arXiv:0711.3472v1 [hep-ex] 21 Nov 2007
Search for Lepton Flavor Violating Decays of the Neutral Kaon
E. Abouzaid,4M. Arenton,11A.R. Barker,5, ∗L. Bellantoni,7A. Bellavance,9E. Blucher,4G.J. Bock,7E. Cheu,1
R. Coleman,7M.D. Corcoran,9, †B. Cox,11A.R. Erwin,12C.O. Escobar,3A. Glazov,4A. Golossanov,11
R.A. Gomes,3P. Gouffon,10Y.B. Hsiung,7D.A. Jensen,7R. Kessler,4K. Kotera,8A. Ledovskoy,11
P.L. McBride,7E. Monnier,4, ‡H. Nguyen,7R. Niclasen,5D.G. Phillips II,11H. Ping,12E.J. Ramberg,7
R.E. Ray,7M. Ronquest,11E. Santos,10W. Slater,2D. Smith,11N. Solomey,4E.C. Swallow,4,6P.A. Toale,5
R. Tschirhart,7Y.W. Wah,4J. Wang,1H.B. White,7J. Whitmore,7M. J. Wilking,5B. Winstein,4
R. Winston,4E.T. Worcester,4M. Worcester,4T. Yamanaka,8E. D. Zimmerman,5and R.F. Zukanovich10
1University of Arizona, Tucson, Arizona 85721
2University of California at Los Angeles, Los Angeles, California 90095
3Universidade Estadual de Campinas, Campinas, Brazil 13083-970
4The Enrico Fermi Institute, The University of Chicago, Chicago, Illinois 60637
5University of Colorado, Boulder, Colorado 80309
6Elmhurst College, Elmhurst, Illinois 60126
7Fermi National Accelerator Laboratory, Batavia, Illinois 60510
8Osaka University, Toyonaka, Osaka 560-0043 Japan
9Rice University, Houston, Texas 77005
10Universidade de S˜ ao Paulo, S˜ ao Paulo, Brazil 05315 -970
11The Department of Physics and Institute of Nuclear and Particle
Physics, University of Virginia, Charlottesville, Virginia 22901
12University of Wisconsin, Madison, Wisconsin 53706
The Fermilab KTeV experiment has searched for lepton-flavor-violating decays of the KL meson
in three decay modes. We observe no events in the signal region for any of the modes studied, and
we set the following upper limits for their branching ratios at the 90% CL: BR(KL → π0µ±e∓) <
7.56 × 10−11; BR(KL → π0π0µ±e∓) < 1.64 × 10−10; BR(π0→ µ±e∓) < 3.59 × 10−10. This result
represents a factor of 82 improvement in the branching ratio limit for KL → π0µe and is the first
reported limit for KL → π0π0µ±e∓.
PACS numbers: 13.20.Eb, 11.30Fs
In the Standard Model of particle physics lepton-
flavor-violating (LFV) decays are possible with non-zero
neutrino masses and mixing, but the rates for such de-
cays are far beyond the reach of any current experiment
. Therefore, the observation of LFV decays would be
an indication of new physics. Many scenarios for physics
beyond the Standard Model allow LFV decays. Super-
symmetry , new massive gauge bosons [1, 3], and Tech-
nicolor  all can lead to LFV decays which might be
within reach of current experiments. Searches in KLde-
cays are complementary to searches in the charged lepton
sector, since KLdecays probe the s → dµe transition .
In this letter we report on searches for three LFV
processes in the KTeV experiment at Fermilab.
present improved limits on the decays KL → π0µ±e∓
and π0→ µ±e∓(tagged from KL → π0π0π0), and we
report the first limit on the decay KL→ π0π0µ±e∓.
The KTeV E799-II experiment at Fermilab took data
in 1997 and 1999. The combined results from both peri-
ods are presented here. The KTeV beam was produced
by 800 GeV/c protons from the Tevatron which were di-
rected onto a BeO target and collimators to create two
nearly-parallel KL beams.
long vacuum tank which defined the fiducial volume for
The beams entered a 65m
Charged particles were detected by two pairs of drift
chambers separated by an analysis magnet that provided
a transverse momentum kick of either 0.250 GeV/c (for
the 1997 data) or 0.150 GeV/c (for the 1999 data). Dis-
crimination between charged pions and electrons was pro-
vided by a set of transition radiation detectors (TRDs)
behind the last drift chamber. Downstream of the TRDs
were two planes of trigger hodoscopes, followed by a CsI
electromagnetic calorimeter, which had an energy resolu-
tion σ(E)/E = 0.45%⊕2%/?E(GeV ). The calorimeter
provided powerful electron/pion discrimination based on
the ratio of energy as measured in the calorimeter (E) to
momentum as measured in the spectrometer (p), or E/p.
The lateral shower shape in the calorimeter provided ad-
ditional electron/pion discrimination. The CsI calorime-
ter had two beam holes to allow the undecayed beam
particles to pass through. A Beam Anti (BA) calorime-
ter covered the solid angle behind the two beam holes.
Photon detectors were positioned around the vacuum de-
cay region, the spectrometer, and the calorimeter to veto
particles escaping the fiducial region of the detector.
The muon system was located downstream of the
calorimeter, shielded by 10 cm of lead followed by 4m of
steel. Behind the steel was a plane of muon hodoscopes,
consisting of 15cm wide scintillator paddles oriented ver-
tically. Behind this hodoscope was another meter of steel,
followed by two more planes of scintillator paddles, one
oriented vertically and one horizontally.
The hardware trigger for this analysis required at least
one hit in the last two banks of muon counters and at
least three energetic in-time clusters in the CsI calorime-
ter.The Level 3 software trigger required two tracks
which formed a good vertex, with one one track having
an E/p value greater than 0.7, consistent with an elec-
tron. More detail of the KTeV detector can be found in
A detailed Monte Carlo simulation was used to study
detector performance and acceptance, to simulate back-
grounds, and to select cuts. For the LFV decays, a uni-
form phase space decay distribution was assumed.
The number of KLdecays in our fiducial volume, which
we refer to as the flux, was determined for each decay
mode by comparison to a similar decay with a well-known
branching fraction. Using a normalization mode similar
to the signal mode cancels many systematic uncertain-
ties. For the decay KL → π0µ±e∓, the normalization
mode was KL → π+π−π0. For KL → π0π0µ±e∓and
π0→ µ±e∓, the normalization mode was KL→ π0π0π0
all values of the flux and single event sensitivity quoted
below, the systematic error was determined by varying
the analysis cuts and noting the change in the measured
flux. An additional 2% systematic error on the efficiency
of the muon trigger was included, since there was no
muon requirement for either normalization mode. The
uncertainty in the branching fraction of the normaliza-
tion modes was included as a systematic error.
We first consider the decay KL→ π0µ±e∓. The signa-
ture for this decay was two charged tracks (one electron
and one muon) and two neutral clusters. The charged
tracks were required to form a good vertex within the
fiducial decay volume,and both tracks were required to
match a cluster in the CsI calorimeter. One charged track
was required to have an E/p ratio within 5% of 1.0 and a
transverse shower shape consistent with an electromag-
netic shower. A loose cut on the TRD information (98%
efficient for electrons) gave an additional cross-check on
electron identification. The second track was required
to deposit less than 1 GeV of energy in the calorimeter,
consistent with a minimum ionizing muon, and to have
a momentum greater than 8 GeV/c. The projection of
the downstream segment of the muon track was also re-
quired to match hits in all three hodoscope planes of the
muon detector, within a road determined by the expected
The π0was reconstructed by its decay to two photons
which were detected as clusters in the calorimeter with
no associated charged tracks and with transverse shower
shapes consistent with an electromagnetic shower. The
energy and position of the neutral clusters along with
the location of the charged vertex were used to calculate
Ddenotes a π0Dalitz decay, π0→ e+e−γ. For
Mγγ, the invariant mass of the two photon system. Mγγ
was required to be within 1.4 σ of the π0mass, where σ is
the π0mass resolution of 1.4 MeV/c2, as determined from
the normalization mode. This requirement was chosen to
optimize the ratio S/√B, where S is the number of signal
events and B is the number of background events.
The following kinematic cut further reduced back-
grounds. Assuming a signal mode decay, we calculated
the square of the π0momentum in the KL rest frame.
For many backgrounds this quantity has an unphysical
negative value. We required this quantity to lie between
0 and 0.025 (GeV/c)2, where the upper value is the kine-
matic cutoff in the signal mode.
The flight direction of the parent KLcan be approxi-
mated by a line from the center of the target to the decay
vertex. We defined ptto be the sum of the momentum
components of all final-state particles perpendicular to
this direction. For well-reconstructed signal events p2
should be close to zero. The signal and control regions
were defined using a likelihood variable L derived from
in the following way. Using signal Monte Carlo, the KL
mass distribution was fit with a Gaussian, and the p2
distribution was fit with a three-component exponential,
producing probability density functions (PDFs) for these
variables.Since these variables were found to be un-
correlated, the joint PDF was defined as the product of
the two single-variable PDFs. Then L was calculated for
each event by evaluating the joint PDF at the p2
Mπ0µevalue for that event. The signal (control) region
was defined by a cut on L chosen to retain 95% (99%)
of signal Monte Carlo events after all other cuts were
applied. Both the signal and control regions were blind
during the analysis. Figure 1 shows the p2
with KL→ π0µ±e∓signal Monte Carlo events shown as
points, and the signal and control regions shown as solid
The dominant background for KL→ π0µ±e∓was the
decay KL→ π±e∓νe(Ke3), with a π±decay or punch
through to the muon hodoscopes, accompanied by two
accidental photons faking a π0. Since accidental pho-
tons were often accompanied by other accidental activ-
ity, we made stringent anti-accidental cuts to reduce this
background. An event was cut if any additional charged
tracks were present. We allowed no extra in-time hit pairs
in the drift chambers upstream of the analysis magnet
and at most two extra in-time pairs downstream of the
magnet. We also cut on the number of partial track stubs
in the upstream chambers. No more than 300 MeV of en-
ergy could be present in any of the photon veto counters
surrounding the vacuum decay region, the drift cham-
bers, and the calorimeter. The energy deposited in the
BA calorimeter was required to be less than 15 GeV to
veto events in which an energetic photon escaped through
one of the beam holes.
Figure 2 shows the Mγγ distribution for data out-
tand Mπ0µe, the invariant mass of the π0µe system,
FIG. 1: Signal Monte Carlo events for the decay KL →
π0µ±e∓in the p2
t− Mπ0µeplane. All cuts except the sig-
nal region cut have been made. The inner contour shows the
signal region, and the outer contour indicates the control re-
side the signal and control regions, with all cuts ap-
plied except the Mγγ cut.
shows no peak at the π0mass.
the Mγγ sidebands above and below the π0mass re-
gion (0.11 GeV/c2< Mγγ <0.132 GeV/c2and 0.138
GeV/c2< Mγγ < 0.16 GeV/c2), but inside the signal
or control regions in L, to estimate the Ke3backgrounds.
The Ke3background was thus estimated to be 0.56 ±0.23
events in the signal region and 2.56 ±0.49 events in the
A second source of background was KL→ π0π±e∓νe
(Ke4), with a charged pion decay or punch through. A
kinematic cut to reduce this background was defined by
assuming a Ke4decay and calculating the magnitude of
the unseen neutrino’s momentum in the KLrest frame.
For Ke4 decays, this quantity must be positive, while
for signal decays it is usually negative. Requiring this
variable to be negative removed most Ke4 background.
The remaining Ke4 contribution was determined from
Monte Carlo simulation to be 0.10 ± 0.050 events in the
signal region and 1.65±0.20 events in the control region.
Note that the Ke4and Ke3backgrounds must be added,
since Ke4decays do not contribute to the Ke3sideband
Another possible source of background was KL →
π+π−π0decays. These decays could fake the signal if
one charged pion decayed to a muon and the second was
mistaken for an electron in the calorimeter and TRDs.
However, due to the incorrect mass assignments, Mπ0µe
reconstructed about 50 MeV/c2below the true KLmass,
with no tail extending near the signal region. The π/e
rejection from both the calorimeter and the TRDs sup-
press this background to a negligible level, as confirmed
by both Monte Carlo simulation and KL→ π+π−π0de-
This smooth distribution
We therefore used
0.110.1150.120.1250.130.135 0.140.145 0.150.1550.16
Events per 0.001
FIG. 2: Mγγ distribution for KL → π0µ±e∓search data, for
events outside the signal and control regions, with all cuts in
place except the Mγγ cut. The arrows show the regions used
for the sideband background estimate.
cays in data from a minimum-bias trigger.
Other sources of background were considered but
found to be negligible. We find an expected total back-
ground of 0.66 ±0.23 events in the signal region and 4.21
±0.53 events in the control region.
The signal acceptance for KL → π0µ±e∓was deter-
mined from Monte Carlo simulation to be 3.95% for the
1999 data and 3.91% for the 1997 data. The total num-
ber of KLdecays in the fiducial region was determined
from the normalization mode to be (6.17 ± 0.31) × 1011,
and the single event sensitivity (SES) for the combined
data set was (4.12 ± 0.21) × 10−11.
When we opened the blind regions, we found 0 events
in the signal region and 5 events in the control region,
consistent with background estimations. Figure 3 shows
t− Mπµe plane, with the surviving events shown
as solid dots and the signal and control region shown as
The 90% confidence level (CL) upper limit was deter-
mined for all modes in the following way. We stepped
through a range of possible branching fractions, using a
Monte Carlo simulation to produce a Poisson distribution
at each value. The errors on the SES and backgrounds
were taken into account by allowing these quantities to
vary as Gaussian distributions with widths equal to their
errors. The resulting Poisson distributions were then
used to construct confidence bands, using the Feldman-
Cousins prescription . From these confidence bands we
determined BR(KL→ π0µ±e∓) < 7.56 × 10−11at the
90% CL. This result represents a factor of 82 improve-
ment over the previous best limit for this mode. 
We now consider the decay KL → π0π0µ±e∓. The
addition of a second π0greatly reduces the backgrounds,
so we were able to relax some cuts to improve the signal
acceptance. Since KL → π0π+π−is not a background
for this mode, we did not make a TRD requirement on
KL → π0µ±e∓search data. The signal and control regions
are shown as the inner and outer solid contours.
Surviving events in the p2
t− Mπ0µeplane for the
the electron track, and there was no cut on the number
of partial track stubs. We allowed up to two extra in-
time hits in both the upstream and downstream drift
Since we have two neutral pions in this decay, we can
determine a neutral vertex independently of the charged
vertex. We required that the difference between the neu-
tral and charged vertices be less than 2.5 meters.
addition, we calculated an average vertex from the neu-
tral and charged vertices, and recalculated Mγγ using
the average vertex. The resulting values were required to
lie in the region 0.132 GeV/c2< Mγγ< 0.138 GeV/c2.
Additionally, a kinematic cut on the square of the π0
momentum in the KLrest frame was made on both π0s.
One important source of background for this mode was
the decay KL → π0π0π0
taken for a muon it was mismeasured in the calorimeter
and if an accidental muon fired the appropriate muon ho-
doscope paddles. To suppress this background, we made
a loose cut on the TRD information for the muon track
which rejected 85% of all electrons. This cut effectively
eliminated KL→ π0π0π0
Other backgrounds arose from Ke3or Kµ3decays with
four accidental photons. The Mγγsidebands could not be
used in this case to estimate the background, since they
did not have a smooth distribution. The background es-
timate was obtained instead by the extrapolation of a
linear fit to the log(L) distribution from outside the con-
trol region into the signal and control regions. However,
when all cuts were applied, there were not enough events
remaining to make a reliable extrapolation. We there-
fore defined three independent cut sets (kinematic cuts,
particle ID cuts, and anti-accidental cuts). When we re-
moved all three sets, we had sufficient events to make
an extrapolation into the signal region, as shown in fig-
D. One electron could be mis-
FIG. 4: The log(L) distribution for KL → π0π0µ±e∓search
data.The three cuts sets as described in the text have
been removed.A linear fit over the region -15<log(L)<5
was extrapolated into the signal (log(L)>10) and control
(5 <log(L)< 10) regions to estimate the background. The
upper and lower dashed lines indicate the error bands used to
assign a systematic error to the background estimate.
ure 4. After the extrapolation, we apply the suppression
factor associated with each cut set, as determined from
the data. We verified from the data (by applying the cut
sets in various combinations) that the three sets were in-
deed independent, so that we could multiply the three
separate suppression factors to get the final background
estimate. The total number of background events was
thus estimated to be 0.44±0.23 in the signal region and
0.43±0.17 in the control region. Due to the uncertainties
in both the extrapolation in log(L) and the suppression
factors, we assign a systematic error on the background
estimate by allowing the fit parameters to vary by 2.5 σ
from their central values.
The signal acceptance was 2.04% for the 1999 data
and 1.95% for the 1997 data. The total number of KL
decays was (6.36 ± 0.24) × 1011. The SES for the com-
bined data set was (7.88 ± 0.28) × 10−11.
blind regions were opened, we found no events in either
the signal or control regions. We set the 90% CL limit
BR(KL→ π0π0µ±e∓) < 1.64 × 10−10, which is the first
limit reported for this decay.
The search for π0→ µ±e∓, tagged from KL→ π0π0π0
is identical to the KL → π0π0µ±e∓search with the
additional requirement that Mµe be in the π0mass re-
gion. The background was estimated from both KL→
DMonte Carlo and from an extrapolation of the
log(L) distribution into the signal region as was done
for KL → π0π0µ±e∓.
sistent results, yielding a background estimate of 0.03
±0.015 events in the signal region and an identical value
in the control region. The flux for this mode was de-
termined from (KL decays) ×3 × BR(KL → π0π0π0),
yielding a SES of (1.48 ± 0.059) × 10−10.
The two methods gave con-
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blind regions were opened, we found no events in ei-
ther the signal or control regions. We set the 90% CL
limit BR(π0→ µ±e∓) < 3.59 × 10−10. Our limit on
π0→ µ±e∓is equally sensitive to both charge modes,
while the previous best limits were not ,. Assum-
ing equal contributions from both charge combinations,
our result is about a factor of two better than the pre-
vious best limit on π0→ µ+e−and about a factor of 10
greater than the previous best limit on π0→ µ−e+.
Although no evidence for these flavor-violating modes
has been found, the pursuit should not dropped. Given
that we find negligible backgrounds, our techniques could
clearly be extended to higher intensity neutral kaon
We gratefully acknowledge the support and effort of
the Fermilab staff and the technical staffs of the par-
ticipating institutions for their vital contributions. This
work was supported in part by the U.S. Department of
Energy, The National Science Foundation, The Ministry
of Education and Science of Japan, Fundao de Amparo
a Pesquisa do Estado de S Paulo-FAPESP, Conselho
Nacional de Desenvolvimento Cientifico e Tecnologico-
CNPq and CAPES-Ministerio Educao.
†To whom correspondence should be addressed
‡Permanent address C.P.P. Marseille/C.N.R.S., France
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