon and ${\theta }_{\mu \gamma }$ is the angle between the muon and the photon in the $K^{+}$ rest frame. The results were consistent with theoretical predictions.

Figure 1

Spectra of $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }\gamma$ observables based on ChPT at $O(p^4)$: muon momentum (top left), cosine of ${\theta }_{\mu \gamma }$ (top right), $E_{\gamma }$ (bottom left), and neutrino energy (bottom right). The unhatched and hatched histograms represent the distributions before and after imposing the conditions $E_{\gamma }>30\mathrm{MeV}$ and ${\theta }_{\mu \gamma }>20°$.

Figure 2

Schematic side (a) and end (b) views showing the upper half of the E787 detector. Č: Čerenkov counter; B4: beam counter; I and T: trigger scintillation counters (I-counters and T-counters). Range-stack straw-tube tracking chambers (RSSC) were unused in this measurement.

Figure 3

Plots of the variables $DPSQ$ vs $CHKSPZ$ for the $K_{\mu 3\gamma }$ events (left) and the $K_{\pi 3}$ background events (right) generated by the Monte Carlo simulation.

Figure 4

$M_{\gamma \gamma }$ distributions of the ${\pi }^0$ from the $K_{\mu 3}$ (left) and $K_{\pi 3}$ (right) events.

Figure 5

Cosine of ${\theta }_{\mu \gamma }$ vs $E_{\gamma }$ plots of the events with all analysis cuts imposed in real data (left) and in the sample generated by Monte Carlo $K_{\mu 3\gamma }$ simulation (right). The box indicates the signal region.

Figure 6

Distributions of $\mathrm{Prob}({\chi }_{K_{\mu 3\gamma }}^2)$ from the events in the signal region in real data (left) and in the sample generated by Monte Carlo $K_{\mu 3\gamma }$ simulation (right). All selection cuts except for the cut $\mathrm{Prob}({\chi }_{K_{\mu 3\gamma }}^2)>0.1$ in subsection 6b are imposed.

Figure 7

$M_{\gamma \gamma }$ distributions of the ${\pi }^0$ from the events in the signal region in real data (left) and in the sample generated by Monte Carlo $K_{\mu 3\gamma }$ simulation (right).

Figure 8

$\Delta t_{\gamma }$ distributions of the two photons to form the ${\pi }^0$ (left) and of the radiative photon (right) in real data.

Figure 9

Distributions in $\cos ({\theta }_{\mu \gamma })$ vs $E_{\gamma }$ of events selected as the $K_{\mu 3}\mathrm{\text{−}}1$ (left) and $K_{\pi 3}$ (right) background events as described in the text. The box indicates the signal region.

Figure 10

Spectra of the $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }\gamma$ candidates: $E_{\gamma }$ (top left), ${\pi }^0$ energy (top right), $E_{\nu }$ (bottom left), and muon momentum (bottom right). In each plot, the circles with error bars represent the distributions of the 40 events observed in the signal region. The conditions $E_{\gamma }>30\mathrm{MeV}$ and $E_{\nu }>60\mathrm{MeV}$ have been imposed in the analysis. The right-hatched and left-hatched histograms represent the expected distributions of the $K_{\mu 3}$ and $K_{\pi 3}$ backgrounds, respectively. The unhatched histogram represents the distribution of the Monte Carlo $K_{\mu 3\gamma }$ events with the central value of the measured branching ratio plus all the background contributions, and should be compared to the circles with error bars.