arXiv:hep-ex/0205031v1 13 May 2002
Measurement of Rare Kaon Decay K+→ π+ν¯ ν
TRIUMF, 4004 Wesbrook Mall, Vancouver,
B.C., V6T 2A3, Canada
A decade long search for the rare kaon decay to π+ν¯ ν has been pursued by E787.
Two signal events are observed, giving a measurement of the branching ratio Br(K+→
trix element 0.007 < |Vtd| < 0.030 (68% C.L.).
−0.82× 10−10and a constraint on the Cabibbo-Kobayashi-Maskawa (CKM) ma-
In the Standard Model (SM) the transition K+to π+νν is a Flavor Changing Neutral Current
(FCNC) process in which the first order weak decay is forbidden by the GIM mechanism but
is allowed, though highly suppressed, in second order due to the differing masses of the up,
charm and top quarks in the mediating loops. Theoretically, this decay is sensitive to the
CKM matrix element Vtd, which is one of two CKM matrix elements containing CP violation
information in the SM. A study of this decay can provide a constraint on the range of Vtdfrom
the branching ratio of K+→ π+ν¯ ν. The SM predicts the branching ratio of this decay mode1
to be (0.72 ± 0.21)×10−10from a fit using Bd−¯Bdand Bs−¯Bsmixing and other relevant SM
parameters. The theoretical uncertainty in Br(K+→ π+ν¯ ν) is small (∼ 7%)2, and long distance
contributions to this decay are found to be negligible3. Therefore, a precise measurement can
also serve as a probe for new physics beyond the SM. Most interestingly, this decay together
with the neutral kaon decay KL→ π0ν¯ ν and the third most accurately measured CKM matrix
element Vcbcan also form a unitarity triangle in the ρ−η plane, thus providing an approach for
understanding CP violation.
The E787 experiment at Brookhaven National Laboratory found the first candidate event in
1995 data4and recently found the second candidate event in 1998 data5. This talk will present
the final E787 analysis result using data produced from about 6 × 1012charged kaons at the
Alternating Gradient Synchrotron (AGS) accelerator.
2 The E787 Detector
The E787 experiment (see Figure 1) is designed to capture the signature of K+→ π+ν¯ ν, i.e., a
charged kaon decay to a charged pion of momentum below 227 MeV/c and no other associated
observable product. Potential background can be K+→ µ+νµ(γ) (due to µ+misidentified
as π+or mismeasured kinematics or missed photon), K+→ π+π0(due to missed photon or
mismeasured kinematics), beam backgrounds (due to incoming π+mis-identified as K+or π+
faking K+decay at rest or K+decay in flight or two incoming beam particles), or charge
exchange background (due to K+n → K0p, K0
L→ π+l−νl). A detailed description of the E787
Figure 1: Top half of side (left) and end (right) views of the E787 detector.
detector can be found elsewhere6. The features relevant for this analysis are outlined in the
When 700-800 MeV/c charged kaons with about 20% pion contamination are delivered to
the E787 detector, they pass through a set of beam counters. The first of these is the threshold
ˇCerenkov counter used to identify kaons and pions in the beam. The beam then passes through
two beam wire chambers (BWPC) used for identifying multiple beam particles close to each
other in space and time. The beam is slowed down by a degrader made of beryllium oxide
followed by lead glass, the latter used for detecting pions in the beam or photons from kaon
decay in the target. Located between the degrader and the target is a hodoscope (B4 counter)
consisting of 2 planes of 8 scintillator fingers each, which provides dE/dx, position, and timing
information for the incident kaon, as well as K/π separation and identification of possible two
After passing through the beam counters, kaons are slowed down and finally stopped at
the center of the detector through ionization energy loss in the target, which is made of 413
5-mm-square plastic scintillating fibers, each 310 cm long and connected to a phototube. Pulses
from the phototubes are fed to ADCs, TDCs and 500-MHz CCD transient digitizers. The target
detector can also be used to identify possible two beam particles, and to distinguish K+and π+
using both time and energy measurements.
When a kaon stops and decays in the target, the daughter charged particle will pass through
the I-counters, which consist of six scintillators in a ring surrounding the target. The time
measurement from the I-counters together with the time measurement from the beam counters
are used to form a delayed coincidence requirement in the online trigger which rejects prompt
After the I-counter, the charged particle is tracked by the Ultra Thin Chamber (UTC),
which has 12 layers of anode wires for measuring the transverse momentum in the 1-T magnetic
field. In addition to this, there are six foils etched with helical cathode strips providing a dip
angle or z measurement in the r − z plane. After correction for energy loss in the target and
I-counter, the momentum resolution is measured to be σP/P ∼ 1.1%.
Upon exiting the UTC, the charged particle enters the range stack of plastic scintillators
(RS), which consists of 21 radial layers in 24 azimuthal sectors. Each range stack module is
instrumented with a phototube at each end. Pulses from these phototubes are delivered to ADCs
and 500-Mhz transient digitizers (TDs), thus providing kinetic energy and range measurements.
Located after layer 10 and 14 are two layers of straw-tube tracking chambers (RSSCs), which
provide position measurements of charged tracks in the RS. After making corrections for the
Figure 2: The philosophy of bifurcated analysis.
energy loss in the sub-detectors before entering the RS, the range and kinetic energy resolutions
are measured to be σR/R ∼ 2.9% and σE/?E(GeV) ∼ 1.0%, respectively. A unique feature
for the RS is a measurement of the π+→ µ+→ e+decay sequence from the TDs in the range
stack module in which the π+comes to rest. The decay sequence observation is a powerful tool
in identifying a charged pion. Muon rejection from this information can reach about 105. This
cut is independent of the π+/µ+separation using another cut on the range and momentum
correlation for different particles, where the π+/µ+separation is more than 3σ.
The outermost detectors are the barrel and end-cap photon vetoes.
lead glass beam counter and additional calorimeters for filling minor openings along the beam
direction, they provide a 4π solid angle for detecting photon activity.
Together with the
3 Background study
The study of K+→ π+ν¯ ν adopts the technique of blind analysis, in which selection criteria
(cuts) are designed from a study of background samples to avoid bias. Before looking into the
signal region (“opening the box”), background levels are estimated using the knowledge outside
the signal region. Cuts are designed in such a way to bring the background to the 0.1 event
To get a reliable background estimate, a so-called bifurcated analysis is conducted. The
philosophy of this method can be illustrated in Figure 2. Experimentally, two uncorrelated
cuts giving large background rejection are selected to perform this bifurcated analysis. Based
on the event numbers in region C, B and D, the background level in signal region A can be
estimated if these two cuts are uncorrelated. The cuts used for the bifurcated analyses are listed
in Table 1. In the π+ν¯ ν analysis, the π+π0and µ+νµ(γ) are the two major backgounds. Since
kinematic cuts are based the measurements of the range, kinetic energy and momentum, which
are independent of the detection of photon activity and the particle ID using the TD information
for recognizing the π+→ µ+→ e+decay sequence, the bifurcated analyses can be performed
between them. To check if they are uncorrelated, a so-called outside-the-box study is conducted
by loosening the two cuts and checking if the background level estimated is consistent with the
In estimating background level, π+ν¯ ν data are divided into 1/3 and 2/3 samples. The 1/3
Table 1: Cuts used in the bifurcated analyses for the background.
1 beam bkg
2 beam bkg
RS TD PID
B4 dE/dx cuts
B4 2-hit cuts
Table 2: Background estimates for 1995-97 and 1998 data.
1 beam bkg
2 beam bkg
0.0216 ± 0.0050
0.0092 ± 0.0067
0.0245 ± 0.0155
0.0039 ± 0.0012
0.0004 ± 0.0001
0.0282 ± 0.0098
0.0054 ± 0.0042
0.0157 ± 0.0149
0.0096 ± 0.0068
0.0804 ± 0.0201
sample is used for cuts tuning and initial background evaluation. When the background levels
are satisfactory, all the cuts are applied to the 2/3 sample and the background levels are re-
estimated. If all cuts are set without bias, the background level from the 1/3 and 2/3 samples
should be consistent.
When the checks on the correlation of the two cuts in the bifurcated analysis and the
consistency of background estimates between 1/3 and 2/3 sample were performed, no correlations
or inconsistencies were observed. The final background estimates using the 2/3 sample are
given in Table 2. The charge exchange background estimate is from Monte Carlo. The kaon
regeneration rate and beam profile are from the actual measurement using data for the process
of K+n → K0
4Search for signal
Since the background level of 0.15 event estimated for the full E787 data is small, satisfying
the single event search in the signal region, the box is opened. Figure 3 shows the range versus
kinetic energy for the events surviving all the selection criteria. The box indicated by the solid
lines depicts the signal search region. Two signal events are found inside this signal region and
the events outside this box are from the K+→ π+π0background due to photons escaping
detection. Detailed studies of the candidate events as well as a signal probability study showed
that they are consistent with the signature of K+→ π+ν¯ ν.
The E787 experiment can also perform a search below the kinematic peak of the decay7
K+→ π+π0. The study shows the search in this region is limited by the background from
K+→ π+π0, which should be improved in the ongoing E949 experiment by increasing the
photon veto capability.
L 1995-97 data
H 1998 data
G M.C. π+νν
Figure 3: Range versus kinetic energy distribution for all E787 data with all cuts applied except for the range
and kinetic energy cuts.
5Acceptance and branching ratio
The acceptance is estimated using µ+νµ, π+π0, and π+-scattering monitor samples taken simul-
taneously with the π+ν¯ ν trigger and by means of a Monte Carlo π+ν¯ ν sample. Table 3 gives
the acceptances for each cut category and the final acceptance. The acceptances for π+ν¯ ν phase
space, solid angle acceptance and π+nucleus interaction are estimated using Monte Carlo. Also
given are the total K+triggers and the corresponding branching ratios assuming no background.
The validity is checked against the branching ratio of K+→ π+π0as given below
Br(K+→ π+π0)=0.208 ± 0.003stat.(1995-97)
=0.217 ± 0.003stat.(1998)
=0.212 ± 0.001 (PDG)
The acceptances of the K+→ π+ν¯ ν and K+→ π+π0decays should differ only in the decay
phase space. Agreement with the PDG value is observed.
To combine searches with small statistics for both signal and background level, a statistical
analysis8is performed giving the final branching ratio measurement on K+→ π+π0from E787:
Br(K+→ π+ν¯ ν)= 1.57+1.75
Assuming unitarity, ¯ mt(mt) = 166 ± 5 GeV/c2, MW = 80.41 GeV/c2and Vcb= 0.041 ± 0.002,
one can derive the constraint
0.007 < |Vtd| < 0.030 (68% C.L.),
without requiring any knowledge of Vubor ǫK.
The E787 experiment has pursued a decade long search for the rare kaon decay to π+ν¯ ν with
two signal events observed. The branching ratio is measured to be 1.57+1.75
−0.82× 10−10. The
Table 3: Acceptance study for K+→ π+ν¯ ν
K+decay after 2 ns
π+ν¯ ν phase space
Solid angle acceptance
Other kinematic constraints
π+→ µ+→ e+decay acc.
Beam and target analysis
Total K+triggers (×1012)
Br(K+→ π+ν¯ ν) (×10−10)
central value is a factor of two larger than what the Standard Model predicts, though the
large uncertainty prevents any solid conclusion on possible new physics. It is expected that the
ongoing E949 experiment, which continues the study of the K+→ π+ν¯ ν decay at BNL will be
able to collect 5 times more statistics and provide a critical test on the Standard Model.
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