PHYSICAL
REVIEW
D
VOLUME
53,
NUMBER
3
1
FEBRUARY
1996
Search
for
exclusive
charmless
hadronic
B
decays
D.
M.
Asner,
M.
Athanas,
D.
W.
Bliss,
W.
S.
Braver,
G.
Masek,
and
H.
P.
Paar
University
of
Califwnia,
San
Diego,
La
Jolla,
California
92093
J.
Gronberg,
C.
M.
Korte,
R.
Kutschke,
S.
Menary,
R.
J.
Morrison,
S.
Nakanishi,
H.
N.
Nelson,
T.
K.
Nelson,
C.
Qiao,
J.
D.
Richman,
D.
Roberts,
A.
Ryd,
H.
Tajima,
and
M.
S.
Wither4
University
of
California,
Santa
Barbara,
California
93106
R.
Balest,
K.
Cho,
W.
T.
Ford,
M.
Lohner,
H.
Park,
P.
Rankin,
and
J.
G.
Smith
University
of
Colorado,
Boulder,
Colorado
80309.0390
J.
P.
Alexander,
C.
Bebek,
B.
E.
Berger,
K.
Berkelman,
K.
Bloom,
T.
E.
Browder;
D.
G.
Cassel,
H.
A.
Cho,
D.
M.
Coffman,
D.
S.
Crowcroft,
M.
Dickson,
P.
S.
Drell,
D.
J.
Dumas,
R.
Ehrlich,
R.
Elia,
P.
Gaidaev,
M.
Garcia-Sciveres,
B.
Gittelman,
S.
W.
Gray,
D.
L.
Hartill,
B.
K.
Heltsley,
S.
Henderson,
C.
D.
Jones,
S.
L.
Jones,
J.
Kandaswamy,
N.
Katayama,
P.
C.
Kim,
D.
L.
Kreinick,
T.
Lee,
Y.
Liu,
G.
S.
Ludwig,
J.
Masui,
J.
Mevissen,
N.
B.
Mistry,
C.
R.
Ng,
E.
Nordberg,
J.
R.
Patterson,
D.
Peterson,
D.
Riley,
and
A.
Soffer
Cornell
University,
Ithaca,
New
York’14853
P.
Avery,
A.
Freyberger,
K.
Lingel,
C.
Prescott,
J.
Rodriguez,
S.
Yang,
and
J.
Y&on
University
of
Florida,
Gainesuille,
Florida
32611
G.
Brandenburg,
D.
Cinabro,
T.
Liu,
M.
Saulnier,
R.
Wilson,
and
H.
Yamamoto
Hamwd
University,
Cambridge,
Massachusetts
02138
T.
Bergfeld,~B.
I.
Eisenstein,
J.
Ernst,
G.
E.
Gladding,
G.
D.
Gollin,
M.
Palmer,
M.
S&n,
and
J.
J.
Thaler
University
of
Illinois,
Champaign-
Urbana,
Illinois
61801
K.
W.
Edwards,
K.
W.
McLean,
and
M.
Ogg
Carleton
University,
Ottawa,
Ontario
KlS
586
and
the
Institute
of
Particle
Physics,
Canada
A.
Bellerive,
D.
I.
Britton,
E.
R.
F.
Hyatt,
R.
Jan&k,
D.
B.
MacFarlane,
P.
M.
Patel,
and
B.
Spaan
McGill
University,
Montr&xl,
Qudbec
H3A
22’8
and
the
Institute
of
Particle
Physics,
Canada
A.
J.
Sadoff
Ithaca
College,
Ithaca,
New
York
14950
R.
Ammar,
P.
Baringer,
A.
Bean,
D.
Besson,
D.
Coppage,
N.
Copty,
R.
Davis,
N.
Hancock,
S.
Kotov,
I.
Kravchenko,
and
N.
Kwak
University
of
Kansas,
Lawrence,
Kansas
66045
Y.
Kubota,
M.
Lattery,
M.
Mornay&,
J.
K.
Nelson,
S.
Patton,
R.
Poling,
V.
Savinov,
S.
Schrenk,
and
R.
Wang
University
of
Minnesota,
Minneapolis,
Minnesota
55455
M.
S.
Alam,
I.
J.
Kim,
2.
Ling,
A.
H.
Mahmood,
J.
J.
O’Neill,
H.
S
everini,
C.
R.
Sun,
and
F.
Wappler
State
University
of
New
York
at
Albany,
Albany,
New
York
12222
G.
Crawford,
R.
F&on,
D.
Fujino,
K.
K.
Can,
K.
Honscheid,
H.
Kagan,
R.
Kass,
J.
Lee,
M.
Sung,
C.
White,
A.
Wolf,
and
M.
M.
Zoeller
Ohio
State
University,
Columbus,
Ohio
43910
X.
Fu,
B.
Nemati,
W.
R.
Ross,
P.
Skubic,
and
M.
Wood
University
of
Oklahoma,
Norman,
Oklahoma
73019
M.
Bishai,
J.
Fast,
E.
Gerndt,
J.
W.
Hinson,
T.
Miao,
D.
H.
Miller,
M.
Modesitt,
E.
I.
Shibata,
I.
P.
J.
Shipsey,
and
P.
N.
Wang
Pwdzle
University,
West
Lafayette,
Indiana
47907
‘Permanent
address:
University
of
Hawaii
at
Manoa.
0556-2821/96/53(3)/10390/%06.00
12
1039
01996
The
American
Physical
Society
1040
D.
M.
ASNER
et
al.
L.
Gibbons,
S.
D.
Johnson,
Y.
Kwon,
S.
Roberts,
and
E.
H.
Thorndike
University
of
Rochester,
Rochester,
New
York
14627
53
T.
E.
Coan,
3.
Dominick,
V.
Fadeyev,
I.
Korolkov,
M.
Lambrecht,
S.
Sanghera,
V.
Shelkov,
T.
Skwarnicki,
R.
Stroynowski,
I.
Volobouev,
and
G.
Wei
Southern
Methodist
University,
Dallas,
Texas
75275
M.
Artuso,
M.
Gao,
M.
Goldberg,
D.
He,
N.
Horwitz,
S.
Kopp,
G.
C.
Moneti,
R.
Mountain,
F.
Muheim,
Y.
Mukhin,
S.
Playfer,
S.
Stone,
and
X.
Xing
Syracuse
University,
Syracuse,
New
York
13244
J.
Bartelt,
S.
E.
Csorna,
V.
Jain,
and
S.
Marka
Vanderbilt
University,
Nashville,
Tennessee
37235
D.
Gibaut,
K.
Kinoshita,
and
P.
Pomianowski
Virginia
Polytechnic
Institute
and
State
University,
Blacksburg,
Virginia
24061
B.
Barish,
M.
Chadha,
S.
Ghan,
D.
F.
Cowen,
G.
Eigen,
J.
S.
Miller,
C.
O’Grady,
J.
Urheim,
A.
J.
Weinstein,
and
F.
Wiirthwein
California
Institute
of
Technology,
Pasadena,
California
91125
(CLEO
Collaboration)
(Received
19
July
1995)
We
have
searched
for
two-body
charmless
hadronic
decays
of
B
mesons.
Final
states
include
?rr,
Klr,
and
KK
with
both
charged
and
neutral
kaons
and
pions:
wp,
Kp,
and
K’n;
and
K+,
K’$,
and
$4.
The
data
used
in
this
analysis
consist
of
2.6
x
10”
BB
pairs
produced
at
the
T(4S)
taken
with
the
CLEO
II
detector
at
the
Cornell
Electron
Storage
Ring
(CESR).
We
measure
the
branching
fraction
of
the
sum
of
B”
7‘
r+?r-
and
B0
+
K+x-
to
be
(1.8+0,:~‘~:23
&
0.2).x
lo-‘.
In
addition,
we
place
upper
limits
on
individual
branching
fractions
in
the
range
from
10e4
to
IO-‘.
PACS
number(s):
13.25.Hw,
14.40.Nd
I.
INTRODUCTION
The
decays
of
B
mesons
to
two
charmless
hadrons
can
be
described
by
a
b
-+
u
tree-level
spectator
diagram
[Fig.
l(a)],
or
a
b
+
sg
one-loop
“penguin
diagram”
[Fig.
l(b)]
and
to
a
lesser
extent,
by
the
color-suppressed
tree
[Fig.
l(c)]
or
Cabibbo-Kobayashi-Maskawa
(CKM)-
suppressed
b
-+
dg
penguin
diagrams.
Although
such
decays
can
also
include
contributions
from
b
--f
u
W-
exchange
[Fig.
l(d)],
annihilation
[Fig.
l(e)],
or
vertical
W
loop
[Fig.
l(f)]
processes,
these
contributions
are
ex-
pected
to
be
negligible
in
most
cases.
Decays
such
as
B”
+
1~+r-
and
B”
--f
,*p+
are
ex-
pected
to
be
dominated
by
the
b
--t
u
spectator
tran-
sition,
and
measurements
of
their
branching
fractions
could
be
used
to
extract
a
value
for
IV&l.
The
decay
mode
B”
+
?r+r-
can
be
used
to
measure
CP
violation
in
the
B
sector
at
both
asymmetric
B
factories
[l]
and
hadron
colliders
[Z].
Since
the
&x-
final
state
is
a
CP
eigenstate,
CP
violation
can
arise
from
interference
be-
tween
the
amplitude
for
direct
decay
and
the
amplitude
for
the
process
in
which
the
B”
first
mixes
into
a
B”
and
then
decays.
Measurement
of
the
time
evolution
of
the
rate
asymmetry
leads
to
a
measurement
of
sin2a,
where
a
is
one
of
the
angles
in
the
unitarity
triangle
[3].
If
the
B”
+
&r-
decay
has
a
non-negligible
contribution
from
the
b
+
dg
penguin
diagram,
interference
between
the
spectator
and
penguin
contributions
will
contaminate
the
measurement
of
CP
violation
via
mixing
[4],
an
ef-
fect
known
as
“penguin
pollution.”
If
this
is
the
case,
the
penguin
and
spectator
effects
can
be
disentangled
by
,i,s
B+
;>..“...<c
II
(e)
-
FIG.
1.
Feynman
diagrams
for
rare
hadronic
B
decays:
(a)
b
+
u
external
W
emission,
(b)
6
-i
s,d
loop
or
gluonic
pen-
guin,
(c)
b
+
u
internal
W
emission,
(d)
b
+
u
W
exchange,
(e)
annihilation,
and
(f)
vertical
W
loop.
12
SEARCH
‘FOR
EXCLUSIVE
CHARMLESS
HADRONIC
B
DECAYS
1041
also
measuring
the
isospin-related
decays
B”
+
&r”
and
B*
+
?T*;?T”
(51.
Alternatively,
SU(3)
symmetry
can
be
used
to
relate
B”
+
r+li-
and
B”
+
K+?r-
[6,7].
Pen-
guin
and
spectator,
effects
may
then
be
disentangled
[S]
once
the
ratio
of
the
two
branching
fractions
and
sin20
[3]
are
measured.
Decays
such
as
B”
+
K+?r-
and
B”
+
K*+n-
are
expected
to
be
dominated
by
the
b
+
sg
penguin
process,
with
a
small
contribution
from
a
Cabibbo-suppressed
b
-+
u
spectator
process.
Interference
between
the
pen-
guin
and
spectator
amplitudes
can
give
rise
to
direct
CP
violation,
which
will
manifest
itself
as
a
rate
asymme-
try
for
decays
of
B”
and
@’
mesons,
but
the
presence
of
hadronic
phases
complicates
the
extraction
of
the
CP
violation
parameters.
There
has
been
discussion
in
recent
literature
about
extracting
the
unitarity
angles
using
precise
time-
integrated
measurements
of
B
decay
rates.
Gronau,
Ros-
ner,
and
London
have
proposed
[s]
using
isospin
relations
and
flavor
SU(3)
symmetry
to
extract,
for
example,
the
unitarity
angle
7
by
measuring
the
rates
of
B+
decays
to
KO?r+,
K+nO,
and
zi#
and
their
charge
conjugates.
More
recent
publications
[9-121
have
questioned
whether
electraweak
penguin
contributions
(b
+
sy,
b
-+
sZ)
are
large
enough
to
invalidate
isospin
relationships
and
whether
SU(3)
symmetry-breaking
effects
can
be
taken
into
account.
If
it
is
possible
to
extract
unitarity
angles
from
rate
measurements
alone,
the
measurements
could
be
made
at
either
symmetric
or
asymmetric
B
factories
(CESR,
KEK,
SLAC),
but
will
require
excellent
paxti-
cle
identification
to
distinguish
between
the
KT
and
?(?r
modes.
Decays
such
as
B
+
Kc++
and
B+
+
K%+
cannot
oc-
cur
via
a
spectator
process
and
are
expected
to
be
dom-
inated
by
the
penguin
process.
Measurement
of
these
decays
will
give
direct
information
on
the
strength
of
the
penguin
amplitude.
Various
extensions
or
alternatives
to
the
standard
model
have
been
suggested.
Such
models
characteris-
tically
involve
hypothetical
higli
mass
particles,
such
as
fourth-generation
quarks,
leptoquarks,
squawks,
gluinos,
charged
Higgs
bosons,
charginos,
right-handed
W’s,
and
so
on.
They
have
negligible
effect
on
tree
diagram
dom-
inated
B
decays,
such
as
those
involving
b
+
cW-
and
b
-+
uW-,
but
can
contribute
significantly
to
loop
pro-
ceases
such
as
b
--t
sg
and
b
+
dg.
Since
nonstandard
models
can
have
enhanced
CP
vio-
lating
effects
relative
to
predictions
based
on
the
stan-
dard
Kobayashi-Maskawa
mechanism
[13,14],
such
ef-
fects
might
turn
out
to
be
the
key
to
the
solution
of
the
baryogenesis
problem,
that
is,
the
obvious
asymme-
try
in
the
abundance
of
baryons
over
antibaryons
in
the
universe.
Many
theorists
believe
that
the
KM
mecha-
nism
for
CP
violation
is
not
sufficient
to
generate
the
observed
asymmetry
or
even
to
maintain
an
initial
asym-
metry
through
cooldown
1151.
Loop
processes
in
B
decay
may
be
our
most
sensitive
probe
of
physics
beyond
the
standard
model.
This
paper
reports
results
on
the
decays
B
--t
?r?r,
B
+
Kn,
B
+
KK,
B
-i
“~3
B
+
Kp,
B
+
K*n,
B
-i
Kd,
B
--t
K*&
and
B
--t
$4
[16].
Recent
observations
of
the
sum
of
the
two-body
charmless
hadronic
decays
B”
--t
?r+?r-and
K+n-
[17]
and
of
the
electromagnetic
penguin
decay
B
+
K’y
[18],
indicate
that
we
have
reached
the
sensitivity
required
to
observe
such
decays.
The
size
of
the
data
set
and
efficiency
of
the
CLEO
detector
allow
us
to
place
upper
limits
on
the
branching
fractions
in
the
range
10-4
to
10-6.
II.
DATA
SAMPLE
AND
EVENT
SELECTION
The
data
set
used
in
this
analysis
was
collected
with
the
CLEO
II
detector
[19]
at
the
Cornell
Electron
Stor-
age
Ring
(CESR).
It
consists
of
2.42
fb-’
taken
at
the
T(4S)
(on-resonance)
and
1.17
fb-’
taken
at
a
,center
of
mass
energy
about
35
MeV
below
BB
threshold.
The
on-resonance
sample
contains
2.6
x
lo6
BB
pairs.
The
below-threshold
sample
is
used
for
continuum
back-
ground
estimates.
The
momenta
of
charged
particles
are
measured
in
a
tracking
system
consisting
of
a
B-layer
straw
tube
cham-
ber,
a
lo-layer
precision
drift
chamber,
and
a
51.layer
main
drift
chamber,
all
operating
inside
a
1.5
T
supercon-
ducting
solenoid.
The
main
drift
chamber
also
provides
a
measurement
of
the
specific
ionization
loss,
dE/dx,
used
for
particle
identification.
Photons
are
detected
us-
ing
7800
CsI
crystals,
which
are
also
inside
the
magnet.
Muons
are
identified
using
proportional
counters
placed
at
various
depths
in
the
steel
return
yoke
of
the
magnet.
The
excellent
efficiency
and
resolution
of
the
CLEO
II
detector
for
both
charged
particles
and
photons
are
cru-
cial
in
extracting
signals
and
suppressing
both
continuum
and
combinatoric
backgrounds.
Charged
tracks
are
required
to
pass
track
quality
cuts
based
on
the
average
hit
residual
and
the
impact
param-
eters
in
both
the
r-4
and
T-Z
planes.
We
require
that
charged
track
momenta
be
greater
than
175
MeV/c
to
reduce
low
momentum
combinatoric
background.
Pairs
of
tracks
with
vertices
displaced
from
the
pri-
mary
interaction
point
are
taken
as
Ki
candidates.
The
secondary
vertex
is
required
to
be
displaced
from
the
pri-
mary
interaction
point
by
at
least
1
mm
for
candidates
with
momenta
less
than
1
GeV/c
and
at
least
3
mm
for
candidates
with
momenta
greater
than
1
GeV/c.
We
make
a
momentum-dependent
cut
on
the
?r+x-
invari-
ant
mass.
Isolated
showers
with
energies
greater
than
30
Me%’
in
the
central
region
of
the
CsI
detector,
1
cos0l
<
0.71,
where
0
is
the
angle
with
respect
to
the
beam
axis,
and
greater
than
50
MeV
elsewhere,
are
defined
to
be
pho-
tons.
Pairs
of
photons
with
an
invariant
mass
within
two
standard
deviations
of
the
nominal
&’
mass
[20]
are
kinematically
fitted
with
the
mass
constrained
to
the
#
mass.
To
reduce
combinatoric
backgrounds
we
require
that
the
x0
momentum
be
greater
than
175
MeV/c,
that
the
lateral
shapes
of
the
showers
be
consistent
with
those
from
photons,
and
that
IcosB*l
<
0.97,
where
0’
is
the
angle
between
the
direction
of
flight
of
the
?y”
and
the
photons
in
the
#
rest
frame.
We
form
p
candidates
from
&?T-
or
x+x”
pairs
with
an
invariant
mass
within
150
MeV
of
the
nominal
p
1042
D.
M.
ASNER
et
al.
53
FIG.
2.
Distribution
of
S,
for
kinematically
identified
high
momentum
kaons
and
pions
from
D*+
--f
D’n”D’
--t
K-r+
decays.
The
solid
line
shows
S,,
for
pions
and
the
dashed
line
shows
s,
for
kaons.
masses.
K’
candidates
are
selected
from
K+a-,
K+#,
Kgn+
or
Kg?r’
pairs
[Zl]
with
an
invariant
mass
within
75
MeV
of
the
nominal
K’
masses.
We
form
4
candidates
from
K+K-
pairs
with
invariant
mass
within
6.5
MeV
of
the
nominal
4
mass.
Charged
particles
are
identified
as
kaons
or
pions
ac-
cording
to
dE/dx.
We
first
reject
electrons
based
on
dEfdx
and
the
ratio
of
the
track
momentum
to
the
as-
sociated
shower
energy
in
the
CsI
calorimeter.
We
re-
ject
muons
by
requiring
that
the
tracks
not
penetrate
the
steel
absorber
to
a
depth
of
five
nuclear
interaction
lengths.
We
define
S
for
a
particular
hadron
hypothesis
as
where
g
is
the
expected
resolution,
which
depends
pri-
marily
on
the
number
of
hits
used
in
the
dE/dx
mea-
surement.
We
measure
the
S
distribution
in
data
for
kaons
and
pions
using
D”
+
K-n”
decays
where
the
Do
flavor
is
tagged
using
D’+
+
D”vr+
decays.
In
par-
ticular,
we
are
interested
in
separating
pions
and
kaons
with
momenta
near
2.6
G+V/c.
The
S,
distribution
for
the
pion
hypothesis
is
shown
in
Fig.
2
for
pions
and
kaons
with
momenta
between
2.3
and
3.0
GeV/c.
At
these
mo-
menta,
pions
and
kaons
are
separated
by
1.8
f
0.1
in
S,.
III.
CANDIDATE
SELECTION
A.
Energy
constraint
Since
the
B’s
are
produced
via
e+e-
+
T(4S)
+
BB,
where
the
T(4S)
is
at
rest
in
the
lab
frame,
the
energy
of
either
of
the
two
B’s
is
given
by
the
beam
energy,
Eb.
We
define
AE
=
El
+
Ez
-
E,,
where
El
and
Es
are
the
energies
of
the
daughters
of
the
B
meson
candidate.
The
AE
distribution
for
signal
peaks
at
AE
=
0,
while
the
background
distribution
falls
linearly
in
AE
over
the
region
of
interest.
The
resolution
of
AE
is
mode
de-
pendent
and
in
some
cases
helicity
angle
dependent
(see
Sec.
III
C)
because
of
the
difference
in
energy
resolution
between
neutral
and
charged
pions.
For
modes
including
high
momentum
neutral
pions
in
the
final
state,
the
AE
resolution
tends
to
be
asymmetric
because
of
energy
loss
out
of
the
back
of
the
CsI
crystals.
The
AE
resolutions
for
the
modes
in
this
paper,
obtained
from
Monte
Carlo
simulation,
are
listed
in
Tables
I
and
II.
We
check
that
the
Monte
Carlo
simulation
accurately
reproduces
the
data
in
two
ways.
First,
the
rms
AE
resolution
for
B”
+
h+h-
(where
h*
indicates
a
?y*
or
K*)
is
given
by
~A,E~+&-
=
&&
where
oP
is
the
rms
momentum
resolution
at
p
=
2.6
GeV/c.
We
mea-
sure
the
momentum
+zsolution
at
p
=
5.3
GeV/c
using
muon
pairs
and
in
the
range
p
=
1.5-2.5
GeV/c
using
TABLE
I.
Resolutions
of
AE
and
the
signal
regions
for
AE
and
AMB
=
Mg
-
5280
MeV
for
the
event-counting
analyses.
Indicated
in
parentheses
are
the
K’
decay
modes
used.
Mode
Signal
region
CAE
IAEI
IAMBI
(MeV)
(Me’0
WV)
?i*“F
25-46
<
28
<
6.0
46
<
90
<
6.0
23
<
50
<
6.0
50
<
100
<
6.0
25-46
<
2u”
<
6.0
22
<
50
<
6.0
23
<
50
<
6.0
22-45
<
2c=
<
6.0
v
25-40
<
28
<
6.0
21
<
50
<
6.0
44
<
90
<
6.0
50
<
100
<
6.0
45
<
90
<
6.0
23
<
50
<
6.0
22-40
<
2LP
<
6.0
18
<
45
<
6.5
23
<
60
<
6.5
20
<
50
<
6.5
24
<
60
<
6.5
23
<
60
<
6.5
17
<
45
<
6.5
16
<
40
<
6.5
K+p-.
K”po
K+p”
K’p+
K’+?r-
(K+lr’)
(K%+)
K’Q110
(K+v-)
K’+a’
(K+n’)
(K%+)
K”T+
(K+T-)
(K%“)
“The
AE
resolution
and
cut
are
functions
ofthe
helicity
angle.
5s
SEARCH
FOR
EXCLUSIVE
CHARMLESS
HADRONIC
B
DECAYS
1043
TABLE
II.
Resolutions
of
AE,
the
fit
regions
in
AE
and
ML+;
and
the
number
of
events,
N,
in
the
fit
regions
for
the
likelihood
analyses.
Mode(s)
P+Z-/K+a-/K+K-
n+li”/K+d’
7PvTQ
KO?iO
K’?r+
Fit
region
OAE
(MeV)
(its)
(2)
N
*25
-185
<
AE
<
140
5.21
<
ME,
<
5.30
453
+43/-55
+300
5.20
<
MB
<
5.30
896
-w-85
f300
5.20
<
MB
<
5.30
104
f44/-53
*200
5.20
<
MB
<
5.30
44
f27
*200
5.20
<
MS
<
5.30
220
the
modes
B
+
dK.
B
+
Dn.
and
B
+
D”?r.
We
I
find
~a~,+,..
=
24.7G.3’;:;
MeV,
where
the
first
error
is
statistical
and
the
second
is
systematic.
This
result
is
in
good
agreement
with
the
Monte
Carlo
prediction.
We
also
test
our
Monte
Carlo
simulation
in
the
modes
B+
-i
DOS+
and
B”
--f
D-r+
(where
D”
-+
K+lr-,
6”
+
Kzn’,
and
D-
--f
Ks?r-)
using
an
analysis
simi-
lar
to
our
B
+
K*n
analysis.
Again,
AE
resolutions
for
data
and
Monte
Carlo
simulation
are
in
good
agreement.
The
energy
constraint
also
helps
to
distinguish
between
modes
of
the
~atlle
topology.
When
a
real
K
is
recon-
structed
as
a
?r,
AZ
mill
peak
below
zero
by
an
amount
dependent
on
the
particle’s
momentum.
For
example,
AE
for
B
+
K+n-,
calculated
assuming
B
+
?r+n-,
has
a
distribution
which
is
centered
at
-42
MeV,
giving
a
separation
of
1.70
between
B
+
K+?r-
and
B
+
?y+r-.
B.
Beam-constrained
mass
Since
the
energy
of
a
B
meson
is
equal
to
the
beam
energy,
we
use
E,,
instead
of
the
reconstructed
energy
of
the
B
candidate
to
calculate
the
beam-constrained
B
mass:
Mg
=
dw.
The
beam
constraint
improves
the
mass
resolution
by
about
an
order
of
magnitude,
since
1~~1
is
only
0.3
GeV/c
and
the
beam
energy
is
known
to
much
higher
precision
than
the
measured
energy
of
the
B
decay
products.
Mass
resolutions
range
from
2.5
to
3.0
MeV,
where
the
larger
resolution
corresponds
to
decay
modes
with
high
momentum
?y%.
Again,
we
verify
the
accuracy
of
our
Monte
Carlo
simulation
by
studying
full:,
reconstructed
B
decays.
The
MB
distribution
for
continuum
background
is
de-
scribed
by
the
empirical
shape
f(MB)
m
MBmexP
[-((I
-z”)]
,
(2)
where
I
is
defined
as
MB/E*
and
5
is
a
parameter
to
be
fit.
As
an
example,
Fig.
3
shows
the
fit
for
B
+
h+?r’
background
from
data
taken
below
BB
threshold.
C.
H&city
angle
5.200
5.225
5.250
5.275
5.300
MB
GW
The
decays
B
4
rpl
B
--t
Kp,
B
+
K*n,
and
FIG.
3.
Mg
distribution
from
below-threshold
background
B
+
Kqb
are
of
the
form
pseudoscalar
-+
vector
+
pseu-
events
(squares)
and
the
fit
to
the
parametrization
given
in
the
doscalar.
Therefore
we
expect
the
h&city
angle,
0x,
be-
text
(curve).
The
mass
for
the
below-threshold
data
is
shifted
tween
a
resonance
daughter
direction
and
the
B
direction
up
to
match
the
kinematic
endpoint
of
the
on-resonance
data.
in
the
resonance
rest
frame
to
have
a
cos’
0~
distribution.
For
these
decays
we
require
1
cos
0~1
>
0.5.
D.
D
veto
We
suppress
events
from
the
decay
B’
-+
Don+
(where
Do
+
K+?r-
or
D”
+
K$r”)
or
B”
+
D-n+
(where
D-
+
Ki?r-)
by
rejecting
any
candidate
that
can
be
interpreted
as
B
+
Dr,
with
a
K?r
invariant
mass
within
2~
of
the
nominal
D
mass.
We
expect
less
than
half
an
event
background
per
mode
from
B
+
hr
events
after
this
veto.
The
vetoed
D?r
signal
is
used
as
a
crosscheck
of
signal
distributions
and
efficiencies.
IV.
BACKGROUND
SUPPRESSION
USING
EVENT
SHAPE
The
dominant
background
in
all
modes
is
from
con-
tinuum
production,
e+e-
+
qq
(Q
=
u,d,s,c).
After
the
D
veto,
background
from
b
+
c
decays
is
negligible
300
,,1,,,11,,1,,,
,1111,
1044
D.
M.
ASNER
et
al.
53
in
all
modes
because
final
state
particles
in
such
decays
have
maximum
momenta
lower
than
what
is
required
for
the
decays
of
interest
here.
We
have
also
studied
back-
grounds
from
the
rtie
processes
b
+
sy
and
b
--t
uev
and
find
these
to
be
negligible
as
well.
Since
the
B
mesons
are
approximately
at
rest
in
the
lab,
the
angles
of
the
decay
products
of
the
two
B
decays
are
uncorrelated
and
the
event
looks
spherical.
On
the
other
hand,
hadrons
from
continuum
qq
production
tend
to
display
a
two-jet
structure.
This
event
shape
distinc-
tion
is
exploited
in
two
ways.
First,
we
calculate
the
afigle,
6’~,
between
the
thrust
axis
of
the
B
candidate
and
the
thrust
tiis
of
all
the
remaining
charged
and
neutral
particles
in
the
event.
The
distribution
of
cos&n
is
strongly
peaked
near
fl
for
qtj
events
and
is
nearly,flat
for
BB
events.
Figure
?
compares
the
cos@~
distributions
for
Monte
Carlo
sig-
nal
events
and
background
data.
We
require
1
cos
6~1
<
0.7
which
removes
more
than
90%
of
the
continuum
background
with
approximately
65%
efficiency
for
signal
events
[22].
Second,
we
characterize
the
event
shape
by
dividing
the
space
around
the
candidate
thrust
axis
into
nine
po-
lar
angle
intervals
of
10’
each,
the
first
three
of
which
are
illustrated
in
Fig.
5;
the
ith
interval
covers
angles
with
respect
to
the
candidate
thrust
axis
from
(i
-
1)
x
lo0
to
i
x
10’.
We
fold
the
event
such
that
the
forward
and
backward
intervals
are
combined.
We
then
define
the
mqmentum
flow,
2;
(i
=
1,9),
into
the
ith
interval
as
the
scalar
sum
of
the
momenta
of
all
charged
tracks
and
neu-
tral
showers
pointing
in
that
interval.
The
10’
binning
was
chosen
to
enhance
the
distinction
between
Bl?
and
continuum
background
events.
Angular
momentum
conservation
considerations
pro-
vide
additional
distinction
between
BB
and
continuum
qq
events.
In
qcj
events,
the
direction
of
the
candidate
FIG.
4.
The
cos&
distributions
for
background
data
(squares)
and
B”
+
m+K
Monte
Carla
signal
(histogram).
FIG.
5.
Illustration
of
the
first
three
of
the
nine
polar
angle
intervals.
thrust
axis,
Bna,
with
respect
to
the
beam
axis
in
the
lab
frame
tends
to
maintain
the
1
+
cos2
opp
distribution
of
the
primary
quarks.
The
direction
of
the
candidate
thrust
axis
for
BB
events
is
random.
The
candidate
B
direction,
0~,
with
respect
to
the
beam
axis
exhibits
a
sin’
0~
distribution
for
BB
events
and
is
random
for
qq
events.
A
Fisher
discriminant
[23]
is
formed
from
these
11
vari-
ables:
the
nine
momentum
flow
variables,
1
cosB,,&
and
1
cos
0~1.
The
discriminant
?=
is
the
linear
combination
&Yizi
(3)
i=1
of
the
input
variables,
Q,
that
maximizes
the
separation
between
signal
and
background.
The
Fisher
discriminant
FIG.
6.
The
7
distribution
for
B”
+
T%T-
Monte
Carlo
signal
(solid
histogram),
B
+
Dn
signal
data
(filled
squares),
the
fit
to
the
signal
data
(solid
curve),
the
background
Monte
Carlo
signal
(dotted
histogram),
background
data
(open
squares),
and
the
fit
to
the
background
data
(dotted
CUW).
1?
SEARCH
FOR
EXCLUSIVE
CHARMLESS
HADRONIC
B
DECAYS
parameters,
a;,
are
given
by
where
U&
and
U$
are
the
covariance
matrices
of
the
input
variables
for
signal
and
background
events,
and
&,
@:
are
the
mean.values
of
the
input
variables.
We
calculate
ai
using
Monte
Carlo
samples
of
signal
and
background
events
in
the
mode
B
+
?T+T-.
Figure
6
shows
the
F
distributio&
for
the
Gonte
Carlo
signal
in
the
mode
B”
+
?(+x-,
and
the
data
signal
in
the
modes
B
--t
&.
Figure
6
also
shows
the
F
distributions
for
Monte
Carlo
background
in
the
mode
B
4
h+?r-
and
below-threshold
background
data
for
modes
comprising
~three
charged
tracks
or
two
charged
tracks
and
a
x0.
The
F
distribution
for
the
signal
is
fit
by
a
Gaussian
distribution,
while
the
T
distribu-
tion
for
background
data
iS
best
fit
by
the
sum
of
two
Gaussians
with
the
same
mean
but
different
variances
and
normalizations.
The
separation
between
signal
and
background
means
is
approximately
1.3
times
the
signal
width.
We
find
that
the
Fisher
coefficients
calculated
for
B”
-i
r+?r-
work
equally
well
for
all
other
decay
modes
presented
in
this
paper.
Figure
7
shows
the
remarkable
consistency
of
the
means
and
widths
of
the
F
distribu-
tions
for
signal
and
background
Monte
Carlo
simulations
for
the
modes
in
this
study.
V.
ANALYSIS
For
the
decay
modes
B
+
mr,
B
+
K?r,
and
B
--t
KK,
we
extract
the
signal
yield
using
a
maximum
like-
lihood
fit.
For
the
other
decay
modes,
we
use
a
simple
counting
analysis.
Both
techniques
are
described
below.
A.
Maximum
likelihood
At
We
perform
unbinned
maximum
likelihood
fits
using
AE,
MB,
T,
and
dE/dx
(where
appropriate)
as
input
in-
formation
for
each
candidate
event
to
determine
the
sig-
nal
yields
for
B”
+
T+?T-,
K+n-,
K+K-,
?y”?yo,
KV,
and
B+
+
r+#,
K+T”,
K%+.
Five
different
fits
are
performed
as
listed
in
Table
II.
For
each
fit
a
likelihood
function
L
is
defined
as
kl
where
P(h,
.
.
..f.,,;
(AE,M~,T,~E/&c)~)
is
the
proba-
bility
density
function
evaluated
at
the
measured
point
(AE,
MB,
T,
dE/dx);
for
a
single
candidate
event,
i,
for
some
assumption
of
the
values
of
the
yield
fractions,
fi,
that
are
determined
by
the
fit.
N
is
the
total
number
of
events
that
are
fit.
The
fit
includes
all
the
candidate
FIG.
7.
The
means
of
the
Fisher
output
distributions
for
signal
(solid
circles)
and
background
(open
circles)
for
the
modes
in
this
study.
The
error
bars
indicate
the
width
of
the
distributions.
Since
the
backgrounds
in
the
r$
modes
are
small,
their
background
means
are
poorly
measured.
events
that
pass
the
selection
criteria
discussed
above
as
well
as
1
cos&-1
<
0.7,
and
0
<
2=
<
1.
The
AE
and
Mg
fit
ranges
are
given
in
Table
II.
For
the
case
of
B
+
h+h-,
the
probability
Pi
=
P(f,,
.
.
.
.
f,,,;
(AE,
MB,
7,dE/d~)~
)
is
then
defined
by
+u
-
f2
-
f&
-
fiLrPC,
(‘3)
PC
=
fE,“,p,“,
+
f&P&
+
(I-
f2.
-
fL)PKK,
where,
for
example,
Pz,,
(Pzj)
is
the
product
of
the
indi-
vidual
probability
density
functions
for
AE,
MB,
F‘,
and
dE/dx
for
?T+?T-
slgnal
(continuum
background).
The
signal
yield
in
B”
-+
~T+?T-,
for
example,
is
then
given
by
N,,
=
fzr
x
N.
The
central
values
of
the
individual
signal
yields
from
the
fits
are
given
in
Table
III.
None
of
the
individual