of 15
PHYSICAL
REVIEW
D
VOLUME
53,
NUMBER
1
Measurement
of
the
mass
of
the
T
lepton
1
JANUARY
1996
J.
Z.
Bai,’
0.
Bardon,e
R.
A.
Becker-Szendy,8
I.
Blum,”
A.
Breakstone,’
T.
Burnett,”
G.
P.
Chen,’
H.
F.
Chen,4
.I.
Chen,5
S.
J.
Chen,l
S.
M.
Chen,l
Y.
Chen,’
Y.
B.
Chen,’
Y.
Q.
Chen,’
B.
S.
Cheng,’
R.
F.
Cowan,e
H.
C.
Cu&l
X.
Z.
Cui,’
H.
L.
Ding,’
Z.
Z.
Du,’
W.
Dunwoodie,e
X.
L.
Fan,’
J.
Fang,
1
C.
S.
Gao,’
M.
L.
Gao,l
S.
Q.
Gao,’
W.
X.
Gao
1
P.
Gratton,”
J.
H.
Go,’
S.
D.
Gu,’
W.
X.
Gu,’
Y.
F.
Gu,’
Y.
N.
Guo,’
S.
W.
Han,’
Y.
Han,’
F.
A.
H&ie,s
M.
Hatanaka,
J.
He,’
K.
R.
He,’
M.
He,’
D.
G.
Hitlin,3
G.
Y.
Hu,’
T.
Hu,’
X.
Q.
Hu,l
D.
Q.
Huang,’
Y.
Z.
Huang,’
J.
M.
Izen,”
Q.
Pr
Jia:
C.
H.
Jiang,’
Z.
Z.
Jiang:
S.
Jin,’
Y.
Jin,’
L.
Jone~,~
S.
H.
Kang,’
Z.
J.
Ke,’
M.
H.
Kel~ey,~
B.
K.
Kim,
l1
Y.
F.
Lai,’
H.
B.
Lm,’
P.
F.
Lang,’
A.
Lankford,”
F.
Li,’
J.
Li,’
P.
Q.
Li,’
Q.
Li,’
R.
B.
Li,’
W.
Li,’
W.
D.
Li,’
W.
G.
Li,l
X.
H.
Li,
X.
N.
Li,’
Y.
S.
Li,’
S.
Z.
Lin,’
H.
M.
Liu,l
J.
Liu,’
J.
H.
Liu,’
Q.
Liu,’
R.
G.
Liu,’
Y.
Liu,’
Z.
A.
Liu,’
X.
C.
Lou,”
B.
Lowery,“,*
F.
Lu,’
J.
G.
Lu,’
Y.
Luo,l
A.
M.
Ma,l
D.
H.
Ma,’
E.
C.
Ma,’
J.
M.
Ma,l
H.
S.
Mao,’
Z.
P.
Mao,l
R.
Malchow,’
M.
Mandelkern,
lo
H.
Marsiske,e
X.
C.
Meng,’
H.
L.
Ni,’
J.
Nie,’
S.
L.
0lser1,~
J.
Oyang,3
D.
Paluselli:
L.
J.
Pan,’
J.
Panetta,3
F.
Porter,3
E.
Prabhakar,3
N.
D.
Qi,’
Y.
K.
Que,
1
J.
Quigley,e
G.
Rang,’
M.
Schernau,l”
B.
Schmid,“’
J.
Schultz,
lo
Y.
Y.
Shao,’
B.
W.
Shen,’
D.
L.
Shea,’
H.
Shen,’
X.
Y.
Shen,
H.
Y.
Shag,’
H.
Z.
Shi,’
X.
R.
Shi,3
A.
Smith,‘O
E.
Soderstrom,e
X.
F.
Song,’
J.
Standifird,”
D.
Stoker,”
F.
Sun,’
H.
S.
Sun,’
S.
J.
Sun,’
J.
Synodinos,’
Y.
P.
Tan,l
S.
Q.
Tang,
W.
Toki,5
G.
L.
Tong,’
E.
Torrence,e
F.
Wang,’
L.
S.
Wang,’
L.
Z.
Wang,’
M.
Wang,’
P.
Wang,’
P.
L.
Wang,’
S.
M.
Wang,
1
T.
J.
Wang,’
Y.
Y.
Wang,’
C.
L.
Wei,’
S.
Whittaker,’
R.
Wilson,5
W.
J.
Wisniewski,13’t
Y.
G.
Wu,l
D.
M.
Xi,’
X.
M.
Xia,’
P.
P.
Xie,’
X.
X.
Xie,’
W.
J.
Xiong,’
D.
Z.
Xu,’
M.
K.
Xu,
l4
R.
S.
Xu,’
Y.
D.
XU,‘~
Z.
Q.
Xu,l
S.
T.
Xue,’
R.
Yamamoto,e
J.
Yan,’
W.
G.
Yan,l
C.
M.
Yang,’
C.
Y.
Yang,l
J.
Yang,’
W.
Yang,’
H.
B.
Yao,’
M.
H.
Ye,’
S.
W.
Ye,4
S.
Z.
Ye,’
C.
S.
Yu,l
C.
X.
Yu,’
Y.
H.
Yu,14
Z.
Q,
Yu,’
C.
Z.
Yuan,’
J.
Y.
Zag,’
B.
Y.
Zhang,’
C.
C.
Zhang,l
D.
H.
Zhang,l
H.
L.
Zhang,’
J.
Zhang,’
J.
W.
Zhang,’
L.
S.
Zhang,’
S.
Q.
Zhang,’
Y.
Zhang,l
Y.
Y.
Zhang,’
D.
X.
Zhao,’
H.
W.
Zhao,’
J.
W.
Zhao,l
M.
Zhao,’
P.
D.
Zhao,’
W.
R.
Zhao,’
J.
P.
Zheng,’
L.
S.
Zheng,’
Z.
P.
Zheng,l
G.
P.
Zhou,l
H.
S.
Zhou,’
Li
Zhou,’
X.
F.
Zhou,’
Y.
H.
Zhou,’
H.
G.
Zhu,’
Q,
M.
Zhu,’
Y.
C.
Zhu,’
Y.
S.
Zhu,’
B.
A.
Zhuang,’
G.
Zioulas”
(BES
Collaboration)
‘Institute
of
High
Energy
Physics,
Beijing
100039,
People’s
Republic
of
China
‘Boston
University,
Boston,
Massachusetts
02215
3Ca1ijomia
Institute
of
Technology,
Pasadena,
Calijomia
91125
4
University
of
Science
and
Technology
of
China,
Hejei
230026,
People’s
Republic
of
China
5Colorado
State
University,
Fort
Collins,
Colorado
80523
eMassachusetts
Institute
of
Technology,
Cambridge,
Mossachwetti
02139
‘Shandong
University,
Jinan
250100,
People’s
Republic
of
China
eStanford
Linear
Accelerator
Center,
Stanford,
California
94309
‘University
of
Hawaii,
Bonokdu,
Hawaii
96822
‘“University
of
California
at
Irvine,
Irvine,
Calijomia
92717
University
of
Term
at
Dallas,
Richardson,
Tezas
75083-0688
la
University
of
Washington,
Seattle,
Washington
98195
‘3Superconducting
Supercollider
Laboratory,
Dallas,
Texas
75237-3946
‘*Hangdou
University,
Hangzhou
310028,
People’s
Republic
of
China
(Received
25
July
1995)
A
data-driven
energy
ecan
in
the
immediate
vicinity
of
the
7
pair
production
tbreshold
has
been
performed
using
the
Beijing
Spectrometer
at
the
Beijing
Electron-Positron
Collider.
Approximately
5
pb-’
of
data,
distributed
over
12
ecan
points,
have
been
collected.
A
previous
maee
value
for
the
7
lepton,
obtained
using
only
the
ep
final
state,
has
been
published.
In
this
paper,
the
final
BES
result
on
the
maes
measurement
is
presented.
The
analysis
is
based
on
the
combined
data
from
the
ee,
ep,
eh,
VW,
ph,
and
hh
final
states,
where
h
denotes
a
charged
?(
or
K.
A
maximum
likelihood
fit
to
the
r
pair
production
cross
section
data
yields
the
value
rn,
=
1776.96+~:~~!~:~~
MeV.
PACS
number(s):
14.60.Fg,
13.1O.+q
I.
INTRODUCTION
‘Present
address:
Kansas
State
University,
Manhattan,
Measurements
of
the
mass,
lifetime,
and
electronic
Kansas
66506-2601.
branching
fraction
of
the
7
lepton
have
been
improved
to
tpresent
address:
Stanford
Linear
Accelerator
Center,
Stan-
the
extent
that
they
can
be
used
to
provide
a
significant
ford,
California
94309.
test
of
lepton
universality.
The
most
precise
measure-
0556-2821/96/53~1~/20~15~/%06.00
53
20
0
1996
The
American
Physical
Society
53
MEASUREMENT
OF
THE
MASS
OF
THE
7
LEPTON
21
ment
to
date
of
the
mass
of
the
7
lepton
is
described
in
this
paper.
As
the
third
of
the
sequential
charged
leptons,
the
7
decays
similarly
to
the
/I
by
virtue
of
its
coupling
to
a
virtual
W
boson
and
a
neutrino;
however,
the
7
has
many
more
open
decay
channels
as
a
consequence
of
its
large
mass.
Within
the
standard
model,
leptonic
decay
rates
are
given
by
[lj
r(L
+
~~L4)
=
~F&L,
ml)
1
(1)
where
mr,
is
the
mass
of
the
parent
lepton
L,
ml
is
the
mass
of
the
daughter
lepton
1,
GL
is
the
Fermi
weak
coupling
constant,
and
the
correction
factor
F,,,
is
given
by
with
f(z)
=
1
-
83:
+
8z3
-
z4
-
12~~
Inz
,
(3)
and
L=
[l+q$($4)]
(5)
The
function
f(z)
results
from
the
integration
of
the
squared
matrix
element
for
7
decay
over
the
three-body
final
state
phase
space.
The
correction
factor
Fw
ac-
counts
for
the
nonlocal
structure
of
the
W
propaga-
tor,
where
rnw
is
the
mass
of
the
W
boson;
the
fac-
tor
Frad
arises
due
to
initial
and
final
state
radiative
corrections
[a(mT)-l
=
133.3
[l)].
It
should
be
noted
that
the
current
value
of
the
Fermi
weak
coupling
con-
stant,
GF
=
1.16639(2)
x
10m5
GeV-‘,
is
obtained
from
Eqs.
(l)-(5)
in
the
case
of
@
decay
by
inserting
the
val-
ues
rn,
=
105.658389f0.000034
MeV,
IQ
+
evp)-’
=
(2.19703
ZL
0.00004)
x
lo@
s,
mw
=
80.22
f
0.26
GeV
[2],
with
a(m,,-’
=
136
[l].
The
electronic
decays
of
the
7
and
muon
can
be
related
through
Eq.
(1)
where
the
substitutions
r(7
+
evi?)
=
B,-,,,,o/t,
and
r(p
--t
Eve)
=
l/t,
yield
(‘3)
where
tr
denotes
the
lepton
lifetime,
and
B,,,,,
the
branching
&&ion
for
the
decay
7
+
evD;
the
functions
F
car,
whose
contributions
are
listed
in
Table
I,
together
contribute
to
the
ratio
of
the
squared
coupling
constants
at
the
level
of
0.0004.
The
value
of
tbis
ratio
is
unity
under
the
assumption
of
lepton
universality.
Prior
to
the
TABLE
I.
The
corrections
to
the
p
and
7
decay
rates,
cal-
culated
using
01(m,,)-~
=
136
and
a(mr)-’
=
133.3
[l].
Correction
W&e
f
(d/4‘)
0.9998
h+b)
1.0000
Fdh‘)
0.9958
1.0000
1.0003
0.9957
&mh,m.)
0.99558
~,,.&;~.j
0.99597
present
experiment,
the
uncertainty
in
the
value
of
rn,
was~3-4
MeV.
Since
rn,
enters
Eq.
(6)
at
the
fifth
power,
lepton
universality
could
be
tested
only
at
the
1%
level
at
best.
The
goal
of
this
experiment
was
to
improve
the
measurement
precision
of
rn7
by
an
order
of
magnitude,
thus
making
possible
tests
of
universality
down
to
the
0.1%
level.
The
experimental
procedure
has
been
described
pre-
viously
[3].
A
data-driven
search
near
threshold
for
e+e-
+
7+~-
was
performed
in
which
candidate
events
were
identified
by
requiring
that
one
7
decay
via
7
+
evp,
and
the
other
via
7
+
pvv.
The
7
lepton
mass
value,
ob-
tained
from
a
fit
to
the
energy
dependence
of
the
resulting
T+T-
cross
section
data,
was
rn,
=
1776.9’$&0.2
MeV
r31.
In
this
paper
the
analysis
is
extended
to
include
the
ee,
pp,
eh,
ph,
and
hh
final
states,
where
h
can
be
either
a
charged
?r
or
K.
These
final
states
provide
additional
information
which
is
independent
of
the
ep
events
which
drove
the
energy
scan,
and
result
in
a
reduction
in
the
statistical
uncertainty
in,the
mass
value
by
a
factor
of
2.
II.
THE
BEIJING
COLLIDER
AND
BEIJING
SPECTROMETER
The
Beijing
Electron
Positron
Collider
(BEPC)
[4],
shown
schematically
in
Fig.
1,
operates
in
the
3
-
5
GeV
FIG.
1.
The
Beijing
Electron
Positron
Collider
(BEPC).
The
202
‘rn
injection
linac
leading
to
the
240
rn
circumfer-
ence
storage
ring
is
shown
at
the
left.
The
electrons
circulate
clockwise
and
the
positrons
counterclockwise.
The
BES
sits
on
the
side
of
the
ring
opposite
the
injection
linac.
22
.I.
Z.
BAI
et
al.
53
c.m.
energy
range.
Neti
T+T-
threshold,
the
peak
lu-
minosity
is
5
x
IO3
CIX-~S-~,
the
luminosity-weighted
uncertainty
in
the
mean
cm.
energy
is
-0.1~
MeV,
and
the
distribution
of
cm.
energy
about
its
nominal
value
is
described
by
a
Gaussian
with
standard
deviataion
-
1.4
MeV.
The
absolute
energy
scale
and
energy
spread
are
determined
by
linear
interpolation
between
the
re-
sults
of
repeated
scans
of
the
.7/$
and
$’
[+(2S)],
reso-
nances.
The
Beijing
Spectrometer
(BES),
shown
in
Fig.
2,
is
a
conventional
cylindrical
detector
described
in
detail
in
Ref.
15).
A
four-layer
central
drift
chamber
(CDC)
surrounding
the
beam
pipe
provides
trigger
information.
Charged
tracks
are
reconstructed
in
a
40-layer
main
drift
chamber
(MDC)
which
provides
solid
angle
coverage
of
85%
of
47r.
Momentum
resolution
of
2.1%-
(p
in
GeV/c)
and
energy
loss
(dE/dz)
resolutions
of
8.5%
for
electrons,
9.4%
for
muons,
and
11%
for
hadrons
are
obtained
in
the
present
experiment.
Scintillation
coun-
ters
provide
time-of-flight
(TOF)
measurements
over
76%
of
4n,
with
resolutions
of
390
ps
for
klectrons,
410
ps
for
muons,
and
450
ps
for
hadrons.
A
~12-radiation-
length,
lead-gas
barrel
shower
counter
(BSC),
operating
in
limited
streamer
mode,
measwes
the
energies
of
elec-
trons
and
photons
over
80%
of
the
total
solid
angle,
and
achieves
energy
resolution
q/E
=
0.22/o
(E
in
GeV)
for
electrons,
and
spatial
resolutions
04
=
4.5
mrad
and
o,
=
2
cm.
A
solenoidal
magnet
provides
a
0.4
T
mag-
tietic
field
in
the
central
tracking
region
of
the
detector.
Three
double-layer
muon
counters
instrument
the
mag-
net
flux
return,
and
serxto
identify
muons
of
momentum
greater
than
500
MeV/c.
They
cover
68%
of.the
total
solid
angle
with
longitudinal
(transverse)
spatial
resolu-
tion
5
cm
(3
cm).
End-cap
time-of-flight
and
shower
counters
extend
coverage
to
the
forward
and
backward
regions.
III.
r+r-
PRODUCTION
CROSS
SECTION
NEAR
THRESHOLD
The
likelihood
function
used
to
estimate
the
7
lepton
mass
value
incorporates
the
r+r-
production
cross
sec-
tion
near
threshold
[6].
Including
the
c.m.
energy
spread
A,
initial
state
radiation
corrections
[7]
F(z,W),
and
vacuum
polarization
corrections
[S]
II(W),
the
cross
sec-
tion
is
1-s
c7(W,m,)
=
-
AA
2:T
dW’exp
s
dzF(z,W’)ul(W’diG,m,)
,
(7)
where
01
is
given
by
W
is
the
cm.
energy,
and
p
=
dm.
The
Coulomb
interaction
and
final
state
radiation
corrections
9
“‘^
P2)
F&w,(P)
.
are
described
by
the
functions
F&3)
and
F,.(p)
[9].
The
-
II
-
TTIW\lZ
'
(8)
effect
of
these
corrections
on
the
lowest
order
QED
cross
-.
^
Muon
Counter
Barrel
Shower
Counter
Central
Drift
Chamber
-.
TTbA
ce-
Beam
Luminosity
Monitor
Endcap
Shower
Counter
.
Endcap
TOF
Counter
FIG.
2.
The
Beijing
Spec-
trometer
(BES)
in
y-z
projec-
tion,
53
MEASUREMENT
OF
THE
MASS
OF
THE
7
LEPTON
23
/-
_.
1.5
,/
,‘,....’
,,/
..
z
,‘.......
,‘,
2”
.g
1.0
,‘,...’
c%
,‘/
/
,,..’
g
b
0.5
II-
,p
I
:’
I/
I:’
I:’
I
o-
3.54
3.56
3.56
3.60
W
(GeV)
FIG.
3.
The
T+T-
production
cross
section
near
threshold
as
a
function
of
cm.
energy
W.
The
dotted
curve
shows
the
lowest
order
QED
cross
section,
the
dashed
curve
takes
into
account
the
Coulomb
interaction
and
final
state
radia-
tion,
and
the
solid
curve
shows
the
final
cross
section
used
in
this
analysis
after
initial
state
radiation,
vacuum
polariaa-
tion,
and
beam
energy
spread
have
been
taken
into
account.
Note
that
the
beam
energy
spread
and
the
initial
state
radia-
tion
correction
smear
out
the
sharp
step
at
threshold
caused
by
the
Coulomb
interaction.
The
curves
are
calculated
using
rn,
=
1776.9
MeV
[3].
IV.
c.m.
ENERGY
SCAN
A
total
of
5
pb-l
of
e+e-
collision
data
were
collected
near
T+T-
threshold
over
a
2
month
period
beginning
in
November
1991.
The
range
of
c.m.
energy
in
which
the
~+~-~cross
section
is
most
sensitive
to
the
7
mass
is
of
the
order
of
the
beam
energy
spread
around
@T-
threshold;,
it
was
important,
therefore,
to
devise
a
run-
ning
strategy
which
would
locate
the
T+T-
threshold
re-
gion
and
maximize
the
integrated
luminosity
there.
To
accomplish
this,
the
beam
energy
was
set
initially
to
ap
proximately
1784.1
MeV,
which
was
the
average
value
of
the
mass
of
the
7
lepton
at
that
time
[lo].
During
the
run,
the
data
were
searched
for
events
in
which
one
7
decayed
via
WD
and
the
other
via
pv.?.
Such
so-called
ep
events
provide
a
very
clean
signature
for
7
pair
pro-
duction;
indeed,
it
was
this
signature
which
led
to
the
discovery
of
the
7
lepton
[ll].
After
each
250
-
400
nb-l
of
integrated
luminosity,
a
new
estimate
of
the
mass
was
made
based
on
the
number
and
distribution
in
cm.
energy
of
the
ep
events
observed
in
all
of
the
data
accumulated
to
that
point
131;
in
this
way
a
new
prediction
of
the
most
sensitive
cm.
energy
at
which
to
run
was
obtained.
The
c.m.
energy
was
changed
to
the
new
value
only
if
the
difference
was
greater
than
0.4
MeV.
Following
tbis
strategy,
an
integrated
luminos-
ity
of
-
4.3
pb-’
was
accumulated
at
ten
cm.
energy
values
within
a
range
of
24
MeV
around
T+T-
threshold.
The
sequence
of
energies
is
shown
in
Fig.
4,
and
the
corresponding
data
[12]
are
summarized
in
Table
II.
The
ten-step
search
yielded
seven
ep
events.
The
11th
and
01
3
6
7
9
Scan
Point
FIG.
4.
(a)
The
variation
of
the
beam
energy
value
with
scan
point,
showing
the
convergence
to
r+r-
production
threshold.
The
J/Q
and
$’
resonance
scans
(Tables
VIII
and
IX,
and
Fig.
19)
were
performed
in
the
sequence
indicated.
(b)
The
integrated
luminosity
accumulated
at
each
scan
point.
The
luminosity
per
scan
point
is
approximately
constant
for
the
first
eight
points,
then
increases
significantly
for
the
last
two
points.
This
is
because
the
likelihood
fit
indicates
that
a
change
in
beam
energy
is
required
less
frequently
as
threshold
is
approached.
12th
points
in
Table
II
were
taken
well
above
thresh-
old,
where
the
cross
section
is
relatively
large
and
slowly
varying
with
c.m.
energy,
in
order
to
provide
an
im-
proved
estimate
of
the
absolute
detection
efficiency
(see
Sec.
VIII).
The
mass
value
obtained
from
a
fit
to
the
energy
dependence
of
the
~+r-
cross
section
was
rn,
=
1776.9+“,:;
i
0.2
MeV
131.
V.
EXTENDED
ANALYSIS
A
more
general
analysis
of
the
data,
which
uses
a
sim-
plified
scheme
of
event
selection
and
particle
identifica-
TABLE
II.
A
chronological
summary
of
the
~+r-
thresh-
old
scan
data;
W
denotes
the
corrected
c.m.
energy,
A
the
spread
in
cm.
energy
1121
[see
Eq.
(6)],
and
I:
the
integrated
luminosity.
Scan
Doint
w/2
A
.c
N
(Md+)
(MeV)
(nb-‘)
(el.c
events)
1
1784.19
1.34
245.8
2
2
1780.99
1.33
248.9
1
3
1772.09
1.36
232.8
0
4
1776.57
1.37
323.0
0
5
1778.49
1.44
322.5
2
6
1775.95
1.43
7
1776.75
!
1.47
296.9
0
384.0
0
8
1776.98
1.47
360.8
1
9
1776.45
1.44
794.1
0
10
1776.62
1.40
1109.1
1
11
1799.51
1.44
499.7
5
12
1789.55
1.43
250.0
2
600
M
400
-
200
(a)
-
0
40
-
0
0.2
0.4
0.6
0.8
1.0
24
J.
Z.
BA1
er
al.
53
tion,
is
presented
in
this
paper.
This
second
analysis
incorporates
the
ep
final
state
and
several
additional
two-
prong
T+Y
final
states,
and
results
in
a
reduction
of
the
statistical
error
in
the
mass
value
of
the
7
lepton
to
the
level
of
the
systematic
uncertainty.
To
select
candidate
two-prong
T+T-
decay
events
from
the
11.7~10~
triggers
representing
the
data
listed
in
Ta-
ble
II,
it
is
fist
required
that
exactly
two
charged
tracks
be
well
reconstructed,
without
regard
to
net
charge.
For
each
track,
the
point
of
closest
approach
to
the
beam
line
must
have
radius
<
1.5
cm
and
Itl
5
15
cm
where
I
is
measured
along
the
beam
line
from
the
nominal
beam
crossing
point;
in
addition
Izl
-
~21
must
be
less
than
5
cm.
Furthermore,
each
track
is
required
to
satisfy
1
cose
5
0.75,
where
0
is
the
polar
angle,
to
ensure
that
it
is
contained
within
the
barrel
region
of
the
detector.
These
criteria
reduce
the
data
sample
by
a
factor
of
N
20.
Next,
it
is
required
that
the
transverse
momentum
of
each
charged
track
be
above
the
100
MeV/c
minimum
needed
to
traverse
the
barrel
time-of-flight
counter
and
reach
the
outer
radius
of
the
barrel
shower
counter
in
the
0.4
T
axial
magnetic
field.
In
addition,
the
magnitude
of
the
momentum
must
be
less
than
the
maximum
expected
in
any
7
decay
at
the
given
cm.
energy
within
a
tolerance
of
three
standard
deviations
in
momentum
resolution.
These
constraints
on
momentum
reduce
the
data
sample
by
over
an
order
of
magnitude,
leaving
-
40
000
events.
Most
of
this
reduction
is
due
to
the
removal
of
Bhabha
scattering
and
p
pair
production
events.
FIG.
5.
The
confidence
level
distributions
for
samples
of
(a)~
pions
from
J/q
+
W?TT
events
and
beam-gas
electropro-
duction
events,
(b)
electrons
from
radiative
Bhabha
events,
(c)
muons
from
fi
pair
production,
and
(d)
muons
from
radia-
tive
p
pair
production.
behavior
is
observed
for
each
particle
type
in
each
indi-
vidual
detector
system,
confirming
that
this
is
indeed
the
case.
The
search
for
T+Y
production
events
is
restricted
to
final
states
which
do
not
contain
x0’s
or
7’s.
Conse-
quently,
a
further
requirem&t
is
that
there
be
no
isolated
photon
present
in
the
barrel
or
end-cap
shower
counters.
For
this
purpose,
an
isolated
photon
is
defined
by
requir-
ing
that
it
have
energy
greater
than
60
MeV;
it
must
make
an
angle
of
greater
than
12”
with
respect
to
the
original
direction
of
each
of
the
charged
tracks,
and
also
with
respect
to
the
direction
defined
for
each
charged
track
by
connecting
its
point
of
entry
to
the
barrel
shower
counter
to
the
origin
of
the
coordinate
system.
This
re-
duces
the
data
sample
to
N
33
000
events.
At
this
point
there
remains
a
significant
number
of
cosmic
ray
events.
The
bulk
of
these
are
removed
by
rejecting
any
event
for
which
either
track
has
a
measured
time-of-flight
value
less
than
2.5
ns
or
greater
than
8.5
ns.
The
particle
identification
procedure
is
applied
to
the
-
25000
remaining
events.
For
each
allowed
mass
hy-
pothesis
(e,
p,
z,
K)
for
each
track,
the
measured
mo-
mentum
is
used
to
predict
the
expected
values
of
dE/dx,
time
of
flight,
and
shower
counter
energy.
The
corre-
sponding
measured
quantities
and
resolutions
are
then
used
to
create
an
overall
x2
value,
which
is
converted
to
a
confidence
level
using
the
number
of
contributing
subdetectors
as
the
number
of
degrees
of
freedom.
The
confidence
level
distributions
found
for
samples
of
known
pious,
electrons,
and
muons
within
the
momentum
range
accessible
to
7
decay
are
shown
in
Fig.
5.
These
distri-
butions
are
all
consistent
with
being
flat,
as
would
be
expected
for
pure
samples
if
the
individual
device
reso-
lutions
were
reliably
assigned.
Similar
confidence
level
Events
are
rejected
if
either
track
has
confidence
lev-
els
of
less
than
5%
for
all
particle
hypotheses.,
Next,
the
p
hypothesis
is
assigned
to
a
track
if
its
momen-
tum
is
greater
than
500
MeV/c,
it
has
confidence
level
greater
than
5%
as
a
,u,
and
there
are
corroborating
muon
counter
hits.
Failing
the
p
requirement,
a
track
is
as-
signed
either
the
e
or
h
(for
hadron,
i.e.,
?r
or
K)
hy-
pothesis
debending
on
which
has
the
higher
confidence
level,
and
provided
that
confidence
level
is
at
least
5%.
If
the
confidence
level
for
the
x
(K)
assignment
is
over
5%,
it
is
further
required
that
the
track
momentum
be
consistent
with
two-body
7
+
?YY
(Kv)
decay
at
the
3
0
level.
For
the
calculation
of
the
relevant
momentumu
limits,
rn,
is
taken
1.0
MeV
below
the
previous
measure-
ment
[3]
to
reduce
the
dependence
of
the
7
+
?iv
(Kv)
selection
efficiency
on
the
cm.
energy;
in
extracting
the
7
mass
value
from
the
data,
the
small
residual
depen-
dence
is
taken
into
account
as
described
in
Sec.
VIII.
The
momentum
limits
for
pions
and
kaons
are
shown
as
a
function
of
cm.
energy
in
Fig.
6;
for
scan
point
3,
which
is
well
below
threshold
[3],
the
threshold
momen-
tum
limits
are
used.
It
should
be
emphasized
that
if,
for
a
given
track,
either
the
?r
or
the
K
hypothesis
has
confidenck
level’greater
than
5%
and
does
not
satisfy
the
momentum
criterion,
the
event
is
rejected,
even
if
the
electron
interpretation
yields
a
higher
confidence
level.
More
generally,
for
each
event
any
mass
hypothesis
combination
for
which
both
tracks
satisfy
the
5%
confi-
dence
level
criterion
is
required
to
satisfy
any
subsequent
seIec$on
criteria
applied
to
that
final
state.
If
one
such
hypothesis
fails
this
requirement,
the
event
is
rejected,