arXiv:hep-ex/0107025v1 11 Jul 2001
B
A
B
AR
-PUB-01/07
SLAC-PUB-8909
Measurement of branching fractions for exclusive
B
decays to charmonium final states
The
B
A
B
AR
Collaboration
B. Aubert, D. Boutigny, J.-M. Gaillard, A. Hicheur, Y. Karyo
takis, J. P. Lees, P. Robbe, and V. Tisserand
Laboratoire de Physique des Particules, F-74941 Annecy-le
-Vieux, France
A. Palano
Universit`a di Bari, Dipartimento di Fisica and INFN, I-701
26 Bari, Italy
G. P. Chen, J. C. Chen, N. D. Qi, G. Rong, P. Wang, and Y. S. Zhu
Institute of High Energy Physics, Beijing 100039, China
G. Eigen, P. L. Reinertsen, and B. Stugu
University of Bergen, Inst. of Physics, N-5007 Bergen, Norw
ay
B. Abbott, G. S. Abrams, A. W. Borgland, A. B. Breon, D. N. Brow
n, J. Button-Shafer, R. N. Cahn, A. R. Clark,
M. S. Gill, A. Gritsan, Y. Groysman, R. G. Jacobsen, R. W. Kade
l, J. Kadyk, L. T. Kerth, S. Kluth,
Yu. G. Kolomensky, J. F. Kral, C. LeClerc, M. E. Levi, T. Liu, G
. Lynch, A. Meyer, M. Momayezi, P. J. Oddone,
A. Perazzo, M. Pripstein, N. A. Roe, A. Romosan, M. T. Ronan, V
. G. Shelkov, A. V. Telnov, and W. A. Wenzel
Lawrence Berkeley National Laboratory and University of Ca
lifornia, Berkeley, CA 94720, USA
P. G. Bright-Thomas, T. J. Harrison, C. M. Hawkes, A. Kirk, D.
J. Knowles,
S. W. O’Neale, R. C. Penny, A. T. Watson, and N. K. Watson
University of Birmingham, Birmingham, B15 2TT, United King
dom
T. Deppermann, K. Goetzen, H. Koch, J. Krug, M. Kunze, B. Lewa
ndowski, K. Peters, H. Schmuecker, and M. Steinke
Ruhr Universit ̈at Bochum, Institut f ̈ur Experimentalphys
ik 1, D-44780 Bochum, Germany
J. C. Andress, N. R. Barlow, W. Bhimji, N. Chevalier, P. J. Cla
rk, W. N. Cottingham,
N. De Groot, N. Dyce, B. Foster, J. D. McFall, D. Wallom, and F.
F. Wilson
University of Bristol, Bristol BS8 1TL, United Kingdom
K. Abe, C. Hearty, T. S. Mattison, J. A. McKenna, and D. Thiess
en
University of British Columbia, Vancouver, BC, Canada V6T 1
Z1
S. Jolly, A. K. McKemey, and J. Tinslay
Brunel University, Uxbridge, Middlesex UB8 3PH, United Kin
gdom
V. E. Blinov, A. D. Bukin, D. A. Bukin, A. R. Buzykaev, V. B. Gol
ubev, V. N. Ivanchenko, A. A. Korol,
E. A. Kravchenko, A. P. Onuchin, A. A. Salnikov, S. I. Seredny
akov, Yu. I. Skovpen, V. I. Telnov, and A. N. Yushkov
Budker Institute of Nuclear Physics, Novosibirsk 630090, R
ussia
D. Best, A. J. Lankford, M. Mandelkern, S. McMahon, and D. P. S
toker
University of California at Irvine, Irvine, CA 92697, USA
A. Ahsan, K. Arisaka, C. Buchanan, and S. Chun
University of California at Los Angeles, Los Angeles, CA 900
24, USA
J. G. Branson, D. B. MacFarlane, S. Prell, Sh. Rahatlou, G. Ra
ven, and V. Sharma
University of California at San Diego, La Jolla, CA 92093, US
A
C. Campagnari, B. Dahmes, P. A. Hart, N. Kuznetsova, S. L. Lev
y,
O. Long, A. Lu, J. D. Richman, W. Verkerke, M. Witherell, and S
. Yellin
University of California at Santa Barbara, Santa Barbara, C
A 93106, USA
J. Beringer, D. E. Dorfan, A. M. Eisner, A. Frey, A. A. Grillo,
M. Grothe, C. A. Heusch,
R. P. Johnson, W. Kroeger, W. S. Lockman, T. Pulliam, H. Sadro
zinski, T. Schalk, R. E. Schmitz,
B. A. Schumm, A. Seiden, M. Turri, W. Walkowiak, D. C. William
s, and M. G. Wilson
University of California at Santa Cruz, Institute for Parti
cle Physics, Santa Cruz, CA 95064, USA
2
E. Chen, G. P. Dubois-Felsmann, A. Dvoretskii, D. G. Hitlin,
S. Metzler,
J. Oyang, F. C. Porter, A. Ryd, A. Samuel, M. Weaver, S. Yang, a
nd R. Y. Zhu
California Institute of Technology, Pasadena, CA 91125, US
A
S. Devmal, T. L. Geld, S. Jayatilleke, G. Mancinelli, B. T. Me
adows, and M. D. Sokoloff
University of Cincinnati, Cincinnati, OH 45221, USA
T. Barillari, P. Bloom, M. O. Dima, S. Fahey, W. T. Ford, D. R. J
ohnson, U. Nauenberg,
A. Olivas, H. Park, P. Rankin, J. Roy, S. Sen, J. G. Smith, W. C.
van Hoek, and D. L. Wagner
University of Colorado, Boulder, CO 80309, USA
J. Blouw, J. L. Harton, M. Krishnamurthy, A. Soffer, W. H. Toki
, R. J. Wilson, and J. Zhang
Colorado State University, Fort Collins, CO 80523, USA
T. Brandt, J. Brose, T. Colberg, G. Dahlinger, M. Dickopp, R.
S. Dubitzky, E. Maly,
R. M ̈uller-Pfefferkorn, S. Otto, K. R. Schubert, R. Schwierz
, B. Spaan, and L. Wilden
Technische Universit ̈at Dresden, Institut f ̈ur Kern- und T
eilchenphysik, D-01062, Dresden, Germany
L. Behr, D. Bernard, G. R. Bonneaud, F. Brochard, J. Cohen-Ta
nugi, S. Ferrag,
E. Roussot, S. T’Jampens, C. Thiebaux, G. Vasileiadis, and M
. Verderi
Ecole Polytechnique, F-91128 Palaiseau, France
A. Anjomshoaa, R. Bernet, A. Khan, F. Muheim, S. Playfer, and
J. E. Swain
University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom
M. Falbo
Elon College, Elon College, NC 27244-2010, USA
C. Borean, C. Bozzi, S. Dittongo, M. Folegani, and L. Piemont
ese
Universit`a di Ferrara, Dipartimento di Fisica and INFN, I-
44100 Ferrara, Italy I-44100 Ferrara, Italy
E. Treadwell
Florida A&M University, Tallahassee, FL 32307, USA
F. Anulli,
∗
R. Baldini-Ferroli, A. Calcaterra, R. de Sangro, D. Falciai
,
G. Finocchiaro, P. Patteri, I. .M. Peruzzi,
∗
M. Piccolo, Y. Xie, and A. Zallo
Laboratori Nazionali di Frascati dell’INFN, I-00044 Frasc
ati, Italy
S. Bagnasco, A. Buzzo, R. Contri, G. Crosetti, P. Fabbricato
re, S. Farinon, M. Lo
Vetere, M. Macri, M. R. Monge, R. Musenich, M. Pallavicini, R
. Parodi, S. Passaggio,
F. C. Pastore, C. Patrignani, M. G. Pia, C. Priano, E. Robutti
, and A. Santroni
Universit`a di Genova, Dipartimento di Fisica and INFN, I-1
6146 Genova, Italy
M. Morii
Harvard University, Cambridge, MA 02138, USA
R. Bartoldus, T. Dignan, R. Hamilton, and U. Mallik
University of Iowa, Iowa City, IA 52242, USA
J. Cochran, H. B. Crawley, P.-A. Fischer, J. Lamsa, W. T. Meye
r, and E. I. Rosenberg
Iowa State University, Ames, IA 50011-3160, USA
M. Benkebil, G. Grosdidier, C. Hast, A. H ̈ocker, H. M. Lacker
, V. LePeltier, A. M. Lutz,
S. Plaszczynski, M. H. Schune, S. Trincaz-Duvoid, A. Valass
i, and G. Wormser
Laboratoire de l’Acc ́el ́erateur Lin ́eaire, F-91898 Orsay
, France
R. M. Bionta, V. Brigljevi ́c, D. J. Lange, M. Mugge, X. Shi,
K. van Bibber, T. J. Wenaus, D. M. Wright, and C. R. Wuest
Lawrence Livermore National Laboratory, Livermore, CA 945
50, USA
M. Carroll, J. R. Fry, E. Gabathuler, R. Gamet, M. George, M. K
ay, D. J. Payne, R. J. Sloane, and C. Touramanis
University of Liverpool, Liverpool L69 3BX, United Kingdom
M. L. Aspinwall, D. A. Bowerman, P. D. Dauncey, U. Egede, I. Es
chrich,
N. J. W. Gunawardane, J. A. Nash, P. Sanders, and D. Smith
University of London, Imperial College, London, SW7 2BW, Un
ited Kingdom
D. E. Azzopardi, J. J. Back, P. Dixon, P. F. Harrison, R. J. L. P
otter,
H. W. Shorthouse, P. Strother, P. B. Vidal, and M. I. Williams
3
Queen Mary, University of London, E1 4NS, United Kingdom
G. Cowan, S. George, M. G. Green, A. Kurup, C. E. Marker, P. McG
rath,
T. R. McMahon, S. Ricciardi, F. Salvatore, I. Scott, and G. Va
itsas
University of London, Royal Holloway and Bedford New Colleg
e, Egham, Surrey TW20 0EX, United Kingdom
D. Brown and C. L. Davis
University of Louisville, Louisville, KY 40292, USA
J. Allison, R. J. Barlow, J. T. Boyd, A. C. Forti, J. Fullwood,
F. Jackson,
G. D. Lafferty, N. Savvas, E. T. Simopoulos, and J. H. Weathera
ll
University of Manchester, Manchester M13 9PL, United Kingd
om
A. Farbin, A. Jawahery, V. Lillard, J. Olsen, D. A. Roberts, a
nd J. R. Schieck
University of Maryland, College Park, MD 20742, USA
G. Blaylock, C. Dallapiccola, K. T. Flood, S. S. Hertzbach, R
. Kofler, T. B. Moore, H. Staengle, and S. Willocq
University of Massachusetts, Amherst, MA 01003, USA
B. Brau, R. Cowan, G. Sciolla, F. Taylor, and R. K. Yamamoto
Massachusetts Institute of Technology, Lab for Nuclear Sci
ence, Cambridge, MA 02139, USA
M. Milek, P. M. Patel, and J. Trischuk
McGill University, Montr ́eal, Canada QC H3A 2T8
F. Lanni and F. Palombo
Universit`a di Milano, Dipartimento di Fisica and INFN, I-2
0133 Milano, Italy
J. M. Bauer, M. Booke, L. Cremaldi, V. Eschenburg, R. Kroeger
, J. Reidy, D. A. Sanders, and D. J. Summers
University of Mississippi, University, MS 38677, USA
J. P. Martin, J. Y. Nief, R. Seitz, P. Taras, A. Woch, and V. Zac
ek
Universit ́e de Montr ́eal, Lab. Rene J. A. Levesque, Montr ́e
al, Canada QC H3C 3J7
H. Nicholson and C. S. Sutton
Mount Holyoke College, South Hadley, MA 01075, USA
C. Cartaro, N. Cavallo,
†
G. De Nardo, F. Fabozzi, C. Gatto, L. Lista, P. Paolucci, D. Pi
ccolo, and C. Sciacca
Universit`a di Napoli Federico II, Dipartimento di Scienze
Fisiche and INFN, I-80126, Napoli, Italy
J. M. LoSecco
University of Notre Dame, Notre Dame, IN 46556, USA
J. R. G. Alsmiller, T. A. Gabriel, and T. Handler
Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
J. Brau, R. Frey, M. Iwasaki, N. B. Sinev, and D. Strom
University of Oregon, Eugene, OR 97403, USA
F. Colecchia, F. Dal Corso, A. Dorigo, F. Galeazzi, M. Margon
i, G. Michelon,
M. Morandin, M. Posocco, M. Rotondo, F. Simonetto, R. Stroil
i, E. Torassa, and C. Voci
Universit`a di Padova, Dipartimento di Fisica and INFN, I-3
5131 Padova, Italy
M. Benayoun, H. Briand, J. Chauveau, P. David, C. De la Vaissi
`ere, L. Del Buono,
O. Hamon, F. Le Diberder, Ph. Leruste, J. Lory, L. Roos, J. Sta
rk, and S. Versill ́e
Universit ́es Paris VI et VII, LPNHE, F-75252 Paris, France
P. F. Manfredi, V. Re, and V. Speziali
Universit`a di Pavia, Dipartimento di Elettronica and INFN
, I-27100 Pavia, Italy
E. D. Frank, L. Gladney, Q. H. Guo, and J. H. Panetta
University of Pennsylvania, Philadelphia, PA 19104, USA
C. Angelini, G. Batignani, S. Bettarini, M. Bondioli, M. Car
pinelli, F. Forti,
M. A. Giorgi, A. Lusiani, F. Martinez-Vidal, M. Morganti, N.
Neri, E. Paoloni,
M. Rama, G. Rizzo, F. Sandrelli, G. Simi, G. Triggiani, and J.
Walsh
Universit`a di Pisa, Scuola Normale Superiore and INFN, I-5
6010 Pisa, Italy
M. Haire, D. Judd, K. Paick, L. Turnbull, and D. E. Wagoner
Prairie View A&M University, Prairie View, TX 77446, USA
4
J. Albert, C. Bula, P. Elmer, C. Lu, K. T. McDonald, V. Miftako
v,
S. F. Schaffner, A. J. S. Smith, A. Tumanov, and E. W. Varnes
Princeton University, Princeton, NJ 08544, USA
G. Cavoto, D. del Re, F. Ferrarotto, F. Ferroni, K. Fratini, E
. Lamanna, E. Leonardi,
M. A. Mazzoni, S. Morganti, G. Piredda, F. Safai Tehrani, M. S
erra, and C. Voena
Universit`a di Roma La Sapienza, Dipartimento di Fisica and
INFN, I-00185 Roma, Italy
R. Faccini
University of California at San Diego, La Jolla, CA 92093, US
A and
Universit`a di Roma La Sapienza, Dipartimento di Fisica and
INFN, I-00185 Roma, Italy
S. Christ and R. Waldi
Universit ̈at Rostock, D-18051 Rostock, Germany
P. F. Jacques, M. Kalelkar, and R. J. Plano
Rutgers University, New Brunswick, NJ 08903, USA
T. Adye, B. Franek, N. I. Geddes, G. P. Gopal, and S. M. Xella
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX
11 0QX, United Kingdom
R. Aleksan, G. De Domenico, S. Emery, A. Gaidot, S. F. Ganzhur
, P.-F. Giraud, G. Hamel de Monchenault,
W. Kozanecki, M. Langer, G. W. London, B. Mayer, B. Serfass, G
. Vasseur, C. Yeche, and M. Zito
DAPNIA, Commissariat `a l’Energie Atomique/Saclay, F-911
91 Gif-sur-Yvette, France
N. Copty, M. V. Purohit, H. Singh, and F. X. Yumiceva
University of South Carolina, Columbia, SC 29208, USA
I. Adam, P. L. Anthony, D. Aston, K. Baird, E. Bloom, A. M. Boya
rski, F. Bulos, G. Calderini, R. Claus,
M. R. Convery, D. P. Coupal, D. H. Coward, J. Dorfan, M. Doser,
W. Dunwoodie, R. C. Field, T. Glanzman,
G. L. Godfrey, S. J. Gowdy, P. Grosso, T. Himel, M. E. Huffer, W.
R. Innes, C. P. Jessop, M. H. Kelsey,
P. Kim, M. L. Kocian, U. Langenegger, D. W. G. S. Leith, S. Luit
z, V. Luth, H. L. Lynch, H. Marsiske,
S. Menke, R. Messner, K. C. Moffeit, R. Mount, D. R. Muller, C. P
. O’Grady, M. Perl, S. Petrak,
H. Quinn, B. N. Ratcliff, S. H. Robertson, L. S. Rochester, A. R
oodman, T. Schietinger, R. H. Schindler,
J. Schwiening, V. V. Serbo, A. Snyder, A. Soha, S. M. Spanier,
J. Stelzer, D. Su, M. K. Sullivan, H. A. Tanaka,
J. Va’vra, S. R. Wagner, A. J. R. Weinstein, W. J. Wisniewski,
D. H. Wright, and C. C. Young
Stanford Linear Accelerator Center, Stanford, CA 94309, US
A
P. R. Burchat, C. H. Cheng, D. Kirkby, T. I. Meyer, and C. Roat
Stanford University, Stanford, CA 94305-4060, USA
R. Henderson
TRIUMF, Vancouver, BC, Canada V6T 2A3
W. Bugg, H. Cohn, and A. W. Weidemann
University of Tennessee, Knoxville, TN 37996, USA
J. M. Izen, I. Kitayama, X. C. Lou, and M. Turcotte
University of Texas at Dallas, Richardson, TX 75083, USA
F. Bianchi, M. Bona, B. Di Girolamo, D. Gamba, A. Smol, and D. Z
anin
Universit`a di Torino, Dipartimento di Fisica Sperimental
e and INFN, I-10125 Torino, Italy
L. Lanceri, A. Pompili, and G. Vuagnin
Universit`a di Trieste, Dipartimento di Fisica and INFN, I-
34127 Trieste, Italy
R. S. Panvini
Vanderbilt University, Nashville, TN 37235, USA
C. M. Brown, A. De Silva, R. Kowalewski, and J. M. Roney
University of Victoria, Victoria, BC, Canada V8W 3P6
H. R. Band, E. Charles, S. Dasu, F. Di Lodovico, A. M. Eichenba
um, H. Hu, J. R. Johnson, R. Liu, J. Nielsen,
Y. Pan, R. Prepost, I. J. Scott, S. J. Sekula, J. H. von Wimmers
perg-Toeller, S. L. Wu, Z. Yu, and H. Zobernig
University of Wisconsin, Madison, WI 53706, USA
T. M. B. Kordich and H. Neal
Yale University, New Haven, CT 06511, USA
5
(Dated: February 7, 2008)
We report branching fraction measurements for exclusive de
cays of charged and neutral
B
mesons into two-body final states containing a charmonium me
son. We use a sample of
22
.
72
±
0
.
36 million
B
B
events collected between October 1999 and October 2000 with
the
B
A
B
AR
detector at the PEP-II storage rings at the Stanford Linear A
ccelerator Center. The
charmonium mesons considered here are
J/ψ
,
ψ
(2
S
), and
χ
c
1
, and the light meson in the decay
is either a
K
,
K
∗
, or
π
0
.
PACS numbers: 11.30.Er, 13.25.Hw
I. INTRODUCTION
Decays of
B
mesons to two-body final states containing
a charmonium resonance (
J/ψ
,
ψ
(2
S
),
χ
c
1
) constitute
a very sensitive laboratory for the study of electroweak
transitions, as well as the dynamics of strong interactions
in heavy meson systems. In particular, neutral
B
decays
to these final states are expected to exhibit a significant
CP
asymmetry, the magnitude of which is cleanly related
to standard model parameters [1].
The tree level and leading penguin diagrams for the
decay modes we consider are shown in Fig. 1. Due to
the contributions of non-perturbative QCD interactions
in the final state, assumptions must be made in estimat-
ing the expected branching fractions of these modes, and
therefore these estimates have some degree of model de-
pendence. A number of such estimates have appeared in
the literature [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. The one
model-independent element common to all of these pre-
dictions is the requirement from isospin symmetry that
the ratio of the charged to neutral partial widths should
be unity, and that this should hold separately for each
light meson accompanying the charmonium meson in the
final state.
Here we report the measurement of branching fractions
of
B
mesons to a charmonium resonance accompanied by
a kaon or
π
0
meson. The channels measured are listed
in Table I. Here and throughout this paper for each final
state mentioned its charged conjugate is also implied. We
reconstruct
J/ψ
decays to lepton pairs
ℓ
+
ℓ
−
, where
ℓ
is
either an electron or muon.
Our large data sample permits a measurement of these
branching fractions with a precision superior to previous
experiments. The simultaneous measurement of a num-
ber of final states allows us to determine ratios such as
vector to pseudoscalar kaon and heavy to light charmo-
nium states production. Many systematic errors cancel
when these ratios are extracted from a single data set us-
ing very similar event selection criteria, further increas
ing
the usefulness of our results for the validation or devel-
opment of phenomenological models.
Another highly relevant input for the understanding of
strong interactions in
B
decays is the measurement of po-
∗
Also with Universit`a di Perugia, Perugia, Italy.
†
Also with Universit`a della Basilicata, Potenza, Italy.
(a)
b
c
W
-
c
s,d
d,
u
B
0
, B
-
J/
ψ
,
ψ
(2S),
χ
c1
K,
K
*
,
π
0
(b)
b
c
W
-
c
s,d
d,
u
B
0
, B
-
J/
ψ
,
ψ
(2S),
χ
c1
K,
K
*
,
π
0
u,c,t
g
FIG. 1: Leading Feynman diagrams for the decays we con-
sider.
larization in vector-vector final states, which is reported
in another publication [13]. Finally, the branching frac-
tion of
B
→
J/ψπ
+
is measured using a specific analysis
method, reported in [14] .
II. THE
B
A
B
AR
DETECTOR
The
B
A
B
AR
detector is located at the PEP-II
e
+
e
−
storage rings operating at the Stanford Linear Acceler-
ator Center. At PEP-II, 9.0 GeV electrons collide with
3.1 GeV positrons to produce a center-of-mass energy of
10.58 GeV, the mass of the
Υ
(4
S
) resonance.
The
B
A
B
AR
detector is described elsewhere [15]; here
we give only a brief overview. Surrounding the interac-
tion point is a 5-layer double-sided silicon vertex tracker
(SVT) which gives precision spatial information for all
charged particles, and also measures their energy loss
(d
E/
d
x
). The SVT is the primary detection device for
low momentum charged particles. Outside the SVT, a
40-layer drift chamber (DCH) provides measurements of
the transverse momenta
p
T
of charged particles with re-
spect to the beam direction. The resolution of the
p
T
measurement for tracks with momenta above 1 GeV
/c
is
parameterized as:
σ
(
p
T
)
p
T
= 0
.
13
p
T
( GeV
/c
)% + 0
.
45%
.
(1)
6
TABLE I: Branching fractions and decay modes considered in
this paper. We always reconstruct the
J/ψ
in the
ℓ
+
ℓ
−
decay
mode.
Branching fraction
Secondary decay
measured
modes used
B
0
→
J/ψK
0
K
0
→
K
0
S
;
K
0
S
→
π
+
π
−
or
π
0
π
0
K
0
→
K
0
L
B
+
→
J/ψK
+
–
B
0
→
J/ψK
∗
0
K
∗
0
→
K
+
π
−
or
K
0
S
π
0
;
K
0
S
→
π
+
π
−
B
+
→
J/ψK
∗
+
K
∗
+
→
K
+
π
0
or
K
0
S
π
+
;
K
0
S
→
π
+
π
−
B
0
→
J/ψπ
0
–
B
0
→
ψ
(2
S
)
K
0
S
ψ
(2
S
)
→
ℓ
+
ℓ
−
or
J/ψ π
+
π
−
;
K
0
S
→
π
+
π
−
B
+
→
ψ
(2
S
)
K
+
ψ
(2
S
)
→
ℓ
+
ℓ
−
or
ψ
(2
S
)
→
J/ψ π
+
π
−
B
0
→
χ
c
1
K
0
S
χ
c
1
→
J/ψ γ
;
K
0
S
→
π
+
π
−
B
+
→
χ
c
1
K
+
χ
c
1
→
J/ψ γ
B
0
→
χ
c
1
K
∗
0
χ
c
1
→
J/ψ γ
;
K
∗
0
→
K
+
π
−
The drift chamber also measures d
E/
d
x
with a precision
of 7.5%. Beyond the outer radius of the DCH is a detector
of internally reflected Cherenkov radiation (DIRC) which
is used primarily for charged hadron identification. The
detector consists of quartz bars in which Cherenkov light
is produced as relativistic charged particles traverse the
material. The light is internally reflected along the length
of the bar into a water-filled stand-off box mounted on
the rear of the detector. The Cherenkov rings expand
in the stand-off box and are measured with an array
of photomultiplier tubes mounted on its outer surface.
A CsI(Tl) crystal electromagnetic calorimeter (EMC) is
used to detect photons and neutral hadrons, as well as
to identify electrons. The resolution of the calorimeter is
parameterized as:
σ
(
E
)
E
=
2
.
3%
(
E
( GeV))
1
4
⊕
1
.
9%
.
(2)
The EMC is surrounded by a superconducting solenoid
that produces a 1.5-T magnetic field. The instrumented
flux return (IFR) consists of multiple layers of resistive
plate chambers (RPC) interleaved with the flux return
iron. In addition to the planar RPC layers in the flux
return, there is an additional cylindrical layer just outsi
de
of the EMC. The IFR is used in the identification of
muons and neutral hadrons.
Data acquisition is triggered with a two-level system.
The first level (Level 1) monitors trigger information from
the DCH and EMC, and generates a trigger upon de-
tection of track or cluster candidates. The second level
(Level 3) retains events in which the track candidates
point back to the beam interaction region (L3 DCH trig-
ger), or EMC clusters candidates remain after the sup-
pression of hits which have less energy than a minimum
ionizing particle or are uncorrelated in time with the rest
of the event (L3 EMC trigger). Over 99.9% of
B
B
events
pass either the L3 DCH or L3 EMC trigger. A fraction of
all events that pass the Level 1 trigger are passed through
Level 3 to allow monitoring of the Level 3 trigger perfor-
mance.
III. DATA SAMPLE
The data used in these analyses were collected between
October 1999 and October 2000 and correspond to an
integrated luminosity of 20.7 fb
−
1
taken on the
Υ
(4
S
)
and 2.6 fb
−
1
taken off-resonance at an energy 0.04 GeV
lower than the peak, which is below the threshold for
B
B
production. The data set contains 22
.
72
±
0
.
36 million
B
B
events.
IV. COORDINATE SYSTEM AND REFERENCE
FRAMES
We use a right-handed coordinate system with the
z
axis along the electron beam direction and
y
axis up-
wards, with origin at the nominal beam interaction point.
Unless otherwise stated, kinematic quantities are calcu-
lated in the rest frame of the detector. The other refer-
ence frame we commonly use is the center of mass of the
colliding electrons and positrons, which we will call the
center-of-mass frame.
V. PARTICLE RECONSTRUCTION
The reconstruction of exclusive
B
decays begins with
identifying candidates for the decay products. Charged
particles are reconstructed as tracks in the SVT and/or
DCH. Leptons and kaons are identified with information
from the DCH, the EMC (for electrons) the IFR (for
muons), and the DIRC (for kaons). Photons are identi-
fied based on their energy deposition in the EMC, and
K
0
L
are identified from either energy deposition in the
EMC or a shower in the IFR.
A. Track Selection
In general, tracks used in this analysis are required to
include at least 12 DCH hits to ensure that their mo-
menta and d
E/
d
x
are well measured. In addition, tracks
are required to have
p
T
>
100 MeV
/c
, and to point back
to the nominal interaction point within 1.5 cm in
xy
and
3 cm in
z
. Roughly 95% of the solid angle about the
interaction point in the center-of-mass frame is covered
by 12 or more DCH layers.
We make exceptions to this requirement for two
types of particles: pions from
K
0
S
, which do not origi-
nate at the nominal interaction point, and pions from
ψ
(2
S
)
→
J/ψ π
+
π
−
, which frequently do not have suf-
ficient transverse momenta to traverse 12 layers of the
DCH. Any track found in the DCH or SVT is used in
reconstructing these particles.
7
TABLE II: Summary of electron identification criteria. Vari
ables used are: d
E/
d
x
, the energy loss measured in the DCH;
E/p
, the ratio of the EMC cluster energy to the momentum measured
in the tracking spectrometer;
N
crys
, the number of EMC
crystals forming the cluster; LAT, the lateral energy distr
ibution [16] of the EMC cluster;
A
42
, one of the Zernike moments
[17] of the EMC cluster; and
θ
C
, the Cherenkov angle measured in the DIRC. In addition, the f
raction of electrons in inclusive
J/ψ
events that pass each set of criteria is shown, along with the
fraction of pions with momentum above 1 GeV
/c
that pass
the selection requirements.
DCH-only
Loose
Tight
Very tight
d
E/
d
x
(measured-expected) -2 to +4
σ
meas
-3 to +7
σ
meas
-3 to +7
σ
meas
-2 to +4
σ
meas
E/p
–
0.65 - 5.0
0.75 - 1.3
0.89 - 1.2
N
crys
–
>
3
>
3
>
3
LAT
–
–
0.0 - 0.6
0.1 - 0.6
A
42
–
–
–
<
0
.
11
θ
C
(measured-expected)
–
–
–
-3 to +3
σ
meas
Efficiency (%)
94.9
97.2
95.4
88.2
π
misID (%)
21.6
4.8
1.2
0.1
TABLE III: Summary of muon identification criteria. Variabl
es used are:
E
EMC
, the energy deposited by the muon candidate
in the EMC (this requirement is only applied for tracks withi
n the fiducial coverage of the EMC);
N
layers
, the number of IFR
layers with hits;
N
λ
, the number of nuclear interaction lengths traversed;
|
N
λ
−
N
λ
(exp)
|
, the difference between the number of
nuclear interaction lengths traversed and the expectation
for a muon of the measured momentum;
h
N
hit
i
, the average number
of hits per IFR layer; RMS
hit
, the RMS of the distribution of the number of hits on each laye
r;
f
hit
, the fraction of layers
between the innermost and outermost hit layers that also hav
e hits (this requirement is only applied in the region covere
d
partly or entirely by the endcap IFR system, 0
.
3
< θ <
1
.
0);
χ
2
IFR
, the
χ
2
of the track in the IFR; and
χ
2
match
, the
χ
2
of the
match between the IFR track and the track from the central det
ector. In addition, the fraction of muons in inclusive
J/ψ
events
that pass each set of criteria is shown, along with the fracti
on of pions with momentum above 1 GeV
/c
that pass the selection
requirements.
MIP Very Loose
Loose
Tight
Very tight
E
EMC
( GeV)
<
0
.
5
<
0
.
5
<
0
.
5
0
.
05
−
0
.
4 0
.
05
−
0
.
4
N
layers
–
>
1
>
1
>
1
>
1
N
λ
–
>
2
>
2
>
2
.
2
>
2
.
2
|
N
λ
−
N
λ
(exp)
|
–
<
2
.
5
<
2
.
0
<
1
<
0
.
8
h
N
hit
i
–
<
10
<
10
<
8
<
8
RMS
hit
–
<
6
<
6
<
4
<
4
f
hit
–
>
0
.
1
>
0
.
2
>
0
.
3
>
0
.
34
χ
2
IFR
–
–
<
4
×
N
layers
<
3
×
N
layers
<
3
×
N
layers
χ
2
match
–
–
<
7
×
N
layers
<
5
×
N
layers
<
5
×
N
layers
Efficiency (%) 99.6
92.2
86.2
70.3
67.0
π
misID (%) 57.9
14.5
7.0
2.4
2.1
B. EMC cluster reconstruction
The energy deposited in contiguous crystals of the
EMC is summed into a cluster. The distribution of en-
ergy among the crystals is used to discriminate between
clusters arising from electromagnetic and hadronic show-
ers. The variables used to describe this distribution are
the lateral energy (LAT) [16] and the Zernike moments
A
mn
[17]. LAT is a measure of the radial energy pro-
file of the cluster; the Zernike moment
A
42
measures the
asymmetry of the cluster about its maximum. Electro-
magnetic showers have LAT peaked at about 0.25 and
A
42
close to zero, while showers from hadrons have a
broader distribution in LAT, and extend to larger values
of
A
42
.
C. Photon Candidate Selection
Photons are identified as EMC clusters that do not
have a spatial match with a charged track, and that have
a minimum energy of 30 MeV. To reject clusters arising
from noise hits, LAT is required to be less than 0.8.
D. Electron and Muon Identification
We derive substantial background rejection from the
positive identification of electrons and muons within the
sample of charged tracks. For electrons, the variables
that distinguish signal from background include LAT and
A
42
, the ratio of energy measured in the EMC to mo-
mentum measured in the tracking spectrometer (
E/p
),
8
d
E/
d
x
measured in the DCH, and the Cherenkov angle
θ
C
measured in the DIRC.
For identifying muons, the presence of an energy depo-
sition consistent with a minimum ionizing particle in the
EMC, and the details of the distribution of hits in the
IFR are used. In particular, the number of interaction
lengths traversed in the IFR
N
λ
must be consistent with
expectations for a muon, both the average and variance
of the number of hits per layer must be small, and the
fit of a track to the hits must have low
χ
2
, both within
the IFR (
χ
2
IFR
) and in the match between the IFR and
central detector track (
χ
2
match
).
Since the optimal tradeoff between efficient selection
and suppression of backgrounds varies between decay
modes, there are several sets of criteria used to select
leptons. These are defined in Table II for electrons
and Table III for muons. In addition to these criteria,
we also restrict the lepton selection to a fiducial region
within which the efficiency is well-known from control
samples, and the material in the detector is accurately
modelled in the Monte Carlo. The accepted range in po-
lar angle
θ
is 0
.
410
< θ <
2
.
409 rad for electrons and
0
.
30
< θ <
2
.
70 rad for muons. This corresponds to a
coverage of 84% of the solid angle in the center-of-mass
frame for electrons, and 92% for muons.
To increase the efficiency of the event selection, elec-
tron candidate tracks are combined with photon can-
didates to recover some of the energy lost through
bremsstrahlung. In addition to the photon selection cri-
teria listed above, photons used in bremsstrahlung re-
covery are required to have
A
42
<
0
.
25. They are also
required to be within 35 mrad in
θ
from the track, and
to have azimuthal angle
φ
intermediate between the ini-
tial track direction and the centroid of the EMC cluster
arising from the track. The initial track direction is es-
timated by subtracting 50 mrad opposite to the bend
direction from the
φ
of the fitted track measured at the
origin. The procedure increases the efficiency for recon-
structing charmonium decays to
e
+
e
−
by about 30%.
E.
K
0
L
Candidate Selection
We identify neutral hadrons through the presence of
an energy deposition in the EMC or a cluster in the
IFR. Neutral hadrons must be spatially separated from
all tracks in the event. In reconstructing the decay
B
0
→
J/ψK
0
L
neutral hadrons are taken as
K
0
L
can-
didates, with requirements specifically tailored for this
mode.
Only the measured direction of the neutral hadron is
used for
K
0
L
reconstruction, as its energy is poorly mea-
sured. The direction of the
K
0
L
candidate is defined by
the line joining the vertex of the
J/ψ
candidate and the
centroid of the EMC or IFR cluster.
For a
K
0
L
to reach the IFR it must traverse the EMC
material, which amounts to approximately one nuclear
interaction length. As a consequence, half of the
K
0
L
mesons undergo detectable interactions in the EMC. We
consider EMC clusters with energy in the 0.2 - 2.0 GeV
range. Most clusters arising from
K
0
L
interactions have
energy below the upper bound; below the lower bound
the contamination from noise becomes significant. All
such EMC clusters which are spatially separated from a
track are considered as
K
0
L
candidates, except those that
combined with another neutral cluster give an invariant
mass compatible with a
π
0
.
About 60% of
K
0
L
mesons from
B
0
→
J/ψK
0
L
leave a
detectable signal in the IFR. We select
K
0
L
candidates
in the IFR starting with clusters of hits not spatially
matched to a track. IFR clusters with hits only in the
outer layers of the forward endcap are rejected to reduce
the contribution from beam backgrounds.
VI. EVENT SELECTION AND
B
MESON
COUNTING
A determination of
B
meson branching fractions de-
pends upon an accurate measurement of the number of
B
mesons in the data sample. We find the number of
B
B
pairs by comparing the rate of multihadron events in data
taken on the
Υ
(4
S
) resonance to that in data taken off-
resonance. The
B
B
purity of the sample is enhanced by
requiring the events to pass the following selection crite-
ria, in which all tracks (including those that do not satisfy
our usual selection requirements) in the fiducial region
0
.
410
< θ <
2
.
54 rad and all neutral clusters with energy
greater than 30 MeV in the region 0
.
410
< θ <
2
.
409 rad
are considered:
•
The event must satisfy either the L3 DCH or L3
EMC trigger.
•
There must be at least three tracks that satisfy the
standard selection requirements in the fiducial re-
gion.
•
The ratio of the second to the zeroth Fox-Wolfram
moment [18] must be less than 0.5.
•
The event vertex is calculated by an iterative pro-
cedure that begins by considering every track in
the event, and then discards those that contribute
a large
χ
2
to the fit (these are presumed to arise
from the decay of long-lived particles) until the ver-
tex fit is stable. This vertex must be within 0.5 cm
of the beam spot center in
xy
and within 6 cm in
z
. The beam spot has an RMS width of about 120
m in
x
, 5.9
m in
y
, and 0.9 cm in
z
. The point
of closest approach of a high-momentum track to
the beam spot is measured with a resolution of 23
m in
x
and
y
, and 29
m in
z
, as determined with
dimuon events.
•
The total energy of charged and neutral particles
is required to be greater than 4.5 GeV.
9
TABLE IV: Summary of observed invariant mass or mass dif-
ference ∆
m
widths for all intermediate mesons considered in
this paper. For most mesons the width is dominated by ex-
perimental resolution, and the value reported in the table i
s
the width
σ
from a Gaussian fit to the data. For the
K
∗
modes the natural width of the resonance dominates, and the
value reported is the full width of a Breit-Wigner fit to the
data. The width for
J/ψ
and
ψ
(2
S
) decaying to
e
+
e
−
is
greater than that for
+
−
due to the energy lost through
bremsstrahlung.
Quantity
Decay mode
Width ( MeV
/c
2
)
J/ψ
mass
e
+
e
−
17
±
2
+
−
13
±
1
ψ
(2
S
) mass
e
+
e
−
29
±
6
+
−
21
±
3
∆
m
(
ψ
(2
S
)
−
J/ψ
)
ψ
(2
S
)
→
J/ψ π
+
π
−
;
7
±
1
J/ψ
→
ℓ
+
ℓ
−
∆
m
(
χ
c
1
−
J/ψ
)
J/ψ
→
ℓ
+
ℓ
−
14
±
1
K
0
S
mass
π
+
π
−
3
.
5
±
0
.
2
π
0
π
0
15
±
2
K
∗
0
mass
K
+
π
−
and
60
±
7
K
0
S
π
0
K
∗
+
mass
K
0
S
π
+
and
50
±
10
K
+
π
0
These requirements are 95
.
4
±
1
.
4% efficient for
B
B
events, as estimated from a Monte Carlo simulation. All
events used in the branching fraction analyses are re-
quired to pass this selection.
VII. MESON CANDIDATE SELECTION
The next step in the analysis is to combine sets of
tracks and/or neutral clusters to form candidates for the
initial or intermediate mesons in the decay. Our general
strategy when forming these candidates is to assign the
expected masses to tracks and neutral clusters, and to
apply a vertex constraint before computing the invariant
mass. In rare instances (less than 1% of all meson candi-
dates) the vertex fit does not converge. The sum of the
track and/or cluster four-vectors is used to compute the
invariant mass for such candidates. If one or more decay
products from a given particle are themselves interme-
diate states, we constrain them to their known masses.
At each step in the decay chain, we require that mesons
have masses consistent with their assumed particle type.
The mass resolutions observed for all of the intermediate
mesons considered in this paper are listed in Table IV.
We choose meson selection criteria to maximize the ex-
pected precision of our branching fraction measurements.
Therefore we use well-understood quantities in our selec-
tion, which lead to a smaller systematic uncertainty. We
set the selection values to maximize the ratio
S/
√
S
+
B
where
S
and
B
are the expected number of signal and
background events respectively, as estimated from Monte
Carlo. If a given mode has been previously observed,
S
0
20
40
60
2.9
3
3.1
3.2
J/
ψ
mass (GeV/c
2
)
Entries/4 MeV/c
2
(a)
0
25
50
75
100
2.9
3
3.1
3.2
J/
ψ
mass (GeV/c
2
)
Entries/4 MeV/c
2
(b)
FIG. 2: Invariant mass distribution for (a)
J/ψ
→
e
+
e
−
and
(b)
J/ψ
→
+
−
candidates mass observed in
B
0
→
J/ψK
0
S
and
B
+
→
J/ψK
+
candidates passing the exclusive branch-
ing fraction selection. The mass interval used to select
J/ψ
candidates for
B
reconstruction is indicated by the arrows.
is estimated using the known branching fraction. Oth-
erwise, selection values similar to those in previously-
observed modes are taken as a starting point, and then
modified to reduce background (as measured in the kine-
matic sidebands) or increase signal efficiency (as mea-
sured using Monte Carlo simulated signal events). In
most cases, we find that
S/
√
S
+
B
does not change sig-
nificantly when selection values are varied near their op-
tima. This allows us to choose standard selection values
across most final states.
A. Charmonium Meson Candidate Selection
10
0
5
10
15
20
3.5
4
Entries/20 MeV/c
2
(a)
0
10
20
30
40
3.5
4
(b)
Entries/20 MeV/c
2
ψ
(2S) mass (GeV/c
2
)
0
20
40
0.5
0.55
0.6
0.65
0.7
(c)
ψ
(2S)-J/
ψ
mass difference (GeV/c
2
)
Entries/5 MeV/c
2
FIG. 3: Background-subtracted
ψ
(2
S
) candidate mass and
mass difference distributions observed in
B
0
→
ψ
(2
S
)
K
0
S
and
B
+
→
ψ
(2
S
)
K
+
candidates passing the exclusive branching
fraction selection, for (a)
ψ
(2
S
)
→
e
+
e
−
, (b)
ψ
(2
S
)
→
+
−
,
and (c) the
ψ
(2
S
)-
J/ψ
mass difference distribution for
ψ
(2
S
)
→
J/ψ π
+
π
−
̇
The intervals used to select
ψ
(2
S
) candidates
for
B
reconstruction are indicated by the arrows.
0
10
20
30
40
0.35
0.4
0.45
0.5
χ
c
- J/
ψ
mass difference (GeV/c
2
)
Entries/7.5 MeV/c
2
FIG. 4: Background-subtracted
χ
c
1
-
J/ψ
candidate mass dif-
ference distribution observed in
B
0
→
χ
c
1
K
0
S
and
B
+
→
χ
c
1
K
+
candidates passing the exclusive branching fraction
selection. The mass difference interval used to select
χ
c
1
can-
didates for
B
reconstruction is indicated by the arrows.
1
J/ψ
Selection
J/ψ
candidates are required to have an invariant mass
in the range 2
.
95
< M
J/ψ
<
3
.
14 GeV
/c
2
and 3
.
06
<
M
J/ψ
<
3
.
14 GeV
/c
2
for
J/ψ
→
e
+
e
−
and
J/ψ
→
+
−
decays respectively. Unless otherwise stated, for
J/ψ
→
e
+
e
−
decays, one track is required to pass the tight elec-
tron selection and the other the loose selection. Tracks
not associated to an EMC cluster that pass the DCH-only
selection are also accepted. For
J/ψ
→
+
−
decays, we
require one track to pass the loose selection and the other
to pass the MIP selection.
The mass distribution for
J/ψ
candidates in the data
is shown in Fig. 2.
2
ψ
(2
S
)
Selection
ψ
(2
S
)
→
+
−
candidates are required to have a
mass within 50 MeV
/c
2
of the known
ψ
(2
S
) value of
3.69 GeV
/c
2
[19]. For
ψ
(2
S
)
→
e
+
e
−
candidates the
lower bound is relaxed to 250 MeV
/c
2
below the known
value. For decays of the
ψ
(2
S
) to
J/ψ π
+
π
−
, the differ-
ence in mass between the
ψ
(2
S
) and
J/ψ
candidates is
required to be within 15 MeV
/c
2
of the expected value,
and the
π
+
π
−
invariant mass
m
π
+
π
−
is required to be be-
tween 0.4 and 0.6 GeV
/c
2
. The latter requirement takes
advantage of the fact that
m
π
+
π
−
is most often in the
upper portion of the kinematically allowed range [20].
All
ψ
(2
S
) candidates are required to have a momentum
in the center-of-mass frame between 1.0 and 1.6 GeV
/c
,
consistent with
B
→
ψ
(2
S
)
K
decays.
We have used the same lepton identification require-
ments as for the
J/ψ
reconstruction. These are applied
either to the leptons from
ψ
(2
S
)
→
ℓ
+
ℓ
−
decays, or to
the leptons from the
J/ψ
in
ψ
(2
S
)
→
J/ψ π
+
π
−
decays.
The mass and mass difference distributions for
ψ
(2
S
)
candidates in the data are shown in Fig. 3. For Figures 3,
4, and 6 a background subtraction is performed using the
observed distribution of candidates in the ∆
E
sidebands
(see Section VII C).
3
χ
c
1
Selection
In reconstructing
χ
c
1
→
J/ψγ
,
J/ψ
and photon candi-
dates are selected as described above. The muon identi-
fication requirements are subsequently tightened by de-
manding that one lepton from the
J/ψ
pass the loose
selection and the other the very loose selection (rather
than the MIP selection).
In addition, the photon cluster is required to satisfy
E >
150 MeV and
A
42
<
0
.
15 and to have a centroid
in the angular range 0
.
41
< θ <
2
.
409, excluding the
forward direction due to the increased material (from
electronics, cables, and final-focusing magnets) in that
region.
11
0
10
20
30
0.48
0.49
0.5
0.51
K
S
mass (GeV/c
2
)
Entries/0.8 MeV/c
2
(a)
0
5
10
15
0.48
0.5
0.52
0.54
K
S
mass (GeV/c
2
)
Entries/8 MeV/c
2
(b)
FIG. 5:
K
0
S
candidate mass distribution observed in
B
0
→
J/ψK
0
S
candidates passing the exclusive branching fraction
selection, for (a)
K
0
S
→
π
+
π
−
and (b)
K
0
S
→
π
0
π
0
. The
mass intervals used to select
K
0
S
→
π
+
π
−
candidates for
B
reconstruction is indicated by the arrows in (a); the full ra
nge
of (b) is used in selecting
K
0
S
→
π
0
π
0
candidates.
We require the mass difference between the recon-
structed
χ
c
1
and
J/ψ
candidates to satisfy 0
.
35
<
M
γJ/ψ
−
M
J/ψ
<
0
.
45 GeV
/
c
2
.
The mass difference distribution for
χ
c
1
candidates in
the data is shown in Fig. 4.
B. Light Meson Candidate Selection
1
π
0
→
γγ
Selection
We reconstruct
π
0
candidates as pairs of photons. Indi-
vidual photons separated by distances of 10 cm or more in
0
25
50
75
100
0.8
1
K
*0
mass (GeV/c
2
)
Entries/13 MeV/c
2
(a)
0
20
40
60
0.8
1
K
*+
mass (GeV/c
2
)
Entries/13 MeV/c
2
(b)
FIG. 6: Background-subtracted (a)
K
∗
0
and (b)
K
∗
+
can-
didate mass distributions observed in
B
0
→
J/ψK
∗
0
and
B
+
→
J/ψK
∗
+
candidates passing the exclusive branching
fraction selection. The mass interval used to select
K
∗
can-
didates for
B
reconstruction is indicated by the arrows.
the EMC are reconstructed as distinct clusters. Photons
from
π
0
’s with energies above 2 GeV can have less sepa-
ration, in which case the two photons are reconstructed
as a single cluster. We refer to these as “merged”
π
0
’s.
They are distinguished from single photons based on their
shower shape.
2
K
0
S
→
π
+
π
−
Selection
We construct
K
0
S
candidates from all pairs of oppo-
sitely charged tracks, and retain those that have invari-
ant mass between 489 and 507 MeV
/c
2
after applying a
vertex constraint. To further reject background we ex-
ploit the flight length of the
K
0
S
by demanding that the
K
0
S
vertex be more than 1 mm (in three dimensions)
from the
J/ψ
,
ψ
(2
S
), or
χ
c
1
vertex.
The mass distribution for
K
0
S
→
π
+
π
−
candidates in
the data is shown in Fig. 5.
3
K
0
S
→
π
0
π
0
Selection
The
K
0
S
→
π
0
π
0
→
4
γ
decay chain is reconstructed
from photon combinations satisfying
E
γ
>
30 MeV,
E
π
0
>
200 MeV and
E
K
0
S
>
800 MeV, with 110
≤
m
π
0
≤
155 MeV
/c
2
and 300
≤
m
K
0
S
≤
800 MeV
/c
2
. We per-
form a mass-constrained fit to each photon pair with the
known
π
0
mass. This fit is repeated assuming different
decay points along the
K
0
S
flight path, as defined by the
J/ψ
vertex and the initial
K
0
S
momentum vector direc-
tion. The point where the product of the fit
χ
2
proba-
bilities for the two
π
0
’s is maximal is defined as the
K
0
S