Study of the decay $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ in the momentum region $140<P_{\pi }<199\mathrm{MeV}/c$

Experiment E949 at Brookhaven National Laboratory has observed three new events consistent with the decay $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ in the pion momentum region $140<P_{\pi }<199\mathrm{MeV}/c$ in an exposure of $1.71\times {10}^{12}$ stopped kaons with an estimated total background of $0.93\pm 0.17(\mathrm{stat}{)}_{-0.24}^{+0.32}(\mathrm{syst})$ events. This brings the total number of observed $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ events to seven. Combining this observation with previous results, assuming the pion spectrum predicted by the standard model, results in a branching ratio of $\mathcal{B}(K^{+}\to {\pi }^{+}\nu \overline{\nu })=({1.73}_{-1.05}^{+1.15})\times {10}^{-10}$. An interpretation of the results for alternative models of the decay $K^{+}\to {\pi }^{+}+nothing$ is also presented.

Figure 1

Momentum spectra of charged particles from $K^{+}$ decay in the rest frame. The values in parentheses represent the branching ratios of the decay modes [24]. The hatched spectrum represents the ${\pi }^{+}$ spectrum from $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ decay assuming the $V-A$ interaction. The densely hatched regions represent the $\pi \nu \overline{\nu }(1)$ and $\pi \nu \overline{\nu }(2)$ E949 signal regions.

Figure 2

Schematic side (a) and end (b) views of the upper half of the E949 detector. An incoming $K^{+}$ is shown traversing the beam instrumentation, stopping in the target and decaying to ${\pi }^{+}{\pi }^0$. The outgoing charged pion and one photon from the ${\pi }^0\to \gamma \gamma$ decay are illustrated. Elements of the detector are described in the text.

Figure 3

(Upper panel) Contribution of each photon veto detector in radiation lengths as a function of $\cos \theta$ for a photon emitted from the origin of the detector coordinate system. (Lower panel) Contribution of each photon veto element in the upstream and downstream regions within 18° of the beam.

Figure 4

Range in plastic scintillator vs momentum for charged particles accepted by the $\pi \nu \overline{\nu }(1+2)$ trigger. The concentrations of events due to the two-body decays are labeled $K_{\pi 2}$ peak and $K_{\mu 2}$ peak. The decays $K^{+}\to {\pi }^0{\mu }^{+}{\nu }_{\mu }$ and $K^{+}\to {\mu }^{+}{\nu }_{\mu }\gamma$ contributed to the muon band. The pion band resulted from $K^{+}\to {\pi }^{+}{\pi }^0\gamma$ decays, $K_{\pi 2}$ decays in which the ${\pi }^{+}$ scattered in the target or range stack and beam ${\pi }^{+}$ that scatter in the target. The boxes at low and high momentum represent the signal regions for this analysis and the previous $\pi \nu \overline{\nu }(1)$ analysis [2], respectively. This distribution represents 0.13% of the total kaon exposure.

Figure 5

Schematic of the bifurcation method. The background level in region $A$ can be estimated from the number of events observed in regions $B$, $C$, and $D$ assuming CUT1 and CUT2 are uncorrelated. See text for details.

Figure 6

Example target $xy$ display showing the assignment of pion, kaon, photon, and opposite-side pion fibers as described in the text. The arc that terminates in the reconstructed kaon vertex fiber represents the extrapolated UTC track. The circles on the track represent the UTC hits with the radius giving the drift distance. Only the innermost superlayer of the UTC is shown. The IC and VC elements with hits are indicated. The position of the incoming $K^{+}$ as reconstructed by the B4 hodoscope information is also indicated in the figure as are the kaon fiber “tips” described in Sec. 3b2. This event was selected in the $K_{e4}$ normalization branch (Sec. 3c2). The measured time, energy, and apparent curvature of the contiguous fibers classified as “photon” fibers are consistent with a positron and the time and energy of the opposite-side pion fibers are consistent with a negative pion.

Figure 7

The energy per pion fiber or kaon fiber in events in the $K_{\pi 2}$-peak region, defined in Sec. 3b4, in $\pi \nu \overline{\nu }(1+2)$ triggers. The height of the pion energy distribution was normalized to that of the kaon energy distribution for the purpose of display. The average number of pion (kaon) fibers per event in the selected events is 10.2 (5.3). Note the logarithmic abscissa.

Figure 8

CCD pulse fit example. The histogram represents the pulse height distribution for the high-gain CCD data. The histogram was terminated at 42 ns due to a software cutoff. The dashed (solid) line represents the fitted total pulse shape for the single- (double-) pulse hypothesis. The filled area represents the fitted second pulse for the double-pulse hypothesis. The arrow indicates $t_{\mathrm{rs}}$, the expected time of the second pulse based on the reconstructed ${\pi }^{+}$ in the range stack. This event was rejected because the 2.5 MeV of the fitted second pulse was coincident with $t_{\mathrm{rs}}$.

Figure 9

Extrapolated target $z$ distribution of the charged track. The “$\pi$-scatter” and “signal-like” events are taken from ${\pi }_{\mathrm{scat}}$ and $K_{\mu 2}$ monitor trigger data, respectively. The required minimum on the extrapolated $z$ position and the upstream end of the target are indicated in the figure.

Figure 10

The off-line rejection vs total acceptance for the optimized photon veto cuts. The error bars represent the statistical uncertainty. The labeled starred points are described in the text.

Figure 11

Schematic representation of a $K_{\pi 2}$ target scatter in which the ${\pi }^{+}$ initially traveled in the $z$ direction, scattered in a kaon fiber, and was directed into the barrel region. The two photons from the decay of the recoiling ${\pi }^0$ were directed into the beam region.

Figure 12

(Top panel) Pion momentum distribution for the normalization branch in the $2/3$ data sample. The black histogram represents the distribution after inversion of the photon veto cut. The blue dashed histogram shows the suppression of all the target cuts except for the CCDPUL cut and the red shaded histogram shows the suppression of all the target cuts including the CCDPUL cut. (Bottom panel) Pion momentum distribution of the rejection branch in the $2/3$ data sample. The events obtained from the inversion of the target cuts are shown in black and the red shaded histogram shows the events that survive the photon veto cut. The events surviving the photon veto cut that peak near $236\mathrm{MeV}/c$ were due to $K_{\mu 2}$ decays. The cuts on pion kinetic energy and range were not applied for these distributions in order to show the momentum distribution outside the $\pi \nu \overline{\nu }(2)$ signal region.

Figure 13

The sum of the ${\pi }^{-}$ and $e^{+}$ kinetic energies vs the reconstructed momentum of the ${\pi }^{+}$ for simulated $K_{e4}$ events that passed the $\pi \nu \overline{\nu }(1+2)$ trigger.

Figure 14

Momentum distribution of the ${\pi }^{+}$ in the $K_{e4}$ normalization branch for the $1/3$ sample before the application of the CCDPUL cut. The points represent the data. The unshaded histogram is the distribution as expected from simulated $K_{e4}$ events. The histogram area is normalized to the number of data events. The shaded histogram represents the normalization branch for $K_{\pi 2}$ target-scatter events. The ratio of the area of the shaded to the unshaded histogram has been arbitrarily set to $1/8$ times the ratio of the $K_{\pi 2}$ target-scatter background to the $K_{e4}$ background for display purposes.

Figure 15

Schematic diagram of the charge-exchange process in the target.

Figure 16

Kinetic energy vs range of all events passing all other cuts. The squares represent the events observed by this analysis. The circles and upward-pointing triangles represent the events observed by the E787 and E949 $\pi \nu \overline{\nu }(1)$ analyses, respectively. The downward-pointing triangles represent the events observed by the E787 $\pi \nu \overline{\nu }(2)$ analyses. The solid (dashed) lines represent the limits of the $\pi \nu \overline{\nu }(1)$ and $\pi \nu \overline{\nu }(2)$ signal regions for the E949 (E787) analyses. Despite the smaller signal region in $R_{\pi }$ vs $E_{\pi }$, the $\pi \nu \overline{\nu }(1)$ analyses were 4.2 times more sensitive than the $\pi \nu \overline{\nu }(2)$ analyses. The points near $E_{\pi }=108\mathrm{MeV}$ were $K_{\pi 2}$ decays that survived the photon veto cuts and were predominantly from the $\pi \nu \overline{\nu }(1)$ analyses due to the higher sensitivity and the less stringent photon veto cuts. The light gray points are simulated $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ events that were accepted by the $\pi \nu \overline{\nu }(1+2)$ trigger.

Figure 17

(Top panel) The generated ${\pi }^{+}$ kinetic energy spectrum for SM (solid line), scalar (dashed line), and tensor (dotted line) interactions. (Bottom panel) The distributions for events passing the $\pi \nu \overline{\nu }(1+2)$ trigger.

Figure 18

The solid lines represent the 90% C.L. upper limit on $\mathcal{B}(K^{+}\to {\pi }^{+}X)$ as a function of the mass of $X$ assuming $X$ is stable. The dashed lines represent the 90% C.L. for $X$ with the indicated lifetimes as described in the text.