

 15 Mar 1994

CLNS 94-1270, CLEO 94-5 Exclusive Hadronic B Decays to Charm and Charmonium Final

States

M.S. Alam,1 I.J. Kim,1 B. Nemati,1 J.J. O'Neill,1 H. Severini,1 C.R. Sun,1 M.M. Zoeller,1

G. Crawford,2 C. M. Daubenmier,2 R. Fulton,2 D. Fujino,2 K.K. Gan,2 K. Honscheid,2

H. Kagan,2 R. Kass,2 J. Lee,2 R. Malchow,2 F. Morrow,2 Y. Skovpen,2\Lambda M. Sung,2

C. White,2 F. Butler,3 X. Fu,3 G. Kalbfleisch,3 W.R. Ross,3 P. Skubic,3 J. Snow,3 P.L. Wang,3 M. Wood,3 D.N. Brown,4 J.Fast ,4 R.L. McIlwain,4 T. Miao,4 D.H. Miller,4 M. Modesitt,4 D. Payne,4 E.I. Shibata,4 I.P.J. Shipsey,4 P.N. Wang,4 M. Battle,5 J. Ernst,5

Y. Kwon,5 S. Roberts,5 E.H. Thorndike,5 C.H. Wang,5 J. Dominick,6 M. Lambrecht,6

S. Sanghera,6 V. Shelkov,6 T. Skwarnicki,6 R. Stroynowski,6 I. Volobouev,6 G. Wei,6

P. Zadorozhny,6 M. Artuso,7 M. Goldberg,7 D. He,7 N. Horwitz,7 R. Kennett,7 R. Mountain,7 G.C. Moneti,7 F. Muheim,7 Y. Mukhin,7 S. Playfer,7 Y. Rozen,7 S. Stone,7

M. Thulasidas,7 G. Vasseur,7 G. Zhu,7 J. Bartelt,8 S.E. Csorna,8 Z. Egyed,8 V. Jain,8

K. Kinoshita,9 K.W. Edwards,10 M. Ogg,10 D.I. Britton,11 E.R.F. Hyatt,11 D.B. MacFarlane,11 P.M. Patel,11 D.S. Akerib,12 B. Barish,12 M. Chadha,12 S. Chan,12

D.F. Cowen,12 G. Eigen,12 J.S. Miller,12 C. O'Grady,12 J. Urheim,12 A.J. Weinstein,12

D. Acosta,13 M. Athanas,13 G. Masek,13 H.P. Paar,13 J. Gronberg,14 R. Kutschke,14 S. Menary,14 R.J. Morrison,14 S. Nakanishi,14 H.N. Nelson,14 T.K. Nelson,14 C. Qiao,14

J.D. Richman,14 A. Ryd,14 H. Tajima,14 D. Schmidt,14 D. Sperka,14 M.S. Witherell,14

M. Procario,15 R. Balest,16 K. Cho,16 M. Daoudi,16 W.T. Ford,16 D.R. Johnson,16 K. Lingel,16 M. Lohner,16 P. Rankin,16 J.G. Smith,16 J.P. Alexander,17 C. Bebek,17 K. Berkelman,17 K. Bloom,17 T.E. Browder,17y D.G. Cassel,17 H.A. Cho,17 D.M. Coffman,17

P.S. Drell,17 R. Ehrlich,17 M. Garcia-Sciveres,17 B. Geiser,17 B. Gittelman,17 S.W. Gray,17

D.L. Hartill,17 B.K. Heltsley,17 C.D. Jones,17 S.L. Jones,17 J. Kandaswamy,17 N. Katayama,17 P.C. Kim,17 D.L. Kreinick,17 G.S. Ludwig,17 J. Masui,17 J. Mevissen,17

N.B. Mistry,17 C.R. Ng,17 E. Nordberg,17 J.R. Patterson,17 D. Peterson,17 D. Riley,17 S. Salman,17 M. Sapper,17 F. W"urthwein,17 P. Avery,18 A. Freyberger,18 J. Rodriguez,18

R. Stephens,18 S. Yang,18 J. Yelton,18 D. Cinabro,19 S. Henderson,19 T. Liu,19 M. Saulnier,19 R. Wilson,19 H. Yamamoto,19 T. Bergfeld,20 B.I. Eisenstein,20 G. Gollin,20

B. Ong,20 M. Palmer,20 M. Selen,20 J. J. Thaler,20 A.J. Sadoff,21 R. Ammar,22 S. Ball,22 P. Baringer,22 A. Bean,22 D. Besson,22 D. Coppage,22 N. Copty,22 R. Davis,22 N. Hancock,22

M. Kelly,22 N. Kwak,22 H. Lam,22 Y. Kubota,23 M. Lattery,23 J.K. Nelson,23 S. Patton,23

D. Perticone,23 R. Poling,23 V. Savinov,23 S. Schrenk,23 and R. Wang23

(CLEO Collaboration) 1State University of New York at Albany, Albany, New York 12222

2Ohio State University, Columbus, Ohio, 43210 3University of Oklahoma, Norman, Oklahoma 73019

4Purdue University, West Lafayette, Indiana 47907 5University of Rochester, Rochester, New York 14627

6Southern Methodist University, Dallas, Texas 75275

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7Syracuse University, Syracuse, New York 13244 8Vanderbilt University, Nashville, Tennessee 37235 9Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 10Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada

11McGill University, Montr'eal, Qu'ebec H3A 2T8 and the Institute of Particle Physics, Canada

12California Institute of Technology, Pasadena, California 91125 13University of California, San Diego, La Jolla, California 92093

14University of California, Santa Barbara, California 93106 15Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213

16University of Colorado, Boulder, Colorado 80309-0390

17Cornell University, Ithaca, New York 14853 18University of Florida, Gainesville, Florida 32611 19Harvard University, Cambridge, Massachusetts 02138 20University of Illinois, Champaign-Urbana, Illinois, 61801

21Ithaca College, Ithaca, New York 14850 22University of Kansas, Lawrence, Kansas 66045 23University of Minnesota, Minneapolis, Minnesota 55455

Abstract We have fully reconstructed decays of both _B0 and B\Gamma mesons into final states containing either D, D\Lambda , D\Lambda \Lambda , , 0 or O/c1 mesons. This allows us to obtain new results on many physics topics including branching ratios, tests of the factorization hypothesis, color suppression, resonant substructure, and the B\Gamma \Gamma _B0 mass difference.

13.40.Dk, 14.40.Jz

Typeset using REVTEX \Lambda Permanent address: INP, Novosibirsk, Russia yPermanent address: University of Hawaii at Manoa

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I. INTRODUCTION Since B mesons were first fully reconstructed in 1983 by CLEO [1] there have been several papers by CLEO [2], [3] and ARGUS [4], [5], [6] which reported branching ratios for exclusive decay modes of B mesons. We present here new data from the CLEO II detector using a high resolution photon detector and a much larger data sample than has been available previously.

We are particularly interested in two-body hadronic B meson decays, which occur through the Cabibbo favored b ! c transition. In these circumstances the dominant weak decay diagram is the spectator diagram, shown in Fig. 1(a). The virtual W \Gamma materializes into either a _ud or _cs pair. This pair becomes one of the final state hadrons while the c quark pairs with the spectator anti-quark to form the other hadron. The Hamiltonian [7] , ignoring hard gluon corrections, is

H = GFp2 Vcb nh( _du) + (_sc)i (_cb)o (1) where (_qiqj) = _qifl_(1 \Gamma fl5)qj, GF is the Fermi coupling constant, and Vcb is the CKM matrix element.

The spectator diagram is modified by hard gluon exchanges between the initial and final quark lines. The effect of these exchanges can be taken into account by use of the renormalization group. These gluons induce an additional term so that the effective Hamiltonian is comprised of two pieces, the original one now multiplied by a coefficient c1(_) and an additional term multiplied by c2(_):

Heff = GFp2 Vcb nc1(_) h( _du) + (_sc)i (_cb) + c2(_) h(_cu)( _db) + (_cc)(_sb)io (2) where the ci are Wilson coefficients evaluated at the mass scale _. The Wilson coefficients can be calculated from QCD; however, the calculation of rates is inherently difficult because it is unclear at what scale these coefficients should be evaluated. The usual scale is taken to be _ , m2b . Defining

c\Sigma (_) = c1(_) \Sigma c2(_) (3) the leading-log approximation gives [8]

c\Sigma (_) = ffs(M

2 W )

ffs(_) !

\Gamma 6fl\Sigma (33 \Gamma 2nf ) (4)

where fl\Gamma = \Gamma 2fl+ = 2, and nf is the number of active flavors, five in this case.

The Hamiltonian in Eq. (2) leads to the "color suppressed" diagram shown in Fig. 1(b), which reflects the quark pairings in the term multiplied by the coefficient c2(_). Observation of B ! Xs decays, where Xs is a strange meson, gives experimental evidence for the existence of this diagram. Further information on the size of the color suppressed contribution can be obtained from _B0 ! D0 (or D\Lambda 0)X0 transitions, where X0 is a neutral meson

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containing light quarks. In B\Gamma decays, both types of diagrams are present and can interfere. By comparing the rates for B\Gamma and _B0 decays, the size and the sign of the color suppressed term can be extracted.

Bjorken has suggested [9] that, in analogy to semileptonic decays, two body decays of B mesons that occur via the external spectator process can be expressed theoretically as the product of two independent hadronic currents, one describing the formation of a charm meson and the other the hadronization of the _ud (or _cs) system from the virtual W \Gamma . Qualitatively, he argues that for a B decay with a large energy release the _ud pair, which is produced as a color singlet, travels fast enough to leave the interaction region without interfering with the formation of the second hadron. The assumption that the amplitude can be expressed as the product of two hadronic currents is called "factorization" in this paper. Several tests of the factorization hypothesis can be made by comparing semileptonic and hadronic B meson decays.

This paper is structured in the following manner: the data sample, detector and reconstruction procedures are described in sections II and III. Branching ratios are given for B ! Dss\Gamma and B ! Dae\Gamma modes in section IV. In section V results on branching ratios, polarizations and final state substructure for B ! D\Lambda ss\Gamma , B ! D\Lambda ae\Gamma and B ! D\Lambda a\Gamma 1 are described. Section VI describes a search for D\Lambda \Lambda production in hadronic B decay. This is followed by section VII on exclusive B decays to charmonium, and section VIII on a search for other color suppressed B decays. A B\Gamma \Gamma _B0 mass difference measurement is described in section IX. The interpretation of these results and comparisons to theoretical predictions are discussed in sections X (factorization tests), XI (spin symmetry tests) and XII (determination of the color suppressed amplitude).

II. DATA SAMPLE AND SELECTION CRITERIA

A. Data Sample The data sample used in this paper was collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR). The integrated luminosity is 0:89 fb\Gamma 1 at the \Upsilon (4S) resonance and 0:41 fb\Gamma 1 at energies just below B _B threshold, henceforth referred to as the continuum. It is natural to assume equal production of charged and neutral B's since the difference between their masses is very small (see section IX). Then there are a total of 935; 000 \Sigma 10; 000 \Sigma 15; 000 charged and the same number of neutral B mesons in this sample.

B. Detector The CLEO II detector [10] is designed to detect both charged and neutral particles with excellent resolution and efficiency. The detector consists of a charged particle tracking system surrounded by a time-of-flight (TOF) scintillation system and an electromagnetic shower detector with 7800 thallium-doped cesium iodide crystals. In the "barrel", defined as the region where the angle of the shower with respect to the beam axis lies between 32ffi and 135ffi, the r.m.s. energy resolution is given by ffiE=E(%) = 0:35=E0:75 + 1:9 \Gamma 0:1E (E

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in GeV). In the endcap region, located between 18ffi and 36ffi from the beam axis, the r.m.s energy resolution is given by ffiE=E(%) = 0:26=E + 2:5 . The tracking system, time-of-flight scintillators, and calorimeter are installed inside a 1.5 T superconducting solenoidal magnet. Immediately outside the magnet are iron and chambers for muon detection. The momentum resolution of the tracking system is given by (ffip=p)2 = (0:0015p)2 + (0:005)2 (p in GeV/c). Ionization loss information (dE=dx), provided by the tracking system, is used to identify charged particles in this analysis. The track must have a dE=dx measurement that differs from that expected for the charged particle hypothesis under consideration by less than 3oe (where henceforth oe denotes the r.m.s. resolution).

Muons are identified by a system of drift tubes interleaved with layers of magnet iron. Electron identification utilizes the specific ionization of the track in the drift chamber, the spatial distribution of the energy in the calorimeter, and the ratio of the cluster energy measured in the calorimeter to the track momentum.

C. Photon Selection Photon candidates are selected from showers in the calorimeter barrel that have a minimum energy of 30 MeV, are not matched to a charged particle track from the drift chamber, and have a lateral energy distribution consistent with that expected for photons. In the calorimeter endcap the same criteria are applied but the minimum energy requirement is increased to 50 MeV. A small angular region between 320 and 360 degrees in the barrel-endcap overlap region is excluded. Neutral pion candidates are selected from pairs of photons with an invariant mass within 2.5oe of the known ss0 mass. These candidates are kinematically fitted with a ss0 mass constraint.

Candidate j mesons are reconstructed in the j ! flfl mode. They are required to have an invariant mass within 30 MeV of the known j mass (547.5 MeV) [14]. The candidates which pass the requirements described above, are kinematically constrained to the j mass. Candidate j0 mesons are reconstructed in the jss+ss\Gamma channel with j ! flfl. Candidate ! mesons are reconstructed in the ! ! ss+ss\Gamma ss0 channel.

D. Charm meson selection We select D0; D+; D\Lambda + and D\Lambda 0 mesons based on the following criteria. Candidate D0 mesons are identified in the decay modes D0 ! K\Gamma ss+, D0 ! K\Gamma ss+ss0 and D0 ! K\Gamma ss+ss+ss\Gamma . Candidate D+ mesons are selected using the D+ ! K\Gamma ss+ss+ mode. The decay modes, branching ratios and r.m.s. mass resolutions, oemD , are listed in Table I. We use the CLEO [11] absolute branching ratio for D0 ! K\Gamma ss+ decays [13], and the Mark III value for D+ ! K\Gamma ss+ss+ [12]. We use the Particle Data Group (PDG) values [14] for the ratios B(D0 ! K\Gamma ss+ss0)=B(D0 ! K\Gamma ss+) (where henceforth B denotes the branching ratio) and B(D0 ! K\Gamma ss+ss+ss\Gamma )=B(D0 ! K\Gamma ss+).

Charged D\Lambda candidates are found using the decay D\Lambda + ! ss+D0, while neutral D\Lambda candidates are found using the decay D\Lambda 0 ! ss0D0. Other D\Lambda decay modes are not used because they have much poorer signal to background ratios. CLEO branching ratios (Table II) are used for D\Lambda decays [16]. We form D\Lambda + and D\Lambda 0 candidates by selecting D0 candidates whose

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mass is within 2.5oe of the known D0 mass. Then we require that the D\Lambda -D0 mass difference be within 2.5oe of the measured values [14,17].

E. Charmonium Meson Selection We reconstruct the charmonium states , 0 and O/c1, where mesons are selected by their decay into pairs of identified leptons (e+e\Gamma or _+_\Gamma ). We use the MarkIII value [18]B

( ! l+l\Gamma ) = (5:91 \Sigma 0:25)% for the to dilepton branching ratio. The kinematics of B decay at the \Upsilon (4S) imply that each lepton in a candidate has a momentum between 0.8 GeV/c and 2.8 GeV/c, with one lepton always having momentum greater than 1.5 GeV/c. For the clean modes B\Gamma ! K\Gamma and B0 ! K0S, we obtain good efficiency in the dimuon channel by requiring only one identified muon that penetrates through three interaction lengths. In the dielectron channel, one of the electrons must satisfy a loose electron probability requirement. For modes other than B\Gamma ! K\Gamma and B0 ! K0S, both electrons must be identified, or one muon is required to penetrate five interaction lengths and the partner muon is required to penetrate three interaction lengths.

Final state radiation is included in the Monte Carlo simulation of meson decays. For 's in the dielectron final states we employ an asymmetric mass cut: \Gamma 150 ! m(e+e\Gamma ) \Gamma m() ! 45 MeV in order to reduce the efficiency loss from this source. For the dimuon final state, we require \Gamma 45 ! m(_+_\Gamma ) \Gamma m() ! 45 MeV since final state radiation is less significant in this case. (The mass resolution would be 15 MeV (r.m.s.) in the absence of radiation). In these mass windows the efficiency for detecting mesons in the dielectron and the dimuon final states are 48.1% and 67.8% for the looser cuts, and are 45.7% and 42.4% when both leptons are identified.

The decay modes

0 ! e+e\Gamma , 0 ! _+_\Gamma , and 0 ! ss+ss\Gamma , are used to select 0

candidates. The recontruction of the leptonic decays follows the procedure outlined for mesons. Pion candidates for the third decay mode are required to have dE/dx measurements consistent with the pion hypothesis. In addition, tracks that have been identified as part of a K0S decay are rejected. It has been shown that the ss+ss\Gamma invariant mass spectrum from 0 decays favor larger values relative to that expected from phase space [18]. We require the ss+ss\Gamma invariant mass to be between 0.45 and 0.58 GeV [19]. For 0 mesons reconstructed through the decay 0 ! ss+ss\Gamma we require the

0 \Gamma mass difference, ffim = m

0 \Gamma m, to

be between 0.568 and 0.599 GeV. O/c1 mesons are reconstructed by their decay into a photon

and a meson. We require the photon be in the good portion of the barrel calorimeter (j cos `j ! 0:71). If the photon candidate forms an invariant mass within \Gamma 5 to 3 standard deviations of the known ss0 mass when combined with any other photon in the event, it is rejected.

III. B MESON RECONSTRUCTION PROCEDURES

A. Candidate Selection After selecting D, D\Lambda or charmonium candidates we combine them with one or more additional hadrons to form B candidates. The measured sum of charged and neutral energies,

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Emeas of correctly reconstructed B mesons produced at the \Upsilon (4S) must equal the beam energy, Ebeam, to within the experimental resolution. Depending on the B decay mode, oe\Delta E, the r.m.s. resolution on the energy difference \Delta E = Ebeam \Gamma Emeas varies from 8 to 46 MeV. The modes considered and the corresponding oe\Delta E values are given in Tables III-VII and Tables IX-X. We divide the B candidates into a signal sample where \Delta E is consistent with zero within 2.5 oe, and a "sideband" sample consisting of two intervals, one with \Delta E positive and the other negative, both 2:5oe wide and at least 3oe away from \Delta E = 0. For decay modes with large oe\Delta E, we restrict the sideband width so that the maximum value of \Delta E is less than one pion mass. This avoids contamination from the B decay mode with an additional pion. These \Delta E sidebands are used to study the background shape.

For B decay modes with a fast ae\Gamma the energy resolution depends on the momenta of the pions from the ae\Gamma decay. The momenta of the charged and neutral pions are correlated; a fast ss\Gamma accompanies a slow ss0 and vice-versa. This correlation is most conveniently formulated as a function of the helicity angle \Theta ae, the angle in the ae\Gamma rest frame between the direction of the ss\Gamma and the ae\Gamma direction in the lab frame. When cos \Theta ae = +1, the resolution in the energy measurement is dominated by the momentum resolution on the fast ss\Gamma . In contrast, when cos \Theta ae = \Gamma 1, the largest contribution to the energy resolution comes from the calorimeter energy resolution on the fast ss0. Typically oe\Delta E varies linearly between 20 MeV at cos \Theta ae = \Gamma 1 and 40 MeV at cos \Theta ae = 1. The energy resolution from a Monte Carlo simulation for one such mode (B\Gamma ! D0ae\Gamma ) is shown in Fig. 2 as a function of the ae\Gamma helicity angle. The energy difference resolutions for modes containing a ae\Gamma are given in Tables III-VI.

In addition to the above selection criteria, events are required to satisfy R2 ! 0:5 where R2 is the ratio of the second Fox-Wolfram moment to the zeroth moment determined using charged tracks and unmatched neutral showers [20]. A sphericity angle cut is applied to further reduce continuum background. The sphericity angle \Theta s is the angle between the sphericity axis of the particles which form the B candidate and the sphericity axis of the other particles in the event [21]. For a jet-like continuum event, the absolute value of this angle is small; while for a B _B event, the two axes are almost uncorrelated. Requiringj

cos \Theta sj ! 0:7 typically removes about 80% of the continuum background, while retaining 70% of the B decays. The sphericity cut used here depends on the number of pions which accompany the D or D\Lambda meson. For final states with a D\Lambda and a single (2, 3) pion(s) we require j cos \Theta sj ! 0:9 (0:8; 0:7). For all modes which contain a D and a single (2) pion(s) in the final state, we demand that j cos \Theta sj ! 0:8. In modes with mesons, we maximize the efficiency by applying no sphericity angle cut.

To determine the signal yield and display the data we form the beam constrained mass

M 2B = E2beam \Gamma X

i

~pi!

2

; (5)

where ~pi is the momentum of the i-th daughter of the B candidate. The resolution in this variable is about 2.7 MeV [22] and is about a factor of ten better than the resolution in invariant mass. The width is dominated by the CESR beam energy spread rather than by detector resolution.

For a specific B decay chain, such as B\Gamma ! D0ss\Gamma ; D0 ! K\Gamma ss+ss0, we allow only one

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candidate per event to appear in the MB distribution. If there are multiple candidates with MB ? 5:2 GeV, the entry with the smallest absolute value of \Delta E is selected.

B. Background Studies In order to extract the number of signal events it is crucial to understand the shape of the background in the MB distributions. There are two contributions to this background, continuum and other B _B decays. The fraction of background from continuum events varies between about 58% and 91% depending on the B decay mode [23].

We expect that the MB distribution from the \Delta E sidebands will give a good representation of the background shape. To verify this, a Monte Carlo simulation of B _B events was used to show that the \Delta E sidebands can be used to accurately model the shape of the B _B background under the signal in the beam constrained mass distributions (see Fig. 3). In continuum data, the \Delta E sidebands also model the shape of the background in the signal region. The sum of the B _B Monte Carlo and continuum data agrees in shape with the \Delta E sidebands in data (see Fig. 4). Therefore, the \Delta E sidebands can be used to model the shape of the background under the signal in data. The MB distributions for \Delta E sidebands in data for several modes are shown in Fig. 5. All of these can be fitted with a linear background below MB=5.282 GeV, and a smooth kinematical cutoff at the endpoint, which we choose to be parabolic. The distributions of MB for wrong-sign combinations (e.g. _D0ss+), wrongcharge combinations (e.g. D+ss+), and continuum data can also be adequately fitted with this functional form (henceforth referred to as the CLEO background shape). To determine the number of signal events from the MB spectrum in the \Delta E interval centered on zero, we use the background function as determined from the sidebands and a Gaussian signal with a fixed width of 2:64 MeV.

C. Efficiency Studies In order to extract branching ratios, detection efficiencies are determined from a Monte Carlo simulation of the CLEO II detector. The accuracy of the simulation is checked in several ways. We select radiative Bhabha events (e+e\Gamma ! e+e+fl) using only calorimeter information and then embed the tracks into hadronic events. We find that the efficiency for the detection of charged tracks above 225 MeV/c is correct to better than 2%. The Monte Carlo simulation of charged tracks with transverse momenta below 225 MeV/c is more complicated since these tracks do not traverse the entire drift chamber. The accuracy of the simulation is verified using the D\Lambda decay angle distribution of inclusive D\Lambda + ! D0ss+, D0 ! K\Gamma ss+ decays which must be symmetric after efficiency correction. The simulation of low pT tracks agrees with the Monte Carlo simulation for 100 ! p ! 225 MeV/c. However, the efficiency for tracks in this momentum range is known to only \Sigma 5%.

The accuracy of the photon detection efficiency can be verified by comparing the ratio of branching ratios of j ! ss0ss0ss0 and j ! flfl to the average ratio given by the PDG [14]. This test indicates that the single photon efficiency is modelled to better than \Sigma 2:5%. Other checks of the ss+ and ss0 detection efficiency are performed by comparing the yield of fully reconstructed D0 ! K\Gamma ss+ss0 decays with the yield of partially reconstructed D0 !

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K\Gamma ss0(ss+) where the ss+ is not detected. Additional consistency checks have been performed by comparing inclusive D\Lambda + and D\Lambda 0 cross sections in the continuum, and by comparing the ratios B(D0 ! K\Gamma ss+ss\Gamma ss+) /B(D0 ! K\Gamma ss+) and B(j ! ss\Gamma ss+ss0)/B(j ! flfl) to the values in the PDG compilation [14].

IV. BRANCHING RATIOS FOR Dss\Gamma AND Dae\Gamma FINAL STATES We reconstruct the decay modes _B0 ! D+ss\Gamma , _B0 ! D+ae\Gamma , B\Gamma ! D0ss\Gamma , and B\Gamma ! D0ae\Gamma following the procedures described in sections II and III. There is an additional complication for the analysis of the B ! Dae\Gamma modes. Events which are consistent with the decay chain B ! D\Lambda ss\Gamma , D\Lambda ! Dss0 have the same final state particles and thus form a potential background. We eliminate this background by discarding events for which the D\Lambda \Gamma D mass difference is consistent with the D\Lambda hypothesis. This veto does not reduce the efficiency for B ! Dae\Gamma . A Monte Carlo simulation of B _B decays shows a broad enhancement in the signal region for B\Gamma ! D0ss\Gamma and B\Gamma ! D0ae\Gamma (see Fig. 3). This enhancement contains contributions from B ! D\Lambda 0X; D\Lambda 0 ! D0fl transitions which can be modeled with the CLEO background shape.

To select B ! Dae\Gamma channels we impose additional requirements on the ss\Gamma ss0 invariant mass and decay angle. Specifically, we require that jm(ss\Gamma ss0)\Gamma 770j ! 150 MeV/c2. Since the decay B ! Dae\Gamma is fully longitudinally polarized (helicity zero due to angular momentum conservation), a cut on the ae helicity angle is imposed (j cos \Theta aej ? 0:4) [24]. The beam constrained mass distributions for B ! Dss\Gamma and B ! Dae\Gamma are shown in Fig. 9. Fig. 6 shows the ae helicity angle distributions (with the cut on the helicity angle removed) for_ B0 ! D+ae\Gamma and for B\Gamma ! D0ae\Gamma after B mass sideband subtraction. After efficiency correction, these distributions are given by the functional form:

dN d cos \Theta ae =

\Gamma L

\Gamma cos

2 \Theta ae + 0:5(1 \Gamma \Gamma L

\Gamma ) sin

2 \Theta ae (6)

where \Gamma L=\Gamma is the fraction of longitudinal polarization. The fit gives \Gamma L=\Gamma = 1:07 \Sigma 0:05 for B\Gamma ! D0ae\Gamma and \Gamma L=\Gamma = 0:92 \Sigma 0:07 for _B0 ! D+ae\Gamma . These results are consistent with full polarization as expected and thus provide a consistency check of the background subtraction and efficiency correction. Monte Carlo simulation shows that most of the B _B backgrounds in B ! Dae\Gamma decays are due to combinations with an incorrectly reconstructed low momentum ss0. Therefore a fit to the beam constrained mass distribution with cos \Theta ae ! \Gamma 0:4 is also performed as a consistency check of the analysis [25]. These results agree with the branching ratios obtained using the full range of helicity angle.

The ss\Gamma ss0 invariant mass distribution for the B signal region (\Sigma 6:5 MeV of the nominal B mass), is shown in Figs. 7 and 8 after B sideband subtraction. Fitting this distribution to the sum of a Breit Wigner and a parameterization of non-resonant B ! Dss\Gamma ss0 decay [26] we find that fewer than 2.5% (at 90% C.L.) of the events in the B mass peak arise from non-resonant decays, after applying the helicity angle cut and restricting the ss\Gamma ss0 mass to lie in the rho mass region. The observed Dss\Gamma ss0 events are consistent with B ! Dae\Gamma and any non-resonant contribution can be neglected.

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The resulting branching ratios for B ! Dss\Gamma and B ! Dae\Gamma are given in Tables III and IV.

Two systematic errors are quoted on the branching ratios. The first includes contributions from background shape (, 5%), Monte Carlo statistics (2 \Gamma 4%), and the uncertainty in the modeling of the tracking and ss0 detection efficiencies (which depend on the multiplicity of the decay mode as described earlier) and the relative D0 branching fractions. The second systematic error contains the errors from the D+ ! K\Gamma ss+ss+ (\Sigma 14%) and D0 ! K\Gamma ss+ absolute branching ratios (\Sigma 2:7%).

V. MEASUREMENTS OF D\Lambda (N ss)\Gamma FINAL STATES

A. Branching Ratios We now consider final states containing a D\Lambda meson and one, two or three pions. These include the B ! D\Lambda ss\Gamma , B ! D\Lambda ae\Gamma , and B ! D\Lambda a\Gamma 1 decay channels. A cut on the D\Lambda helicity angle, j cos `D\Lambda j ? 0:4, is made for B ! D\Lambda ss but not for D\Lambda ae and D\Lambda a1. The beam constrained mass distributions for the _B0 ! D\Lambda +ss\Gamma and B\Gamma ! D\Lambda 0ss\Gamma are shown in Fig. 10. Our results for the decays _B0 ! D\Lambda +ss\Gamma and B\Gamma ! D\Lambda 0ss\Gamma are listed in Tables V and VI. The first error quoted on the branching ratios is statistical, followed by two systematic errors. The first systematic error contains contributions from the uncertainties in the efficiency for charged track finding, the uncertainty in photon detection, variations in event yield from changes in background shape, Monte Carlo statistics and the relative D0 branching fractions. The second systematic error contains the errors on the D0 ! K\Gamma ss+ and D\Lambda ! D0ss branching ratios.

Fig. 10 shows the beam constrained mass distributions for the _B0 ! D\Lambda +ae\Gamma and B\Gamma ! D\Lambda 0ae\Gamma . To study the resonant substructure in _B0 ! D\Lambda +ss\Gamma ss0 the cut on the ss\Gamma ss0 mass is removed. For events in the B signal region (jMB \Gamma 5:280j ! 0.006 GeV) the ss\Gamma ss0 spectrum is examined after subtracting the ss\Gamma ss0 spectrum from the low B mass sideband (5:2 ! MB ! 5:26 GeV). The background subtracted ss\Gamma ss0 invariant mass spectrum is then fitted to the sum of a Breit Wigner and a polynomial parameterization of non-resonant _B0 ! D\Lambda +ss\Gamma ss0 obtained from a Monte Carlo simulation. Fig. 11 shows the fit to the background subtracted ss\Gamma ss0 invariant mass spectrum. The fit gives an upper limit of less than 6 non-resonant _B0 ! D\Lambda +ss\Gamma ss0 events in the ae mass window at the 90% confidence level. This implies that the non-resonant contribution to the _B0 ! D\Lambda +ae\Gamma decay is less than 9% at the 90% confidence level. If we instead take the shape of the non-resonant component from a D\Lambda \Lambda (2420)ss+ Monte Carlo we obtain a similar limit for the non-ae component. A similar study has been made of B\Gamma ! D\Lambda 0ae\Gamma which also shows a negligible non-resonant component. The branching ratios for B ! D\Lambda ae can be found in Tables V and VI. In Fig. 12 we show the MB distributions for B\Gamma ! D\Lambda 0ss\Gamma ss\Gamma ss+ and _B0 ! D\Lambda +ss\Gamma ss\Gamma ss+ where the ss\Gamma ss\Gamma ss+ invariant mass is required to be in the interval 1:0 ! ss\Gamma ss\Gamma ss+ ! 1:6 GeV. To show that this signal arises dominantly from a\Gamma 1 we also present the MB distributions for the a1 sidebands 0:6 ! ss\Gamma ss\Gamma ss+ ! 0:9 GeV and 1:7 ! ss\Gamma ss\Gamma ss+ ! 2:0 GeV (Fig. 13), where there are signals of 15 \Sigma 6 and 0 \Sigma 5:5 events for the D\Lambda + and D\Lambda 0 channels respectively. The sideband signals are 18\Sigma 6% (0\Sigma 13 %) of the signals in the a1 peak, as compared to the expectation of about 10% from the tails of a

10

Breit-Wigner distribution. In Figs. 14 and 15 we show the ss\Gamma ss\Gamma ss+ mass distributions for a B ! D\Lambda a\Gamma 1 Monte Carlo simulation, a B ! D\Lambda ss\Gamma ae0 non-resonant background simulation, and the data events in the B signal region with the scaled B mass sideband subtracted. The a1 meson is parameterized in the Monte Carlo simulation as a Breit-Wigner resonance shape with ma1 = 1182 MeV and \Gamma a1 = 466 MeV. The fit gives upper limits of less than 4:2 and 4:6 non-resonant events at the 90% confidence level. This implies that the non-resonant components in this decay are less than 9:4% and 10:6% at the 90 % confidence level. We have verified that a D\Lambda \Lambda (2420)ae\Gamma Monte Carlo simulation gives a similar limit for the non-a1 component. Our results for B meson decays into final states containing a D\Lambda meson and three charged pions are also listed in Tables V and VI.

B. Polarization in B ! D\Lambda +ae\Gamma decays The sample of fully reconstructed B ! D\Lambda +ae\Gamma decays can be used to measure the D\Lambda + and ae\Gamma polarizations. By comparing the measured polarizations in _B0 ! D\Lambda +ae\Gamma with the expectation from the corresponding semileptonic B decay a test of the factorization hypothesis can be performed (see section X C).

The polarization is obtained from the helicity angle distribution. The ae helicity angle \Theta ae was defined earlier. The D\Lambda + helicity angle \Theta D\Lambda is the angle between the ss+ direction and B direction in the D\Lambda + rest frame.

The momentum in the laboratory for pions from the D\Lambda + decay which are emitted in the backward hemisphere (cos \Theta D\Lambda ! 0 in our convention) extends from 160 MeV/c down to about 100 MeV/c. In this momentum range, the reconstruction efficiency for charged tracks is reduced and becomes momentum dependent.

Before examining the _B0 ! D\Lambda +ae\Gamma decay mode, we perform a consistency check of the efficiency correction and analysis procedure by measuring the polarization in _B0 ! D\Lambda +ss\Gamma . Since B mesons and pions are pseudoscalars, the D\Lambda + mesons from the decay _B0 ! D\Lambda +ss\Gamma will be longitudinally polarized giving a cos2 \Theta D\Lambda distribution. The same procedure used in the analysis of the _B0 ! D\Lambda +ae\Gamma polarization is applied to this case. After performing the sideband subtraction and correcting for efficiency, [27] we obtain the D\Lambda + helicity angle distribution shown in Fig. 16 (c). A fit to this distribution gives \Gamma L=\Gamma = 106 \Sigma 7% which is consistent with the expectation from angular momentum conservation of \Gamma L=\Gamma = 100%.

We now proceed to measure the polarization in _B0 ! D\Lambda +ae\Gamma decays. After integration over O/, the angle between the normals to the D\Lambda + and the ae\Gamma decay planes, the helicity angle distribution can be expressed as follows [28]:

d2\Gamma d cos \Theta D\Lambda d cos \Theta ae /

1 4 sin

2 \Theta D

\Lambda sin2 \Theta ae(jH+1j2 + jH\Gamma 1j2) + cos2 \Theta D\Lambda cos2 \Theta aejH0j2 (7)

The fraction of longitudinal polarization is defined by [28]

\Gamma L

\Gamma = j

H0j2j H+1j2 + jH\Gamma 1j2 + jH0j2 (8)

If longitudinal polarization dominates, both the D\Lambda + and the ae\Gamma helicity angles will follow a cos2 \Theta distribution, whereas in the case of transverse polarization we will observe a sin2 \Theta distribution for both helicity angles.

11

To measure the polarization we combine the helicity angle distributions for the three D0 submodes in the B signal region (defined by jMB \Gamma 5:280j ! 0:006 GeV) and then subtract the helicity angle distribution of the scaled sideband (defined by 5:200 ! MB ! 5:260 GeV). We fit the resulting helicity angle distributions to the functional form given in equation (6).

From the fit to the D\Lambda + helicity angle distribution, we find \Gamma L=\Gamma = (85 \Sigma 8)%, and from the corresponding fit to the ae helicity angle distribution we find \Gamma L=\Gamma = (97 \Sigma 8)%. The results of the fits [29] are shown in Fig. 16(a) and (b) . The statistical error can be reduced by taking advantage of the correlation between the two helicity angles (See Fig. 17). The most precise result can be extracted by performing an unbinned two dimensional likelihood fit to the joint (cos \Theta D\Lambda ; cos \Theta ae) distribution. This method gives

(\Gamma L=\Gamma ) _B0!D\Lambda +ae\Gamma = (93 \Sigma 5 \Sigma 5)% (9) The systematic error contains the uncertainties due to the background parameterization and the detector acceptance.

VI. MEASUREMENTS OF D\Lambda \Lambda FINAL STATES In addition to the production of D and D\Lambda mesons, the charm quark and spectator antiquark can also hadronize as a D\Lambda \Lambda meson. The D\Lambda \Lambda 0(2460) has been observed experimentally and identified as the J P = 2+ state, while the D\Lambda \Lambda 0(2420) has been identified as the 1+ state [14]. These states have full widths of approximately 20 MeV. Two other states, a 0+ and another 1+ are predicted but have not yet been observed. Presumably this is due to their large intrinsic widths. There is evidence for D\Lambda \Lambda production in semileptonic B decays [30,31], and it is possible that the D\Lambda \Lambda can also be seen in hadronic B decays.

In order to search for D\Lambda \Lambda mesons from B decays we first study the final states B\Gamma ! D\Lambda +ss\Gamma ss\Gamma and B\Gamma ! D\Lambda +ss\Gamma ss\Gamma ss0. In the latter case we require that one ss\Gamma ss0 invariant mass is consistent with the ae\Gamma mass. The reactions B\Gamma ! D\Lambda +ss\Gamma ss\Gamma and B\Gamma ! D\Lambda +ss\Gamma ss\Gamma ss0 have not been observed clearly in past experiments [3,6] and are not expected to occur in a simple picture in which the c quark plus spectator antiquark form a D\Lambda . We combine the D\Lambda + with a ss\Gamma to form a D\Lambda \Lambda candidate. D\Lambda \Lambda candidates lying within one full width of the nominal mass of either a D\Lambda \Lambda 0(2420) or a D\Lambda \Lambda 0(2460) are then combined with a ss\Gamma or ae\Gamma to form a B\Gamma candidate.

We have also searched for D\Lambda \Lambda production in the channels D+ss\Gamma ss\Gamma and D0ss\Gamma ss+. Since D\Lambda \Lambda 0(2420) ! Dss is forbidden, we only search for D\Lambda \Lambda 0(2460) in the Dssss final state. For this subset of modes, we require the Dss mass to lie within \Sigma 1.5 \Gamma (\Sigma 28 MeV) of the nominal D\Lambda \Lambda (2460) mass.

Figs. 18 and 21 show the B mass distributions for combinations of D\Lambda \Lambda 0(2460) or D\Lambda \Lambda 0(2420), and ss\Gamma or ae\Gamma . In the D\Lambda \Lambda 0(2420)ss\Gamma mode, there is an excess of 8.5 events in the B peak region with an estimated background of 1:5 events. The probability that the excess is due to a background fluctuation is 4 \Theta 10\Gamma 6 which indicates that this is a significant signal. In this channel we give the branching ratio in Table VII, while for the other five combinations where the probability that the observed events are the result of a background fluctuation is larger, we give upper limits. Our results are consistent with theoretical predictions [32,33] based on the factorization hypothesis (Table VIII).

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We have also investigated the final states D\Lambda +ss\Gamma ss\Gamma (D+ss\Gamma ss\Gamma and D0ss+ss\Gamma ) where the D(\Lambda ) and a charged pion are not constrained to lie in any particular mass interval. To observe these signals, the background from the final states D(\Lambda )ae\Gamma must be suppressed. Since the D(\Lambda )ae\Gamma final state is highly polarized (see section V B), it is possible that the slow ss0 from the ae\Gamma decay can be exchanged for a slow charged pion from the decay of the other B meson. To eliminate this background, we make cuts on the cosines of the helicity angles, \Theta D\Lambda and \Theta D\Lambda \Lambda , where \Theta D\Lambda \Lambda is calculated for the D\Lambda +ss\Gamma slow system with ss\Gamma slow being the slower ss\Gamma of the two. This helicity angle is defined as the angle between the B and the fast ss\Gamma in the rest frame of D\Lambda +ss\Gamma slow system. We require cos \Theta D\Lambda \Lambda ! 0:8 and j cos \Theta D\Lambda j ! 0:7. For the B ! Dssss modes, a similar cut, cos \Theta ae ! 0:7, is made using the ssss system. In Figs. 20 and 19, we show the MB candidate mass distributions. There is a significant signal in B ! D\Lambda +ss\Gamma ss\Gamma . For the other two modes we quote upper limits in Table VII.

VII. EXCLUSIVE B ! CHARMONIUM DECAYS

A. Introduction In B decays to charmonium the c quark from the b combines with a _c quark from the virtual W \Gamma to form a charmonium state. This process is described by the color suppressed diagram shown in Fig. 1(b). By comparing B meson decays to different final states with charmonium mesons the dynamics of this decay mechanism can be investigated. The decay modes _B0 ! K0 and _B0 ! 0K0 are of special interest since the final states are CP eigenstates which can be used to determine one of the three CP violating angles accessible to study in B decays. It is also possible to use the _B0 ! K\Lambda 0 decay (where K\Lambda 0 ! K0S ss0) to measure this CP asymmetry. However, this final state has even CP if the orbital angular momentum L, between the and K\Lambda 0 is 0 or 2, and odd CP for L = 1. If both CP states are present the CP asymmetry will be diluted. A measurement of CP violation in this channel may be possible if one of the CP states dominates, or if a detailed moments analysis of the various decay components is performed [34]. We present a measurement of the polarization in the decay _B0 ! _K\Lambda 0 which allows us to determine the fractions of the two CP states.

B. Branching Ratios B meson candidates are formed by combining a charmonium and a strange meson candidate. We reconstruct K0S decays into ss+ss\Gamma pairs which have vertices displaced from the beam axis by greater than 5 mm. Only the K+ss\Gamma channel is used to form K\Lambda 0 mesons while K\Lambda \Gamma candidates are reconstructed in the decay channels K0S ss\Gamma and K\Gamma ss0. The Kss invariant mass must be within \Sigma 75 MeV of the nominal K\Lambda mass. In the B\Gamma ! K\Lambda \Gamma , K\Lambda \Gamma ! K\Gamma ss0 mode, only the half of the K\Lambda \Gamma helicity angle distribution with a fast ss0 is used. The and 0 candidates decaying into lepton pairs were kinematically constrained to the known mass values in order to improve the resolution on \Delta E. Using the procedures described in section III we reconstruct B meson candidates and obtain the beam constrained mass distributions shown in Figs. 22, 23 and 24. The corresponding branching ratios are listed in Table IX.

13

The systematic errors in the branching ratio measurements include contributions from number of B mesons (2.5%), tracking efficiencies (2% per charged track), ss0 detection efficiency (5%), dE=dx efficiency (2% per identified track), lepton detection efficiency (2% per lepton), Monte Carlo statistics (1.5 - 6%), the leptonic branching ratio (4.2%) and the branching ratios for

0 and O/

c1 decays.

The results for the B\Gamma and B0 decay modes can be combined using isospin symmetry to

determine the vector to pseudoscalar production ratio

B(B ! K\Lambda )B

(B ! K) = 1:71 (10)

The revised Bauer-Stech-Wirbel (BSW) model [8] predicts a value of 1.61 for this quantity. This model uses the ratio of B ! K\Lambda /B ! K form factors determined from harmonic oscillator wavefunctions and assumes that the factorization hypothesis is valid for internal spectator decays.

C. Polarization in K\Lambda After integration over the azimuthal angle between the and the K\Lambda decay planes, the angular distribution in B ! K\Lambda decays can be written as [28]

d2\Gamma d cos \Theta d cos \Theta K\Lambda /

1 4 sin

2 \Theta K

\Lambda (1 + cos2 \Theta )(jH+1j2 + jH\Gamma 1j2) + cos2 \Theta K\Lambda sin2 \Theta jH0j2;

(11) where the K\Lambda helicity angle \Theta K\Lambda is the angle between the kaon direction in the K\Lambda rest frame and the K\Lambda direction in the B rest frame, \Theta is the corresponding helicity angle, and the H\Sigma 1;0 are the helicity amplitudes.

There are 29 _B0 ! K\Lambda 0 candidates and 13 B\Gamma ! K\Lambda \Gamma candidates. After correcting for detector acceptance, we perform an unbinned maximum likelihood fit to the double differential distribution described in the equation above. The fit gives the fraction of longitudinal polarization in B ! K\Lambda as`

\Gamma L

\Gamma 'B!K\Lambda = 0:80 \Sigma 0:08 \Sigma 0:05 (12)

The systematic error in this measurement is dominated by the uncertainty in the acceptance. The efficiency corrected distributions for each of the helicity angles cos \Theta and cos \Theta K\Lambda are shown in Fig. 25.

This result can be compared to the theoretical predictions of Kramer and Palmer [66] which depends on the unmeasured B ! K\Lambda form factor. Using the BSW model to estimate the form factor, they find \Gamma L=\Gamma = 0:57. Using Heavy Quark Effective Theory (HQET) and experimental measurements of the D ! K\Lambda form factor, they obtain \Gamma L=\Gamma = 0:73.

The decay mode B ! K\Lambda may not be completely polarized, but it is dominated by a single CP eigenstate (CP = \Gamma 1 produced with L = 1). This mode will therefore be useful for measurements of CP violation.

14

VIII. SEARCH FOR COLOR SUPPRESSED DECAYS We search for B decays which can occur via an internal W -emission graph, but which do not lead to final states with charmonium [39]. One expects that these decays will be suppressed relative to decays which occur via the external W -emission graph. For the internal graph the colors of the quarks from the virtual W must match the colors of the c quark and the accompanying spectator antiquark. In a simple picture, one expects that the suppression factor should be about 1=18 for decays involving ss0, ae0 and ! mesons [36], but in heavy quark decays the effects of gluons cannot be neglected. These decays can be used to test QCD based calculations [8] which predict suppression factors of order 1=50. If color-suppressed B decay modes are not greatly suppressed then these modes could be useful for CP violation studies [38].

We search for color-suppressed decay modes of B mesons which contain a single D meson (or D\Lambda meson) in the final state. The relevant color-suppressed modes are given in Table X. We use the decay modes j ! flfl, ! ! ss+ss\Gamma ss0 and j

0 ! jss+ss\Gamma , followed by j ! flfl [37].

For decays of a pseudoscalar meson into a final state containing a pseudoscalar and a vector meson, a helicity angle cut of j cos \Theta V j ? 0:4 is used [40]. No convincing signals were found in the decay modes that were examined. Upper limits on the branching ratios for color-suppressed modes are given in Table X. The 90% confidence level upper limits are calculated using the prescription described by the PDG [41]. These upper limits take into account the systematic uncertainty in the background level as well as the systematic uncertainty in the detection efficiency. In Figs. 26, 27, and 28 we show the fitted distributions for the color-suppressed modes with the fit superimposed on each plot. Upper limits on the ratios of color-suppressed modes to normalization modes are given in Table XI.

IX. THE B\Gamma \Gamma _B0 MASS DIFFERENCE We now proceed to measurements of the _B0 and B\Gamma masses and the mass difference between them. For this analysis we use the decays B\Gamma ! K\Gamma , _B0 ! K\Lambda 0, B\Gamma ! D0ss\Gamma , B\Gamma ! D0ae\Gamma , B\Gamma ! D\Lambda 0ss\Gamma , B\Gamma ! D\Lambda 0ae\Gamma , _B0 ! D+ss\Gamma , _B0 ! D+ae\Gamma , _B0 ! D\Lambda +ss\Gamma , and_ B0 ! D\Lambda +ae\Gamma for which the signal to background ratio is large. For the decays B\Gamma ! D0ss\Gamma and B\Gamma ! D0ae\Gamma only the D0 ! K\Gamma ss+ mode is used. The MB distributions for the sum of these modes are shown in Fig. 29. We have a total of 362 B\Gamma and 340 _B0 signal events. The data are fitted with a Gaussian of fixed width (2:7 MeV) determined by Monte Carlo simulation. The width is assumed to be the same for all modes. The fitted masses for each mode and their statistical errors are given in Table XII. We apply a correction for initial state radiation as described in Ref. [42], of magnitude -1.1\Sigma 0.5 MeV, to arrive at the final values for the B\Gamma and _B0 masses of 5278:8 \Sigma 0:2 \Sigma 0:5 \Sigma 2:0 MeV and 5279:2 \Sigma 0:2 \Sigma 0:5 \Sigma 2:0 MeV, respectively. The first systematic error results from the uncertainty in the initial state radiation correction. The second systematic error is due to the uncertainty in the absolute value of the CESR energy scale, which is determined by calibrating to the known \Upsilon (1S) mass [43].

The mass difference is determined to be 0:41\Sigma 0:25\Sigma 0:19 MeV. This is more accurate than the masses themselves because the beam energy uncertainty cancels, as do many systematic

15

errors associated with the measurement errors on the charged tracks and ss0 mesons. The remaining systematic error is found by making a number of tests of the stability of our result.

A systematic shift of 0.12 MeV is produced by using different background shapes for the B\Gamma and _B0 modes [44]. We have also investigated the effect of changing the photon energy calibration. A change of 0.5%, the quoted systematic error, results in a 0.15 MeV change in the fitted B mass in both the D\Lambda +ae\Gamma and D\Lambda 0ae\Gamma final states. This effect almost completely cancels in the mass difference measurement where it contributes an error of !0.03 MeV. This is because the shift of the ss0 energy in the ae\Gamma cancels in the difference leaving only the shift of the energy of the slow ss0 from the D\Lambda 0 which is uncorrelated with the direction of the B meson. A similar test where we scale the measured momentum of the slow pion from the D\Lambda + by 5 %, also does not affect the mass difference for the same reason.

We have also checked the stability of the result with changes in event samples. For example, we have used only half of the cos \Theta ae distributions in B ! D(\Lambda )ae modes and we have used less stringent lepton identification criteria for the B ! K \Gamma mode. We estimate a systematic of 0:15 MeV from these studies.

The different sources of systematic errors are listed in Table XIII and are combined in quadrature. We compare our result with previous results in Table XIV.

There are several models which predict the isospin mass difference to be between 1.2 and 2.3 MeV which are larger than the value reported here [45]. However, Goity and Hou (\Gamma 0:5 \Sigma 0:6 MeV) and Lebed (0:89 MeV) can accomodate this small mass difference in their models [46].

X. TESTS OF THE FACTORIZATION HYPOTHESIS

A. Introduction Our large data sample has made possible the precise branching ratio and polarization measurements discussed above. In the following sections we address many important questions about non-leptonic B meson decay.

By comparing rates and polarizations of semileptonic and hadronic decays we can perform tests of the factorization hypothesis, which is the basis of most theoretical treatment of hadronic B decays. In analogy to semileptonic decays, where the amplitude factorizes into the product of a leptonic and hadronic current since leptons are not sensitive to the strong interaction, it is possible that two body decays of B mesons which occur via the external spectator process may be expressed theoretically as the product of two independent hadronic currents, one describing the formation of a charm meson and the other the hadronization of the _ud (or _cs) system from the virtual W \Gamma .

There are few models of hadronic B decays. Those which exist predict widths of twobody decays and assume the validity of the factorization hypothesis. Although factorization fails in many D decays [47], it is hoped that factorization will be a better approximation in B decays due to the larger energy release present [48].

If factorization is valid, then heavy quark effective theory, henceforth referred to as HQET [49], could provide a reliable, model independent framework for the calculation of properties of non-leptonic B meson decays. In addition, if factorization holds, then measurements

16

of non-leptonic B decays may be used to extract fundamental parameters of the Standard Model. For instance the CKM matrix element Vub can be determined from B0 ! ss+ss\Gamma or_ B0 ! D\Gamma s ss+, and the decay constant fDs can be determined from _B0 ! D\Gamma s D\Lambda +.

B. Branching Ratio Tests Assuming factorization, the effective Hamiltonian Eq. (2) for a non-leptonic B decay can be written as a product of two hadronic currents. Consider the case of _B0 ! D\Lambda +h\Gamma , where h is a hadron. The amplitude for this reaction is

A = GF =p2 VcbV \Lambda udhh\Gamma (p)j( _du)j0ihD\Lambda +j(_cb)j _B0i (13) where Vud is the well measured CKM factor from the W \Gamma ! _ud vertex. The first hadron current, which creates the h\Gamma from the vacuum, is related to the decay constant fh, and is known for h = ss; ae. We have

hh\Gamma (p)j( _du)j0i = \Gamma ifhp_; (14) where p_ is the h\Gamma four momentum. The other hadron current can be found from semileptonic_ B0 ! D\Lambda +`\Gamma _*` decays. Here the amplitude is the product of a lepton current and the hadron current that we seek to insert in Eq. (13). Factorization can be tested experimentally by verifying whether the relation

\Gamma i _B0 ! D\Lambda +h\Gamma j d\Gamma dq2 i _B

0 ! D\Lambda +l\Gamma _*ljfifififi

q2=m2h

= 6ss2c21f 2h jVudj2; (15)

is satisfied, where q2 is the four momentum transfer from the B meson to the D\Lambda meson. Since q2 is also the mass of the lepton-neutrino system, by setting q2 = m2h we are simply requiring that the lepton-neutrino system has the same kinematic properties as the h\Gamma in the hadronic decay. The c21 term accounts for hard gluon corrections. Here we use c1 = 1:1 \Sigma 0:1 as deduced from perturbative QCD. The error in c1 reflects the uncertainty in the mass scale at which the coefficent c1 should be evaluated [50]. For the case where h\Gamma = ss\Gamma and c1=1, equation 15 was found to be satisfied by Bortoletto and Stone [51]. In the following the left hand side of Eq. (15) will be denoted Rexp and the right hand side will be denoted RTheo.

This type of factorization test can also be performed using _B0 ! D\Lambda +h\Gamma decays where h\Gamma = ae\Gamma or a1(1260)\Gamma . For the ae\Gamma case Eq. (15) becomes:

R = \Gamma ( _B

0 ! D\Lambda +ae\Gamma )

d\Gamma dq2 (B ! D

\Lambda l *)jq2=m2

ae

= 6ss2c21f 2ae jVudj2 (16)

where the semileptonic decay is evaluated at q2 = m2ae = 0:60 GeV2. The decay constant on the right hand side of this equation can be determined from e+e\Gamma ! ae0 or from o/ decays. The first method leads to fae = 215 \Sigma 4 MeV. Taking into account the ae width, Pham and Vu [52] find that \Gamma (o/ \Gamma ! *ae\Gamma ) = 0:804G2F =16ss jV 2udjM 3o/ f 2ae which gives fae = 212:0 \Sigma 5:3

17

MeV [53]. We take the first value. We also perform this test for _B0 ! D\Lambda +a\Gamma 1 where we use fa1 = 205 \Sigma 16 MeV [33]. To derive numerical predictions for branching ratios, we must interpolate the observed differential q2 distribution [54] for _B ! D\Lambda ` * to q2 = m2ss, m2ae, and m2a1, respectively. Until this distribution is measured more precisely theoretical models must be used for the slope of the distribution. Thus the results are stated below for different models. Fortunately, the spread in the theoretical models which describe _B ! D\Lambda ` * is small (see Fig. 30).

We now have all the required ingredients [55] for the test with decay rates (see Table XV). Using the extrapolation of the q2 spectrum [56] from the WSB model as the central value, we obtain from Eqs. (15) and (16) the results given in Table XVI.

If we form ratios of branching fractions some of the systematic uncertainties on Rexp will cancel, as does the QCD correction c1 in Rtheor. For example in the case of D\Lambda +ae\Gamma /D\Lambda +ss\Gamma , the expectation from factorization is given by Rtheor(ae)/Rtheor(ss) times the ratio of the semileptonic branching ratios evaluated at the appropriate q2 values. In Table XVII we show the comparison of the data, the expectation from factorization as defined above and two theoretical predictions of Bauer, Stech and Wirbel (BSW) [64], and Reader and Isgur (RI) [33]. From the measurements described above, we find that at the present level of precision, there is agreement between experiment and the expectation from factorization for the q2 range: 0 ! q2 ! m2a1.

C. Factorization and Angular Correlations More subtle tests of the factorization hypothesis can be performed by examing the polarization in B meson decays into two vector mesons. This idea was suggested by K"orner and Goldstein [57]. Again, the underlying principle is that hadronic decays are analogous to the appropriate semileptonic decays evaluated at a fixed value of q2. For instance, the ratio of longitudinal to transverse polarization (\Gamma L=\Gamma T ) in _B0 ! D\Lambda +ae\Gamma should be equal to the corresponding ratio for B ! D\Lambda l\Gamma _* evaluated at q2 = mae2 = 0:6 GeV2.

\Gamma L \Gamma T ( _B

0 ! D\Lambda +ae\Gamma ) = \Gamma L\Gamma

T (B ! D

\Lambda l\Gamma _*L)j

q2=m2ae (17)

The advantage of this method is that it is not affected by QCD corrections [58].

For B ! D\Lambda l * decay, longitudinal polarization dominates at low q2. Near q2 = q2max, by contrast, transverse polarization dominates. There is a simple physical argument for the behaviour of the form factors near these two kinematic limits. Near q2 = q2max, the D\Lambda is almost at rest. Its small velocity is uncorrelated with the D\Lambda spin, so all three possible D\Lambda helicities are equally likely. As q2 ! q2max we expect \Gamma T =\Gamma L = 2. At q2 = 0, the D\Lambda has the maximum possible momentum, while the lepton and neutrino are collinear and travel in the direction opposite to the D\Lambda with their helicities aligned to give Sz = 0. Thus, near q2 = 0 longitudinal polarization is dominant.

For _B0 ! D\Lambda +ae\Gamma , Rosner predicts 88% longitudinal polarization from the argument described above [59]. Similar results can be extracted from the work of Neubert [60] and Kramer et al. [68]. Fig. 31 shows Neubert's result for the production of transversely and

18

longitudinally polarized D\Lambda mesons in B ! D\Lambda l * decays. Using this figure we find \Gamma L=\Gamma to be approximately 85% for q2 = mae2 = 0:6, which agrees well with Rosner's prediction [59].

The agreement between these predictions and the experimental result (see section V B)

\Gamma L=\Gamma = (93 \Sigma 5 \Sigma 5)% (18) supports the factorization hypothesis in hadronic B meson decay for q2 values up to m2ae.

XI. TESTS OF SPIN SYMMETRY IN HQET If the factorization hypothesis holds, then certain hadronic B meson decay modes can be used to test the spin symmetry of HQET. In this theory the effect of the heavy quark magnetic moment does not enter to lowest order [61] , so it is expected that

\Gamma ( _B0 ! D+ss\Gamma ) = \Gamma ( _B0 ! D\Lambda +ss\Gamma ) (19) and

\Gamma ( _B0 ! D+ae\Gamma ) = \Gamma ( _B0 ! D\Lambda +ae\Gamma ): (20) After correcting for phase space and deviations from heavy quark symmetry, one expects that B( _B0 ! D+ss\Gamma ) = 1:03 B( _B0 ! D\Lambda +ss\Gamma ) and B( _B0 ! D+ae\Gamma ) = 0:89 B( _B0 ! D\Lambda +ae\Gamma ). A separate calculation by Blok and Shifman using a QCD sum rule approach predicts thatB

( _B0 ! D+ss\Gamma ) = 1:2 B( _B0 ! D\Lambda +ss\Gamma ) due to the presence of non-factorizable contributions [62]. From our data we find

B( _B0 ! D+ss\Gamma )B

( _B0 ! D\Lambda +ss\Gamma ) = 1:12 \Sigma 0:19 \Sigma 0:24 (21)

and B

( _B0 ! D+ae\Gamma )B ( _B0 ! D\Lambda +ae\Gamma ) = 1:10 \Sigma 0:14 \Sigma 0:28 (22)

The contribution in this ratio from the systematic error on the detection efficiency is reduced to 5% for these two cases. Both ratios of branching fractions are consistent with the expectation from HQET spin symmetry as well as the prediction from Blok and Shifman [62].

Mannel et al. [61], also observe that by using a combination of HQET, factorization, and data on B ! D\Lambda `* from CLEO and ARGUS they can obtain model dependent predictions for B( _B0 ! D+ae\Gamma )=B( _B0 ! D+ss\Gamma ). With three different parameterizations of the B ! D form factor [63] this ratio is predicted to be 3.05, 2.52, or 2.61.

From the measurements of the branching ratios we obtain

B( _B0 ! D+ae\Gamma )B

( _B0 ! D+ss\Gamma ) = 2:8 \Sigma 0:5 \Sigma 0:2 (23)

The systematic errors from the D branching fractions and the tracking efficiency cancel in this ratio. Thus we find good agreement with the prediction from HQET combined with factorization.

19

XII. DIRECT AND INDIRECT EFFECTS OF THE COLOR SUPPRESSED

AMPLITUDE

A. Introduction In the QCD treatment described by equations (1) and (2) it is difficult to take into account the effects of multiple soft gluon emission analytically. Instead, in the phenomenological BSW approach [64] two undetermined coefficients are assigned to the effective charged current, a1(_), and the effective neutral current, a2(_), parts of the B decay Hamiltonian. These coefficients were determined from a fit to a subset of the experimental data on charm decays. With these values the decay rates for a large number of non-leptonic decays can then be calculated using the factorization hypothesis, and model dependent hadron form factors. We can relate a1(_) and a2(_) to the QCD coefficients c1(_) and c2(_) by a1 = c1 + ,c2 and a2 = c2 + ,c1 where , = 1=Ncolor. The values a1(m2c ) = 1:3 and a2(m2c) = \Gamma 0:55 which give the best fit to the experimental data on charm decay correspond to 1=Ncolor , 0 [8]. However, there is no rigorous theoretical justification for this choice of Ncolor [65].

In the decays of charmed mesons the effect of color suppression is obscured by the effects of final state interactions (FSI) and soft gluon effects which enhance W exchange diagrams. For instance, Table XVIII gives ratios of several charmed meson decay modes with approximately equal phase space factors where the mode in the numerator is color suppressed while the mode in the denominator is an external spectator decay [67]. These modes are clearly not suppressed. However, the following decay appears to be suppressed.

B(D0 ! _K0ae0)B

(D0 ! K\Gamma ae+) = 0:08 \Sigma 0:04 (24)

In contrast to the charm sector where the mechanism of color suppression is obscured, one expects to find in B meson decays a simple and consistent pattern of color suppression. Partly, it is expected that color suppression is more effective at the b quark mass scale than the charm quark mass scale due to the evolution of the strong coupling constant ffs to smaller values. Using the BSW model and extrapolating from q2 = m2c to q2 = m2b using the values from charm decays, gives the predictions a1(m2b ) = 1:1 and a2(m2b) = \Gamma 0:24 for B decays. Another approach using the factorization hypothesis, HQET and model dependent form factors has been suggested by C. Reader and N. Isgur (RI model) [33]. In this approach, a1 and a2 are determined from QCD (with 1=Ncolor = 1=3) and color suppressed B decays are expected to occur at about 1=1000 the rate of unsuppressed decays. Observation of these decays at a much greater level would indicate the breakdown of the factorization hypothesis. In section VIII we obtained upper limits for color suppressed B decays with a D0 or D\Lambda 0 meson in the final state. In Table XIX these results are compared to prediction of the BSW and the RI model.

In contrast to charm decays, color suppression seems to be operative in hadronic decays of B mesons. The limits on the color suppressed modes with D0(\Lambda ) and neutral mesons are still above the level expected in the model of Bauer, Stech and Wirbel. However, the limit on _B0 ! D0ss0 disagrees with Terasaki's prediction [70] that B( _B0 ! D0ss0) ss 1:8 B( _B0 ! D+ss\Gamma ). To date, the only color suppressed B meson decay modes which have been observed are final states which contain charmonium mesons e.g. B ! K and B ! K\Lambda [71].

20

B. Determination of ja1j, ja2j and the relative sign of (a2=a1) In the BSW model [8,64] , the branching fractions of the B0 normalization modes are proportional to a21 while the branching fractions of the B ! decay modes depend on a22 (Table XX [8]). A fit to the branching ratios that we have measured for the modes_ B0 ! D+ss\Gamma , D+ae\Gamma , D\Lambda +ss\Gamma and D\Lambda +ae\Gamma yields

ja1j = 1:15 \Sigma 0:04 \Sigma 0:05 \Sigma 0:09 (25) and a fit to the modes with mesons in the final state gives

ja2j = 0:26 \Sigma 0:01 \Sigma 0:01 \Sigma 0:02 (26) The first systematic error on ja1j and ja2j includes the experimental uncertainties from the charm or charmonium branching ratios, tracking efficiency, background shapes and the value of jVcbj, but does not include the theoretical uncertainties. There is a second uncertainty due to the B meson production fractions and lifetimes. These are constrained by the value of (f+o/+=f0o/0) determined from the CLEO II [72] measurement of B(B\Gamma ! D\Lambda 0l\Gamma *)=B( _B0 ! D\Lambda +l\Gamma *) = 1:20 \Sigma 0:20 \Sigma 0:19.

The comparison of B\Gamma and _B0 modes can be used to distinguish between the two possible choices for the sign of a2 relative to a1. The BSW model, Ref. [8] predicts the following ratios:

R1 = B(B

\Gamma ! D0ss\Gamma )

B( _B0 ! D+ss\Gamma ) = (1 + 1:23a2=a1)

2 (27)

R2 = B(B

\Gamma ! D0ae\Gamma )

B( _B0 ! D+ae\Gamma ) = (1 + 0:66a2=a1)

2 (28)

The numerical factor which multiplies a2=a1 is proportional to the ratio of B ! D(\Lambda ) to B ! ss(ae) form factors as well as the ratio of the ss(ae) meson to D meson decay constants. We assume fD = fD\Lambda = 220 MeV [69]. Only the B ! D\Lambda form factor and the ss(ae) meson decay constant have been measured experimentally.

Similarly, we define

R3 = B(B

\Gamma ! D\Lambda 0ss\Gamma )

B( _B0 ! D\Lambda +ss\Gamma ) = (1 + 1:29a2=a1)

2 (29)

R4 = B(B

\Gamma ! D\Lambda 0ae\Gamma )

B( _B0 ! D\Lambda +ae\Gamma ) ss (1 + 0:75a2=a1)

2 (30)

Table XXI shows a comparison between the experimental results and the two allowed solutions in the BSW model. In these ratios, the systematic errors due to detection efficiency are reduced. In the ratios R3 and R4 the D0 ! K\Gamma ss+ branching ratio error does not contribute to the systematic error.

It is important to note that the determination of the sign of a2=a1 depends on assumptions about the relative production of B+ and B0 mesons at the \Upsilon (4S) resonance, f+ and f0, as

21

well as their lifetimes, o/+ and o/0. A least squares fit to the above ratios using the CLEO II value for (f+o/+=f0o/0) [72] gives a2=a1 = 0:23 \Sigma 0:04 \Sigma 0:04 \Sigma 0:10 where we have ignored uncertainties in the theoretical predictions for R1 through R4. The second systematic error is due to the uncertainty in (f+o/+=f0o/0). As this ratio increases, the value of a2=a1 decreases. The allowed range of (f+o/+=f0o/0) excludes a negative value of a2=a1. Other uncertainties in the magnitude of fD and the B ! ss form factor can change the magnitude of a2=a1 but not its sign. This result is consistent with the value of a2 determined from the fit to the B ! decay modes. It disagrees with the theoretical extrapolation from data on charmed meson decay in the BSW model [73] which predicts a negative value for a2=a1.

XIII. CONCLUSIONS We have presented new measurements of B branching ratios, resonant substructure and masses. More accurate branching ratios are given for many modes. The modes B ! D\Lambda ae\Gamma and B ! D\Lambda a\Gamma 1 are clearly seen for the first time.

Using a subset of 702 B meson decays reconstructed in channels with good signal to background ratios we have made a precise measurement of the _B0 \Gamma B\Gamma mass difference of 0:41 \Sigma 0:25 \Sigma 0:19 MeV.

We have carried out an extensive series of tests of the factorization hypothesis including comparisons of rates for D\Lambda +h\Gamma (where h\Gamma = ss\Gamma ; ae\Gamma , or a\Gamma 1 ) with rates for D\Lambda +l\Gamma _* at q2 = M 2h , as well as comparisons of the polarizations in D\Lambda +ae\Gamma with D\Lambda +`\Gamma _*`. In all cases the factorization hypothesis is consistent with the data.

We have made improved measurements of branching ratios of two-body decays with a ,

0 or O/

c meson in the final state. The decay B ! K\Lambda is strongly polarized with

\Gamma L=\Gamma = 0:80 \Sigma 0:06 \Sigma 0:08. Therefore this mode will be useful for measuring CP violation.

A search for color suppressed decays with a charmed meson and light neutral hadron in the final state shows no positive evidence for such processes. The most stringent limit,B

( _B0 ! D0ss0)=B( _B0 ! D+ss\Gamma ) ! 0:09, is still above the level where these color suppressed B decays are expected in most models.

The observation of B ! modes shows that color suppressed decays are present. Using only exclusive B ! decays we find a value of the BSW parameter ja2j = 0:26\Sigma 0:01\Sigma 0:01\Sigma 0:02. We also report a new value for the BSW parameter ja1j = 1:15 \Sigma 0:04 \Sigma 0:05 \Sigma 0:09. Comparing B+ and B0 decays, we find a2=a1 = 0:23 \Sigma 0:04 \Sigma 0:04 \Sigma 0:10. We have shown that the sign of a2=a1 is positive, in contrast to what is found in charm decays.

ACKNOWLEDGMENTS We thank N. Cabibbo, Nathan Isgur, W.S. Hou, Volker Rieckert, and J. L. Rosner for useful discussions. We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. J.P.A. and P.S.D. thank the PYI program of the NSF, I.P.J.S. thanks the YI program of the NSF, T.E.B. thanks the University of Hawaii, G.E. thanks the Heisenberg Foundation, K.K.G. thanks the SSC Fellowship program of TNRLC, K.K.G., H.N.N., J.D.R., T.S. and H.Y. thank the OJI program of DOE and P.R.

22

thanks the A.P. Sloan Foundation for support. This work was supported by the National Science Foundation and the U.S. Dept. of Energy.

23 REFERENCES [1] CLEO Collaboration, S. Behrends et al., Phys. Rev. Lett. 50, 881 (1983). [2] CLEO Collaboration, M.S. Alam et al., Phys. Rev. D 36, 1289 (1987). [3] CLEO Collaboration, D. Bortoletto et al., Phys. Rev. D 45, 21(1992). [4] ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 185, 218 (1987). [5] ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 215, 424 (1988). [6] ARGUS Collaboration, H. Albrecht et al., Z. Phys. C 48, 543 (1990). [7] We make the approximation that Vud; Vcs ss 1: [8] M. Neubert, V. Riekert, Q. P. Xu and B. Stech in Heavy Flavours, edited by A. J. Buras

and H. Lindner (World Scientific, Singapore, 1992). [9] J. Bjorken, Nucl. Phys. B (Proc. Suppl) 11, 325 (1989). [10] Y. Kubota et al., Nucl. Inst. and Meth. A 320, 66 (1992); the crystal performance is

described in R. Morrison et al., Phys. Rev. Lett. 67, 1696 (1991). [11] CLEO collaboration, D. Akerib et al., Phys. Rev. Lett. 71, 3070 (1993). [12] Mark III collaboration, J. Adler et al., Phys. Rev. Lett. 60, 89 (1988). [13] The systematic uncertainty from the track reconstruction in D0 ! K\Gamma ss+ is common

to this paper and to ref. [11], and is only included in the systematic error on the B branching fraction. To avoid counting this systematic error twice, we use the value ofB

(D0 ! K\Gamma ss+) = (3:91 \Sigma 0:08 \Sigma 0:07)% which does not include the tracking systematic error. [14] Particle Data Group, K. Hikasa et al., Phys. Rev. D 45, (1992). [15] CLEO Collaboration, M. Daoudi et al., Phys. Rev. D 45, 3965 (1992). [16] CLEO Collaboration, F. Butler et al., Phys. Rev. Lett. 69, 2041 (1992). [17] CLEO Collaboration, D. Bortoletto et al., Phys. Rev. Lett. 69, 2046 (1992). [18] Mark III Collaboration, D. Coffman et al., Phys. Rev. D 68, 282 (1992). [19] This requirement has an efficiency of 86% while reducing the background by a factor of

two. [20] G. Fox and S. Wolfram, Phys. Rev. Lett. 23, 1581 (1978). [21] G. Hanson et al., Phys. Rev. Lett. 35, 1609 (1975) and S.L. Wu and G. Zobernig, Z.

Phys. C. 2, 107 (1979). [22] The resolution in beam constrained mass has a weak dependence on the decay channel.

It varies between 2.6 MeV to 3.3 MeV. [23] The lowest fraction is for the mode _B0 ! D\Lambda +ae\Gamma while the highest fraction is for the

mode B\Gamma ! D0ss\Gamma . [24] For the case of B\Gamma ! D0ae\Gamma , D0 ! K\Gamma ss+ss0, we use only half of the helicity angle

distribution used for the other modes (cos \Theta ae ? 0:4 instead of j cos \Theta aej ? 0:4). [25] The results of the analysis using only the forward hemisphere (cos `ae ? 0:4) areB

( _B0 ! D0ae\Gamma ) = 1:29 \Sigma 0:14 \Sigma 0:11 and B(B\Gamma ! D+ae\Gamma ) = 0:97 \Sigma 0:16 \Sigma 0:14. [26] We consider two models: non-resonant B ! Dss\Gamma ss0 and B ! D\Lambda \Lambda (2460)ss\Gamma . Both give

very similar ss\Gamma ss0 mass spectra and comparable limits on the non-rho contamination in the signal region. [27] Also note that the corrected distribution is symmetric, indicating that the efficiency

correction is reasonable (37:0 \Sigma 5:5 entries in the forward hemisphere and 35:7 \Sigma 5:4 entries in the backward hemisphere).

24

[28] J. D. Richman, California Institute of Technology report CALT-68-1231. [29] The corrected distribution for _B0 ! D\Lambda +ae\Gamma is symmetric, indicating that the efficiency

correction is reasonable (45:6 \Sigma 6:7 entries in the forward hemisphere of D\Lambda + helicity angle and 39:3 \Sigma 6:3 entries in the backward hemisphere of D\Lambda + helicity angle). [30] CLEO Collaboration, S. Henderson et al., Phys. Rev. D 45, 2212 (1992). [31] ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 249, 359 (1990) and H. Albrecht

et al., Z. Phys. C 57, 553 (1993). [32] P. Colangelo, G. Nardulli, N. Paver Phys. Lett. B 303, 152, 1993. [33] C. Reader and N. Isgur, Phys. Rev. D 47, 1007, 1993. The authors emphasize that their

results for color suppressed decay have large theoretical uncertainties and are order of magnitude estimates rather than predictions. [34] I. Dunietz et al. , Phys. Rev. D 43, 2193 (1991). [35] The

0 mode with a K0

s was not included in this calculation.[36] The requirement that the colors match gives a factor of 1=3 in the amplitude. Moreover,

the W couples to the d _d part of the ss0 wave function so there is an additional factor of 1=p2 in the amplitude. This is also true for the ae0 and the ! mesons. The numerical factor is different for the case of the j=j

0 system.

[37] We use the PDG values for the j, j

0 and ! branching ratios [14].

[38] I.Dunietz and A.Snyder, Phys. Rev. D 43, 1593 (1991). The D0 meson, however, must

decay to a CP eigenstate e.g. B ! D0ss0 , D0 ! K\Gamma K+ could be used. [39] These modes are also accessible via the W-exchange graph but this is expected to be

small in B decay due to helicity suppression. [40] In the mode _B0 ! D0!, ! ! ss\Gamma ss+ss0, we require that \Theta N , the angle between the

normal to the ! decay plane and the D0 direction calculated in the D0 rest frame, satisfy j sin \Theta N j ? 0:6. [41] Ref. [14], p. III.38 [42] CLEO Collaboration, D. Bortoletto et al., Phys. Rev. D 37, 1719 (1988). [43] A.S. Artamov et al., Phys. Lett. B137, 272 (1984). [44] The background shape is allowed to vary from being flat all the way to the kinematic

limit, to having the functional form

f (x) = c1xq(1 \Gamma x2)ec2(1\Gamma x

2)

where x = MB=Ebeam. [45] C. P. Singh et al., Phys. Rev. D 24, 788 (1981); L.-H. Chan Phys. Rev. Lett. 51, 253

(1983); K. P. Tiwari et al., Phys. Rev. D 51, 643 (1985); D. Y. Kim and S. N. Sinha, Ann. Phys. (N.Y.) 42, 47 (1985). [46] J. L. Goity and W. S. Hou, Phys. Lett. B 282, 243 (1992); R. F. Lebed, Phys. Rev. D

47, 1134 (1993). [47] S. Stone, in Heavy Flavours, edited by A. J. Buras and H. Lindner (World Scientific,

Singapore, 1992). [48] M. J. Dugan and B. Grinstein, Phys. Lett. B 255, 583 (1991); and references therein. [49] N. Isgur and M.B. Wise, Phys. Lett. B 32, 113 (1989) and Phys. Lett. B 37, 527 (1990). [50] The error is due to the uncertainty in the scale at which to evaluate the Wilson coefficient. [51] D. Bortoletto and S.Stone, Phys. Rev. Lett. 65, 2951 (1990). It should be understood

that the above relation is exact for the case when h\Gamma is a vector meson. When h\Gamma is

25

a pseudoscalar meson only the longitudinal part of the semileptonic width enters into the determination of the left hand state. For the case of h = ss\Gamma discussed here, the correction for this effect is small. [52] X. Y. Pham and X. C. Vu, Phys. Rev. D 46, 261 (1992). [53] The value fae = 196 MeV derived from tau decays is determined using the narrow width

approximation i.e. by assuming the ae resonance is a delta function. [54] Since the form factor for B ! D\Lambda `* is slowly varying, the width of the ae\Gamma meson does

not significantly modify the result. [55] The value of c1 is the Wilson coefficient evaluated at the b quark mass scale. The value

of fae is from e+e\Gamma ! ae0 data as determined by Pham and Vu. The value of Vud is taken from J. Rosner, in B decays, edited by S. Stone, (World Scientific, Singapore, 1992). [56] The q2 spectrum has been corrected for the new values of the CLEO II D\Lambda and D

branching ratios [16], [11]. [57] J. Korner and G. Goldstein, Phys. Lett. B 89, 105 (1979). [58] Peter Lepage (private communication). [59] J.L. Rosner, Phys. Rev. D 42, 3732 (1990). [60] M. Neubert, Phys. Lett. B 264, 455 (1991). [61] T. Mannel et al., Phys. Lett. B 259, 359(1991). Similar observations have been made

by a large number of other authors. [62] B. Blok and M. Shifman, Nucl. Phys. B 389, 534, (1993). [63] Three parameterizations of the Isgur-Wise function ,(vv

0) are considered: (a) ,(vv0) =

1 + 1=4a(v \Gamma v

0)2(v + v0)2 with a = 0:54 \Sigma 0:01, (b) ,(vv0) = 1=[1 \Gamma (v \Gamma v0)2=w2

0] withw

0 = 1:12\Sigma 0:17, due to Rosner [59] , and (c) ,(vv

0) = exp[b(v\Gamma v0)2] with b = 0:91\Sigma 0:03.

All of these parameterizations are constrained by fitting to the average of the CLEO 1.5 and ARGUS data on d\Gamma =dQ2(B ! D\Lambda `*). [64] M. Bauer, B. Stech, and M. Wirbel, Z. Phys. C 29, 637 (1985); Z. Phys. C 34, 103

(1987) and Z. Phys. C 42, 671 (1989). [65] M.A. Shifman, Nucl. Phys. B. 388, 346, (1992). [66] G. Kramer and W.F. Palmer, Phys. Lett. B 279, 181, 1992. [67] The branching ratios with the exception of that for the D0 ! ss0ss0 decay mode are

taken from the PDG (Ref. [14]). The D0 ! ss0ss0 branching ratio is described in B. Ong et al. (CLEO collaboration), Phys. Rev. Lett. 71, 1973 (1993). [68] G. Kramer, T. Mannel and W.F. Palmer, Z. Phys. C 55, 497, 1992. [69] J.L. Rosner, Proceedings of the Theoretical Advanced Summer Institute, TASI-90,p.91-

224, Boulder, Co. 1990. [70] K. Terasaki, Phys. Rev. D 47, 5177 (1993). [71] The branching ratio for the modes B ! K and B ! K\Lambda can be accommodated by

the value , , 0 while , , 1=3 gives a branching ratio that is about a factor of 4 too low (see Ref. [65]). [72] CLEO CONF 93-17, CLEO paper submitted to the EPS conference, Marseille 1993. [73] In the fits of Ref. [8] the CLEO 1.5 data favor a positive sign while the ARGUS data

prefer a negative sign. From a global fit to data from both experiments, they find two solutions either a1 = 1:10 \Sigma 0:08 and a2 = 0:20 \Sigma 0:02 or a1 = 1:14 \Sigma 0:07 and a2 =\Gamma

0:17 \Sigma 0:02

26

TABLES TABLE I. D0 and D+ decay modes D type Decay Mode B(%) oemD (MeV) D0 K\Gamma ss+ 3.91\Sigma 0.08\Sigma 0:17 8.5 D0 K+ss\Gamma ss0 12.1\Sigma 1.1 13.0 D0 K\Gamma ss+ss+ss\Gamma 8.0\Sigma 0.5 8.1

D+ K\Gamma ss+ss+ 9:1 \Sigma 1:4 7.6

TABLE II. D\Lambda decay modes used D\Lambda Mode B(%) oemD\Lambda \Gamma mD (MeV) D\Lambda + ! D0ss+ 68.1\Sigma 1.6 0.8 D\Lambda 0 ! D0ss0 63.6\Sigma 4.0 1.1

TABLE III. Branching Ratios (%) for B\Gamma ! D0(nss)\Gamma B\Gamma Mode D mode oe\Delta E # of ffla B(%) B average (%)

(MeV) events K\Gamma ss+ 22 76.3 \Sigma 9.1 0.433 0.48\Sigma 0.06 D0ss\Gamma K\Gamma ss+ss0 26 134 \Sigma 15 0.193 0.62\Sigma 0.07 0.55\Sigma 0.04\Sigma 0:05 \Sigma 0:02

K\Gamma ss+ss+ss\Gamma 20 94\Sigma 11 0.222 0.57\Sigma 0.07

K\Gamma ss+ 18-38 80 \Sigma 9 0.155 1.40 \Sigma 0.18 D0ae\Gamma K\Gamma ss+ss0 22-42 42 \Sigma 9 0.036 1.04\Sigma 0.23 1.35\Sigma 0.12\Sigma 0:14 \Sigma 0:04

K\Gamma ss+ss+ss\Gamma 17-37 90.4\Sigma 12.1 0.079 1.53\Sigma 0.20

aThis efficiency does not include D branching ratios.

TABLE IV. Branching Ratios (%) for _B0 ! D+(nss)\Gamma _B0 Mode D Mode oe\Delta E # of ffla B(%) B average (%)

(MeV) events D+ss\Gamma K\Gamma ss+ss+ 20.5 80.6\Sigma 9.8 0.32 0.29\Sigma 0.04 0.29\Sigma 0.04\Sigma 0:03 \Sigma 0:05 D+ae\Gamma K\Gamma ss+ss+ 18-38 78.9\Sigma 10.7 0.12 0.81\Sigma 0.11 0.81\Sigma 0.11\Sigma 0:12 \Sigma 0:13

aThis efficiency does not include D branching ratios.

27

TABLE V. Branching Ratios (%) for B\Gamma ! D\Lambda 0(nss) B\Gamma Mode D0 Mode oe\Delta E # of ffla B(%) B average (%)

(MeV) events K\Gamma ss+ 25 13.3\Sigma 3.8 0.16 0.36\Sigma 0.13 D\Lambda 0ss\Gamma K\Gamma ss+ss0 32 37.7\Sigma 6.9 0.08 0.63\Sigma 0.12 0.52\Sigma 0.07\Sigma 0:06 \Sigma 0:04

K\Gamma ss+ss+ss\Gamma 21 20.0\Sigma 4.9 0.08 0.52\Sigma 0.13

K\Gamma ss+ 21-41 25.7\Sigma 5.4 0.064 1.74\Sigma 0.37 D\Lambda 0ae\Gamma K\Gamma ss+ss0 26-46 43.8\Sigma 7.8 0.027 2.24\Sigma 0.40 1.68\Sigma 0.21\Sigma 0:25 \Sigma 0:12

K\Gamma ss+ss+ss\Gamma 19-39 16.9\Sigma 4.6 0.030 1.19\Sigma 0.35

K\Gamma ss+ 14 5.5\Sigma 2.9 0.048 0.51\Sigma 0.26 D\Lambda 0ss\Gamma ss\Gamma ss+b K\Gamma ss+ss0 22 27.7\Sigma 7.2 0.022 1.74\Sigma 0.45 0.94\Sigma 0.20\Sigma 0.16 \Sigma 0.06

K\Gamma ss+ss+ss\Gamma 15 15.0\Sigma 4.5 0.025 1.26 \Sigma 0.37

aThis efficiency does not include D or D\Lambda branching ratios. bThe three pion mass is required to be between 1.0 GeV and 1.6 GeV consistent with an a1 meson.

(If this channel is dominated by a\Gamma 1 , the branching ratio for D\Lambda 0a\Gamma 1 is twice that for D\Lambda 0ss\Gamma ss\Gamma ss+.)

TABLE VI. Branching Ratios (%) for _B0 ! D\Lambda +(nss)\Gamma _B0 Mode D0 Mode oe\Delta E # of ffla B(%) B average (%)

(MeV) events K\Gamma ss+ 25 19.4\Sigma 4.5 0.35 0.22\Sigma 0.05 D\Lambda +ss\Gamma K\Gamma ss+ss0 32 31.9\Sigma 6.4 0.14 0.30\Sigma 0.06 0.26\Sigma 0.03\Sigma 0:04 \Sigma 0:01

K\Gamma ss+ss+ss\Gamma 21 20.5\Sigma 5.2. 0.15 0.27\Sigma 0.07

K\Gamma ss+ 21.5-41.5 21.9\Sigma 5.2 0.12 0.71\Sigma 0.17 D\Lambda +ae\Gamma K\Gamma ss+ss0 23-43 39.8\Sigma 7.2 0.048 1.08\Sigma 0.20 0.74\Sigma 0.10\Sigma 0:14 \Sigma 0:03

K\Gamma ss+ss+ss\Gamma 20.5-40.5 14.6\Sigma 4.6 0.054 0.52\Sigma 0.17

K\Gamma ss+ 14 13.5\Sigma 3.9 0.096 0.58\Sigma 0.17 D\Lambda +ss\Gamma ss\Gamma ss+b K\Gamma ss+ss0 22 21.7\Sigma 5.9 0.043 0.67\Sigma 0.18 0.63\Sigma 0.10\Sigma 0:11 \Sigma 0:02

K\Gamma ss+ss+ss\Gamma 15 13.9\Sigma 4.4 0.042 0.65\Sigma 0.19

aThis efficiency does not include D or D\Lambda branching ratios. bThe three pion mass is required to be between 1.0 GeV and 1.6 GeV consistent with an a1 meson.

(If this channel dominated by a\Gamma 1 , the branching ratio for D\Lambda +a\Gamma 1 is twice that for D\Lambda +ss\Gamma ss\Gamma ss+.)

28

TABLE VII. Branching Ratios (%) for B ! D\Lambda \Lambda (nss) B Mode D Mode oe\Delta E ffla # of B average (%)

(MeV) events D0ss+ss\Gamma K\Gamma ss+ 17 0.19 ! 10:1 ! 0:16 D+ss\Gamma ss\Gamma K\Gamma ss+ss+ 15.5 0.11 ! 10:3 ! 0:14 D\Lambda \Lambda (2460)ss\Gamma ! D+ss\Gamma ss\Gamma K\Gamma ss+ss+ 16 0.21 ! 5:6 ! 0:13

D\Lambda \Lambda (2460)ss\Gamma ! D0ss+ss\Gamma K\Gamma ss+ 17 0.26 ! 5:6 ! 0:22 D\Lambda \Lambda (2460)ae\Gamma ! D+ss\Gamma ss\Gamma ss0 K\Gamma ss+ss+ 16 0.08 ! 6:1 ! 0:47

D\Lambda \Lambda (2460)ae\Gamma ! D0ss+ss\Gamma ss0 K\Gamma ss+ 17 0.11 ! 5:1 ! 0:49

K\Gamma ss+ 16 0.161 D\Lambda ss\Gamma ss\Gamma K\Gamma ss+ss0 23 0.061 14.1 \Sigma 5.4 0:19 \Sigma 0:07 \Sigma 0:03 \Sigma 0:01

K\Gamma ss+ss\Gamma ss+ 19 0.075

K\Gamma ss+ 16 0.161 D\Lambda \Lambda (2420)ss\Gamma ! D\Lambda +ss\Gamma ss\Gamma K\Gamma ss+ss0 23 0.061 8.5 \Sigma 3.8 0:11 \Sigma 0:05 \Sigma 0:02 \Sigma 0:01

K\Gamma ss+ss\Gamma ss+ 19 0.075

K\Gamma ss+ 16 0.161 D\Lambda \Lambda (2460)ss\Gamma ! D\Lambda +ss\Gamma ss\Gamma K\Gamma ss+ss0 23 0.061 3.5 \Sigma 2.3 ! 0:28

K\Gamma ss+ss\Gamma ss+ 19 0.075

K\Gamma ss+ 30 0.078 D\Lambda \Lambda (2420)ae\Gamma ! D\Lambda +ss\Gamma ss\Gamma ss0 K\Gamma ss+ss0 24 0.037 3.4 \Sigma 2.1 ! 0:14

K\Gamma ss+ss\Gamma ss+ 27 0.042

K\Gamma ss+ 30 0.078 D\Lambda \Lambda (2460)ae\Gamma ! D\Lambda +ss\Gamma ss\Gamma ss0 K\Gamma ss+ss0 24 0.037 3.2 \Sigma 2.4 ! 0:5

K\Gamma ss+ss+ss\Gamma 27 0.042

aThe efficiencies do not include the branching ratios for D, D\Lambda and D\Lambda \Lambda . To determine the B decay branching ratios, we assumed B(D\Lambda \Lambda 0(2420) ! D\Lambda +ss\Gamma ) and B(D\Lambda \Lambda 0(2460) ! D\Lambda +ss\Gamma ) are 67% and 20% respectively. We also assume that B(D\Lambda \Lambda 0(2460) ! D+ss\Gamma ) and B(D\Lambda \Lambda +(2460) ! D0ss+) are 30% and 30% respectively.

29

TABLE VIII. Branching Ratio for B ! D\Lambda \Lambda (nss). Mode CLEO II Bari model [32] RI model [33] D\Lambda \Lambda 0(2420)ss\Gamma (11 \Sigma 5 \Sigma 2 \Sigma 1) \Theta 10\Gamma 4 4 \Theta 10\Gamma 4 7:5 \Theta 10\Gamma 4 \Gamma 13 \Theta 10\Gamma 4 D\Lambda \Lambda 0(2460)ss\Gamma ! 2:8 \Theta 10\Gamma 3 6 \Theta 10\Gamma 4 5 \Theta 10\Gamma 4 \Gamma 8 \Theta 10\Gamma 4 (D\Lambda \Lambda 0 ! D\Lambda +ss\Gamma )

D\Lambda \Lambda 0(2460)ss\Gamma ! 1:3 \Theta 10\Gamma 3 6 \Theta 10\Gamma 4 5 \Theta 10\Gamma 4 \Gamma 8 \Theta 10\Gamma 4 (D\Lambda \Lambda 0 ! D+ss\Gamma )

D\Lambda \Lambda +(2460)ss\Gamma ! 2:2 \Theta 10\Gamma 3 6 \Theta 10\Gamma 4 5 \Theta 10\Gamma 4 \Gamma 8 \Theta 10\Gamma 4 (D\Lambda \Lambda + ! D0ss+)

D\Lambda \Lambda 0(2420)ae\Gamma ! 1:4 \Theta 10\Gamma 3 1 \Theta 10\Gamma 3 13 \Theta 10\Gamma 4 \Gamma 24 \Theta 10\Gamma 4 D\Lambda \Lambda 0(2460)ae\Gamma ! 5 \Theta 10\Gamma 3 1 \Theta 10\Gamma 3 10 \Theta 10\Gamma 4 \Gamma 20 \Theta 10\Gamma 4

TABLE IX. Exclusive B ! c_c Branching Ratios and 90% Confidence Level Upper Limits (%).

B Mode oe(\Delta E) # of events ffl a B(%) B\Gamma ! K\Gamma 13 58:7 \Sigma 7:9 0:47 0:110 \Sigma 0:015 \Sigma 0:009

B0 ! K0 13 10:0 \Sigma 3:2 0:34 0:075 \Sigma 0:024 \Sigma 0:008 B0 ! K\Lambda 0 12 29:0 \Sigma 5:4 0:23 0:169 \Sigma 0:031 \Sigma 0:018 B\Gamma ! K\Lambda \Gamma , K\Lambda \Gamma ! K\Gamma ss0 21 6:0 \Sigma 2:4 0:07 0:218 \Sigma 0:089 \Sigma 0:026 B\Gamma ! K\Lambda \Gamma , K\Lambda \Gamma ! K0Sss\Gamma 11 6:6 \Sigma 2:7 0:17 0:130 \Sigma 0:058 \Sigma 0:018

B\Gamma ! K\Lambda \Gamma (combined) 12:6 \Sigma 3:6 0:178 \Sigma 0:051 \Sigma 0:023

B\Gamma !

0K\Gamma 9:8; 11 7:0 \Sigma 2:6 0:36; 0:15 0:061 \Sigma 0:023 \Sigma 0:009

B0 !

0K0 8:4; 10 0 0:28; 0:11 ! 0:08

B0 !

0K\Lambda 0 9:7; 10 4:2 \Sigma 2:3 0:24; 0:091 ! 0:19

B\Gamma !

0K\Lambda \Gamma , K\Lambda \Gamma ! K\Gamma ss0 18; 17 1 \Sigma 1 0:077; 0:023 ! 0:56

B\Gamma !

0K\Lambda \Gamma , K\Lambda \Gamma ! K0

Sss\Gamma 7:9; 9:8 1 \Sigma 1 0:16; 0:057 ! 0:36

B\Gamma !

0K\Lambda \Gamma (combined) 2 \Sigma 1:4 ! 0:30

B\Gamma ! O/c1K\Gamma 18 6 \Sigma 2:4 0:20 0:097 \Sigma 0:040 \Sigma 0:009

B0 ! O/c1K0 16 1 \Sigma 1 0:14 ! 0:27 B0 ! O/c1K\Lambda 0 15 1:2 \Sigma 1:5 0:13 ! 0:21 B\Gamma ! O/c1K\Lambda \Gamma , K\Lambda \Gamma ! K\Gamma ss0 15 0 0:033 ! 0:67

B\Gamma ! O/c1K\Lambda \Gamma , K\Lambda \Gamma ! Ksss\Gamma 17 0 0:11 ! 0:30

B\Gamma ! O/c1K\Lambda \Gamma , (combined) 0 ! 0:21

aThis efficiency does not include the ,0,O/c1,K0,K\Lambda or K0S branching ratios. The two sets of values given for the

0 channels correspond to the two 0 decay modes 0 ! l+l\Gamma and 0 ! ss+ss\Gamma .

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TABLE X. Upper limits (90% C.L) on branching fractions for color suppressed B decays. Decay Mode Events ffle U. L. (%) at 90% C. L.

_B0 ! D0ss0 ! 20:7 0:32; 0:16; 0:18 ! 0:048

_B0 ! D0ae0 ! 19:0 0:21; 0:08; 0:12 ! 0:055 _B0 ! D0j ! 9:5 0:31; 0:11; 0:16 ! 0:068 _B0 ! D0j0 ! 3:5 0:18; 0:08; 0:11 ! 0:086 _B0 ! D0! ! 12:7 0:16; 0:07; 0:09 ! 0:063 _B0 ! D\Lambda 0ss0 ! 11:0 0:13; 0:07; 0:07 ! 0:097 _B0 ! D\Lambda 0ae0 ! 8:1 0:09; 0:04; 0:04 ! 0:117 _B0 ! D\Lambda 0j ! 2:3 0:11; 0:05; 0:06 ! 0:069 _B0 ! D\Lambda 0j0 ! 2:3 0:07; 0:03; 0:03 ! 0:27 _B0 ! D\Lambda 0! ! 9:0 0:06; 0:03; 0:03 ! 0:21

eThe efficiencies for the D0 ! K\Gamma ss+, D0 ! K\Gamma ss+ss0, and D0 ! K\Gamma ss+ss\Gamma ss+ modes are given. These efficiencies do not include D, D\Lambda j, j

0 and ! branching ratios.

TABLE XI. Upper limits on ratios of branching ratios for color suppressed to normalization modes.

Ratio of Branching Ratios U.L. (90% C.L.) B( _B0 ! D0ss0)=B(B\Gamma ! D0ss\Gamma ) ! 0:09

B( _B0 ! D0ae0)=B(B\Gamma ! D0ae\Gamma ) ! 0:05

B( _B0 ! D0j)=B(B\Gamma ! D0ss\Gamma ) ! 0:12 B( _B0 ! D0j

0)=B(B\Gamma ! D0ss\Gamma ) ! 0:16

B( _B0 ! D0!)=B(B\Gamma ! D0ae\Gamma ) ! 0:05 B( _B0 ! D\Lambda 0ss0)=B(B\Gamma ! D\Lambda 0ss\Gamma ) ! 0:20

B( _B0 ! D\Lambda 0ae0)=B(B\Gamma ! D\Lambda 0ae\Gamma ) ! 0:07

B( _B0 ! D\Lambda 0j)=B(B\Gamma ! D\Lambda 0ss\Gamma ) ! 0:14 B( _B0 ! D\Lambda 0j

0)=B(B\Gamma ! D\Lambda 0ss\Gamma ) ! 0:54

B( _B0 ! D\Lambda 0!)=B(B\Gamma ! D\Lambda 0ae\Gamma ) ! 0:09

TABLE XII. B Masses from individual modes (not corrected for initial state radiation).

B\Gamma Modes _B0Modes Mode Mass (MeV) Events Mode Mass (MeV) Events D\Lambda 0ss\Gamma 5279.7\Sigma 0.4 73 D\Lambda +ss\Gamma 5280.1\Sigma 0.4 73 D\Lambda 0ae\Gamma 5280.2\Sigma 0.4 89 D\Lambda +ae\Gamma 5280.5\Sigma 0.4 79 K\Gamma 5279.8\Sigma 0.4 44 K\Lambda 0 5280.4\Sigma 0.5 29 D0ss\Gamma 5279.9\Sigma 0.3 76 D+ss\Gamma 5280.4\Sigma 0.3 80 D0ae\Gamma 5279.7\Sigma 0.4 80 D+ae\Gamma 5280.3\Sigma 0.4 79 All 5279.9\Sigma 0.2 362 All 5280.3\Sigma 0.2 340

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TABLE XIII. Contributions to the systematic error in the B0 \Gamma B\Gamma mass difference. Event sample 0:15 MeV Background shape 0:12 MeV fl energy calibration ! 0:03 MeV Width of B mass peak ! 0:02 MeV Track momentum scale ! 0:01 MeV total 0.19 MeV

TABLE XIV. Measurements of the _B0-B\Gamma Mass difference. Experiment M ( _B0)-M (B\Gamma ) (MeV) CLEO 87 [2] 2:0 \Sigma 1:1 \Sigma 0:3 ARGUS [6] \Gamma 0:9 \Sigma 1:2 \Sigma 0:5 CLEO 92 [3] \Gamma 0:4 \Sigma 0:6 \Sigma 0:5 CLEO 93 (this result) 0:41 \Sigma 0:25 \Sigma 0:19 Average 0:4 \Sigma 0:3

TABLE XV. Ingredients for Factorization Tests. jc1j 1:12 \Sigma 0:10

fss 131:74 \Sigma 0:15 MeV

fae 215 \Sigma 4 MeV fa1 205 \Sigma 16 MeV Vud 0:975 \Sigma 0:001 dB dq2 (B ! D

\Lambda l *)jq2=m2

ss (W SB) 0.0023 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

ss (ISGW ) 0.0020 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

ss (KS) 0.0024 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

ae (W SB) 0.0025 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

ae(ISGW ) 0.0024 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

ae (KS) 0.0027 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

a1 (W SB) 0.0032 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

a1 (ISGW ) 0.0030 GeV

\Gamma 2

dB dq2 (B ! D

\Lambda l *)jq2=m2

a1 (KS) 0.0033 GeV

\Gamma 2

TABLE XVI. Comparison of Rexp and Rtheor

Rexp (GeV2) Rtheor (GeV2) _B0 ! D\Lambda +ss\Gamma 1:1 \Sigma 0:1 \Sigma 0:2 1:2 \Sigma 0:2

_B0 ! D\Lambda +ae\Gamma 3:0 \Sigma 0:4 \Sigma 0:6 3:3 \Sigma 0:5 _B0 ! D\Lambda +a\Gamma 1 4:0 \Sigma 0:6 \Sigma 0:5 3:0 \Sigma 0:5

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TABLE XVII. Ratios of B decay widths.

Exp. Factorization RI Model BSW Model B( _B0 ! D\Lambda +ae\Gamma )=B( _B0 ! D\Lambda +ss\Gamma ) 2:9 \Sigma 0:5 \Sigma 0:5 2:9 \Sigma 0:05 2.2 - 2.3 2.8 B( _B0 ! D\Lambda +a\Gamma 1 )=B( _B0 ! D\Lambda +ss\Gamma ) 5:0 \Sigma 1:0 \Sigma 0:6 3:4 \Sigma 0:3 2.0 - 2.1 3.4

TABLE XVIII. Ratios of color suppressed to external spectator branching ratios. B(D0 ! K0ss0)=B(D0 ! K\Gamma ss+) 0:57 \Sigma 0:13 B(D0 ! _K\Lambda 0ss0)=B(D0 ! K\Lambda \Gamma ss+) 0:47 \Sigma 0:23

B(D0 ! ss0ss0)=B(D0 ! ss\Gamma ss+) 0:77 \Sigma 0:25 B(D+s ! _K\Lambda 0K+)=B(Ds ! OEss+) 0:95 \Sigma 0:10

B(D+s ! _K0K+)=B(Ds ! OEss+) 1:01 \Sigma 0:16

TABLE XIX. Branching fractions of color suppressed B decays and comparisons with models. Decay Mode U. L. (%) BSW (%) B (BSW) RI model(%)

_B0 ! D0ss0 ! 0:048 0:012 0:20a22(fD=220MeV)2 0:0013 \Gamma 0:0018

_B0 ! D0ae0 ! 0:055 0:008 0:14a22(fD=220MeV)2 0:00044 _B0 ! D0j ! 0:068 0:006 0:11a22(fD=220MeV)2 _B0 ! D0j0 ! 0:086 0:002 0:03a22(fD=220MeV)2 _B0 ! D0! ! 0:063 0:008 0:14a22(fD=220MeV)2 _B0 ! D\Lambda 0ss0 ! 0:097 0:012 0:21a22(fD\Lambda =220MeV)2 0:0013 \Gamma 0:0018 _B0 ! D\Lambda 0ae0 ! 0:117 0:013 0:22a22(fD\Lambda =220MeV)2 0:0013 \Gamma 0:0018 _B0 ! D\Lambda 0j ! 0:069 0:007 0:12a22(fD\Lambda =220MeV)2 _B0 ! D\Lambda 0j0 ! 0:27 0:002 0:03a22(fD\Lambda =220MeV)2 _B0 ! D\Lambda 0! ! 0:21 0:013 0:22a22(fD\Lambda =220MeV)2

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TABLE XX. Branching ratios in terms of BSW parameters a1, a2 Mode B %

_B0 ! D+ss\Gamma 0:264a21

_B0 ! D+ae\Gamma 0:621a21 _B0 ! D\Lambda +ss\Gamma 0:254a21 _B0 ! D\Lambda +ae\Gamma 0:702a21

B\Gamma ! D0ss\Gamma 0:265[a1 + 1:230a2 (fD=220)]2 B\Gamma ! D0ae\Gamma 0:622[a1 + 0:662a2 (fD=220)]2 B\Gamma ! D\Lambda 0ss\Gamma 0:255[a1 + 1:292a2 (fD\Lambda =220)]2 B\Gamma ! D\Lambda 0ae\Gamma 0:703[a21 + 0:635a22(fD\Lambda =220)2 + 1:487a1a2 (fD\Lambda =220)] B\Gamma ! K\Gamma 1:819a22 B\Gamma ! K\Lambda \Gamma 2:932a22_ B0 ! _K0 1:817a22_ B0 ! _K\Lambda 0 2:927a22

TABLE XXI. Ratios of normalization modes to determine the sign of a2=a1. The magnitude of a2=a1 is the value in the BSW model which agrees with our result from B ! modes.

Ratio a2=a1 = \Gamma 0:24 a2=a1 = 0:24 CLEO II RI model

R1 0.50 1.68 1:89 \Sigma 0:26 \Sigma 0:32 1:20 \Gamma 1:28 R2 0.71 1.34 1:67 \Sigma 0:27 \Sigma 0:30 1:09 \Gamma 1:12 R3 0.48 1.72 2:00 \Sigma 0:37 \Sigma 0:28 1:19 \Gamma 1:27 R4 0.41 1.85 2:27 \Sigma 0:41 \Sigma 0:41 1:10 \Gamma 1:36

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XIV. APPENDIX In this appendix, we provide the product of the B and charm branching fractions for the decay modes measured in this paper so that the results can be easily renormalized when the intermediate branching fractions for D0; D+; D\Lambda +; D\Lambda 0 and ;

0; O/

c1 mesons are known more

precisely. The results are given in Tables XXII-XXVIII.

TABLE XXII. Product Branching Fractions (%) for B\Gamma ! D0(nss)\Gamma Modes B\Gamma Mode D Mode # of ffl B(B\Gamma ! D0(nss)\Gamma )\Theta

events B(D0 ! K\Gamma [nss]) K\Gamma ss+ 76.3\Sigma 9.1 0.433 0:0189 \Sigma 0:0022 \Sigma 0:0013 D0ss\Gamma K\Gamma ss+ss0 134\Sigma 15 0.193 0:0746 \Sigma 0:0082 \Sigma 0:0065

K\Gamma ss+ss+ss\Gamma 94\Sigma 11 0.222 0:0455 \Sigma 0:0055 \Sigma 0:0049

K\Gamma ss+ 80 \Sigma 9 0.155 0:0524 \Sigma 0:0067 \Sigma 0:0044 D0ae\Gamma K\Gamma ss+ss0 42 \Sigma 9 0.036 0:1254 \Sigma 0:0282 \Sigma 0:0150

K\Gamma ss+ss+ss\Gamma 90.4\Sigma 12.1 0.079 0:1223 \Sigma 0:0164 \Sigma 0:0142

TABLE XXIII. Product Branching Fractions (%) for _B0 ! D+(nss)\Gamma Modes _B0 Mode D Mode # of ffl B( _B0 ! D+(nss)\Gamma )\Theta

events B(D+ ! K\Gamma ss+ss+) D+ss\Gamma K\Gamma ss+ss+ 80.6\Sigma 9.8 0.32 0:0265 \Sigma 0:0032 \Sigma 0:0023 D+ae\Gamma K\Gamma ss+ss+ 78.9\Sigma 10.7 0.12 0:0704 \Sigma 0:0096 \Sigma 0:0070

TABLE XXIV. Product Branching Fractions (%) for B\Gamma ! D\Lambda 0(nss) Modes B\Gamma Mode D0 Mode # of ffl B(B\Gamma ! D\Lambda 0(nss)\Gamma )\Theta

events B(D\Lambda 0 ! D0ss0) \Theta B(D0 ! K\Gamma [nss]) K\Gamma ss+ 13.3\Sigma 3.8 0.16 0:0090 \Sigma 0:0026 \Sigma 0:0009 D\Lambda 0ss\Gamma K\Gamma ss+ss0 37.7\Sigma 6.9 0.08 0:0488 \Sigma 0:0089 \Sigma 0:0063

K\Gamma ss+ss+ss\Gamma 20.0\Sigma 4.9 0.08 0:0267 \Sigma 0:0065 \Sigma 0:0033

K\Gamma ss+ 25.7\Sigma 5.4 0.064 0:0432 \Sigma 0:0090 \Sigma 0:0058 D\Lambda 0ae\Gamma K\Gamma ss+ss0 43.8\Sigma 7.8 0.027 0:1722 \Sigma 0:0305 \Sigma 0:0300

K\Gamma ss+ss+ss\Gamma 16.9\Sigma 4.6 0.030 0:0608 \Sigma 0:0176 \Sigma 0:0095

K\Gamma ss+ 5.5\Sigma 2.9 0.048 0:0124 \Sigma 0:0065 \Sigma 0:0020 D\Lambda 0ss\Gamma ss\Gamma ss+a K\Gamma ss+ss0 27.7\Sigma 7.2 0.022 0:1316 \Sigma 0:0343 \Sigma 0:0237

K\Gamma ss+ss+ss\Gamma 15.0\Sigma 4.5 0.025 0:0632 \Sigma 0:0187 \Sigma 0:0118

aThe three pion mass is required to be between 1.0 GeV and 1.6 GeV consistent with an a1 meson.

(If this channel is dominated by a\Gamma 1 , the branching ratio for D\Lambda 0a\Gamma 1 is twice that for D\Lambda 0ss\Gamma ss\Gamma ss+.)

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TABLE XXV. Product Branching Fractions (%) for _B0 ! D\Lambda +(nss)\Gamma Modes _B0 Mode D0 Mode # of ffla B( _B0 ! D\Lambda +(nss)\Gamma )\Theta

events B(D\Lambda + ! D0ss+) \Theta B(D0 ! K\Gamma [nss]) K\Gamma ss+ 19.4\Sigma 4.5 0.35 0:0058 \Sigma 0:0013 \Sigma 0:0008 D\Lambda +ss\Gamma K\Gamma ss+ss0 31.9\Sigma 6.4 0.14 0:0243 \Sigma 0:0049 \Sigma 0:0035

K\Gamma ss+ss+ss\Gamma 20.5\Sigma 5.2. 0.15 0:0146 \Sigma 0:0033 \Sigma 0:0025

K\Gamma ss+ 21.9\Sigma 5.2 0.12 0:0188 \Sigma 0:0044 \Sigma 0:0034 D\Lambda +ae\Gamma K\Gamma ss+ss0 39.8\Sigma 7.2 0.048 0:0892 \Sigma 0:0162 \Sigma 0:0177

K\Gamma ss+ss+ss\Gamma 14.6\Sigma 4.6 0.054 0:0286 \Sigma 0:0091 \Sigma 0:0059

K\Gamma ss+ 13.5\Sigma 3.9 0.096 0:0151 \Sigma 0:0044 \Sigma 0:0024 D\Lambda +ss\Gamma ss\Gamma ss+a K\Gamma ss+ss0 21.7\Sigma 5.9 0.043 0:0545 \Sigma 0:0147 \Sigma 0:0091

K\Gamma ss+ss+ss\Gamma 13.9\Sigma 4.4 0.042 0:0348 \Sigma 0:0101 \Sigma 0:0069

aThe three pion mass is required to be between 1.0 GeV and 1.6 GeV consistent with an a1 meson.

(If this channel dominated by a\Gamma 1 , the branching ratio for D\Lambda +a\Gamma 1 is twice that for D\Lambda +ss\Gamma ss\Gamma ss+.)

TABLE XXVI. Product Branching Fractions for B ! Modes and 90% Confidence Level Upper Limits (%).

B Mode # of events ffl B(B ! K(\Lambda )) \Theta B( ! l+l\Gamma ) a B\Gamma ! K\Gamma 58:7 \Sigma 7:9 0:47 0:0131 \Sigma 0:0017 \Sigma 0:0011

B0 ! K0 10:0 \Sigma 3:2 0:34 0:0088 \Sigma 0:0028 \Sigma 0:0009 B0 ! K\Lambda 0 29:0 \Sigma 5:4 0:23 0:0200 \Sigma 0:0037 \Sigma 0:0021 B\Gamma ! K\Lambda \Gamma 12:6 \Sigma 3:6 0:0210 \Sigma 0:0061 \Sigma 0:0026

aThe product branching fraction has been corrected for the K0, K\Lambda or K0S branching ratios but not for the branching fractions.

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TABLE XXVII. Product Branching Fractions for B !

0 Modes and 90% Confidence Level

Upper Limits (%).

B Mode B(B !

0K(\Lambda )) \Theta B(0) a

B\Gamma !

0K\Gamma 0 ! l+l\Gamma 0:0011 \Sigma 0:0006 \Sigma 0:0001

B\Gamma !

0K\Gamma ; 0 ! ss+ss\Gamma 0:0173 \Sigma 0:0100 \Sigma 0:0023

B0 !

0K0; 0 ! l+l\Gamma ! 0:0025

B0 !

0K0; 0 ! ss+ss\Gamma ! 0:0200

B0 !

0K\Lambda 0; 0 ! l+l\Gamma ! 0:0051

B0 !

0K\Lambda 0; 0 ! ss+ss\Gamma ! 0:0210

B\Gamma !

0K\Lambda \Gamma ; 0 ! l+l\Gamma ! 0:0065

B\Gamma !

0K\Lambda \Gamma ; 0 ! ss+ss\Gamma ! 0:0600

aThe product branching fraction has been corrected for the K0, K\Lambda or K0S branching ratios but not for the

0 and branching fractions. We give B(B ! 0K(\Lambda )) \Theta B(0 ! l+l\Gamma ) or B(B !



0K(\Lambda )) \Theta B(0 ! ss+ss\Gamma ) \Theta B( ! l+l\Gamma ).

TABLE XXVIII. Product Branching Fractions for B ! O/c1 Modes and 90% Confidence Level Upper Limits (%).

B Mode # of events ffl B(B ! O/c1K(\Lambda )) \Theta B(O/c1) a B\Gamma ! O/c1K\Gamma 6 \Sigma 2:4 0:20 0:0031 \Sigma 0:0013 \Sigma 0:0003

B0 ! O/c1K0 1 \Sigma 1 0:14 ! 0:0087 B0 ! O/c1K\Lambda 0 1:2 \Sigma 1:5 0:13 ! 0:0066 B\Gamma ! O/c1K\Lambda \Gamma 0 ! 0:0066

aFor the modes with O/c1 mesons, we report the product B(B ! [O/c1]K(\Lambda ))\Theta B( ! l+l\Gamma )\Theta O/c1 ! fl branching fraction in the product. The product branching fraction has been corrected for the K0, K\Lambda or K0S branching ratios but not for the branching fractions.

37

