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of Measurement the Branching Fraction for Ds 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 ! 1 3 5 CLNS 95/1387 CLEO 95{23 M. Artuso, A. E mov, M. Gao, M. Goldberg, R. Greene, D. He, N. Horwitz, S. Kopp, G.C. Moneti, R. Mountain, Y. Mukhin, S. Playfer, T. Skwarnicki, S. Stone, X. Xing, J. Bartelt, S.E. Csorna, V. Jain, S. Marka, A. Freyberger, D. Gibaut, K. Kinoshita, P. Pomianowski, S. Schrenk, D. Cinabro, B. Barish, M. Chadha, S. Chan, G. Eigen, J.S. Miller, C. O'Grady, M. Schmidtler, J. Urheim, A.J. Weinstein, F. Wurthwein, D.M. Asner, M. Athanas, D.W. Bliss, W.S. Brower, G. Masek, H.P. Paar, J. Gronberg, C.M. Korte, R. Kutschke, S. Menary, R.J. Morrison, S. Nakanishi, H.N. Nelson, T.K. Nelson, C. Qiao, J.D. Richman, D. Roberts, A. Ryd, H. Tajima, M.S. Witherell, R. Balest, K. Cho, W.T. Ford, M. Lohner, H. Park, P. Rankin, J. Roy, J.G. Smith, J.P. Alexander, C. Bebek, B.E. Berger, K. Berkelman, K. Bloom, D.G. Cassel, H.A. Cho, D.M. Co man, D.S. Crowcroft, M. Dickson, P.S. Drell, D.J. Dumas, R. Ehrlich, R. Elia, P. Gaidarev, B. Gittelman, S.W. Gray, D.L. Hartill, B.K. Heltsley, C.D. Jones, S.L. Jones, J. Kandaswamy, N. Katayama, P.C. Kim, D.L. Kreinick, T. Lee, Y. Liu, G.S. Ludwig, J. Masui, J. Mevissen, N.B. Mistry, C.R. Ng, E. Nordberg, J.R. Patterson, D. Peterson, D. Riley, A. So er, C. Ward, P. Avery, C. Prescott, S. Yang, J. Yelton, G. Brandenburg, R.A. Briere, T. Liu, M. Saulnier, R. Wilson, H. Yamamoto, T. E. Browder, F. Li, J. L. Rodriguez, T. Bergfeld, B.I. Eisenstein, J. Ernst, G.E. Gladding, G.D. Gollin, M. Palmer, M. Selen, J.J. Thaler, K.W. Edwards, K.W. McLean, M. Ogg, A. Bellerive, D.I. Britton, R. Janicek, D.B. MacFarlane, P.M. Patel, B. Spaan, A.J. Sado , R. Ammar, P. Baringer, A. Bean, D. Besson, D. Coppage, N. Copty, R. Davis, N. Hancock, S. Kotov, I. Kravchenko, N. Kwak, S.Anderson, Y. Kubota, M. Lattery, J.K. Nelson, S. Patton, R. Poling, T. Riehle, V. Savinov, M.S. Alam, I.J. Kim, Z. Ling, A.H. Mahmood, J.J. O'Neill, H. Severini, C.R. Sun, S. Timm, F. Wappler, J.E. Duboscq, R. Fulton, D. Fujino, K.K. Gan, K. Honscheid, H. Kagan, R. Kass, J. Lee, M. Sung, A. Undrus, C. White, R. Wanke, A. Wolf, M.M. Zoeller, X. Fu, B. Nemati, S.J. Richichi, W.R. Ross, P. Skubic, M. Wood, M. Bishai, J. Fast, E. Gerndt, J.W. Hinson, T. Miao, D.H. Miller, M. Modesitt, D. Payne, E.I. Shibata, I.P.J. Shipsey, P.N. Wang, M. Yurko, L. Gibbons, S.D. Johnson, Y. Kwon, S. Roberts, E.H. Thorndike, C.P. Jessop, K. Lingel, H. Marsiske, M.L. Perl, S.F. Scha ner, R. Wang, T.E. Coan, J. Dominick, V. Fadeyev, I. Korolkov, M. Lambrecht, S. Sanghera, V. Shelkov, R. Stroynowski, I. Volobouev, and G. Wei 1 3 3 3 3 4 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 11 11 11 11 11 11 12 12 12 13 13 13 13 13 13 13 13 14 14 14 15 15 15 15 15 15 16 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 1 9 17 19 21 (CLEO Collaboration) 1 1 2 3 Syracuse University, Syracuse, New York 13244 Vanderbilt University, Nashville, Tennessee 37235 Wayne State University, Detroit, Michigan 48202 Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 4 5 6 California Institute of Technology, Pasadena, California 91125 7 University of California, San Diego, La Jolla, California 92093 University of California, Santa Barbara, California 93106 8 University of Colorado, Boulder, Colorado 80309-0390 9 10 Cornell University, Ithaca, New York 14853 University of Florida, Gainesville, Florida 32611 11 Harvard University, Cambridge, Massachusetts 02138 University of Hawaii at Manoa, Honolulu, HI 96822 12 13 14 University of Illinois, Champaign-Urbana, Illinois, 61801 Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada McGill University, Montreal, Quebec H3A 2T8 and the Institute of Particle Physics, Canada 16 17 18 19 15 Ithaca College, Ithaca, New York 14850 University of Kansas, Lawrence, Kansas 66045 University of Minnesota, Minneapolis, Minnesota 55455 20 21 State University of New York at Albany, Albany, New York 12222 Ohio State University, Columbus, Ohio, 43210 University of Oklahoma, Norman, Oklahoma 73019 Purdue University, West Lafayette, Indiana 47907 22 23 24 University of Rochester, Rochester, New York 14627 Southern Methodist University, Dallas, Texas 75275 Stanford Linear Accelerator Center, Stanford University, Stanford, California, 94309 25 2 Abstract We present a model-independent measurement of K + B(D s ! )=B(D0 B(D ! ) by partially reconstructing the decay ! B 0 ! D + Ds . Using data s ! collected with the CLEO II detector at CESR, we determine )=B(D0 of B(D K + + ) = 0:92 0:20(stat:) 0:11(syst:). Our measurement B(D 0 ! K ) then gives s ! ) = (3:59 0:77 0:48)%. Nearly all the Ds branching ratios are measured relative to the Ds ! mode. However, this mode is an \uncertain anchor" 1] because its branching fraction has never been reliably measured. The BES experiment has presented B(Ds ! ) = (3:9 )% 2], which is based on only two double-tagged Ds events. Estimates for this branching fraction do exist in the references 3,4], but they all make assumptions either about the decay or production of charm mesons, and in some cases, bottom mesons. In this paper, we report the rst statistically signi cant and model independent measurement of this elusive branching fraction. As this result is a direct measurement of the branching fraction it is much more reliable than previous estimates, including those of CLEO 4], which have uncertain model dependent errors. The data consist of an integrated luminosity of 2.5 fb of e e collisions recorded with the CLEO II detector at the Cornell Electron Storage Ring. The data sample contains about p 2.7 million BB events taken at center-of-mass energies on the (4S) resonance ( s 10:58 GeV). The technique is based on the partial reconstruction of the decay B ! D Ds . This decay is unique because it can be partially reconstructed in two ways. The Ds can be fully reconstructed and combined with the soft pion from the decay D ! D (NDs ), or the D can be fully reconstructed and combined with the soft photon from the decay Ds ! Ds (ND ). Because the Ds is fully reconstructed only in the rst instance, B(Ds ! ) can be extracted by measuring the e ciency corrected B meson yields using both +5:1 +1:8 1:9 1:1 1 + 0 + + 0 + + Permanent address: BINP, RU-630090 Novosibirsk, Russia 3 methods and constraining them to be equal. Although the absolute Ds ! branching fraction is not known, the ratios of other Ds modes relative to it are, so these can also be FS used to improve statistics. If the Ds and D are reconstructed using i = 1; : : : ; NDs and FS j = 1; : : : ; ND0 nal states, 0 where the quantities Ri and Rj are the Ds and D branching ratios relative to Ds ! and D ! K and where ( B)i and ( B)j are the B meson reconstruction e ciency times sub-mode branching fraction for the Ds and D decay modes. A particularly nice feature of this technique is that, since the soft pion and photon are always detected, important systematic errors cancel in the ratio. When the Ds is fully reconstructed (Figure 1a), ~Ds is measured and the constraint p EB = Ebeam is applied. Although the D is not reconstructed here, we can calculate its absolute momentum and one of the angles. If we assume the event is a true B ! D Ds ~ p ~ decay, we can use the constraints EB = ED + EDs and ~B = pD + pDs , which leads p cos Ds D = (pDs +q D pB )=2pDs pD , where Ds D is the angle between the Ds and D and where pD = (EB EDs ) mD . The D direction is constrained to lie on a cone of angle Ds D with respect to the Ds direction. The D is also constrained to lie on a cone of angle D with respect to the soft pion direction where cos D is evaluated in a similar manner. The D direction, therefore, corresponds to one of the two intersections of the two cones, which are symmetric with respect to the plane containing the Ds and the soft pion. The cosine of the azimuthal angle, Ds cos D = cos D cos sinD cos Ds ; (2) sin Ds D Ds measures the location of either solution with respect to this plane and has a very characteristic distribution, satisfying j cos D j < 1, for true B ! D Ds events. When the D is fully reconstructed, we calculate cos Ds in a similar manner. Figures 1 (b),(c) show cos D and cos Ds distributions for Monte Carlo signal events. We use these cos distributions to extract signals. Three Ds decay modes, Ds ! , K K and K K , and three D decay modes, D !K ,K and K , are used. The Ds (D ) mass is required to lie within 2:5 of its nominal value. All charged kaon and pion candidates, with the exception of the soft pion, are required to have ionization energy loss and time-of- ight consistent with the expected hypothesis, when this data is available; otherwise no cut is made. We identify , K , K and candidates using the decay modes ! K K , K (KS ) ! , 0 0 + 0 + 0 + 2 2 2 + 2 2 + + + 0 + + 0 0 0 0 + + 0 0 + 0 0 0 0 + 0 0 + FS PND0 Rj ( B)j NDs B(Ds ! ) = j=1 ; FS B(D ! K ) PNDs Ri( B)i ND i=1 0 + (1) 4 K !K and ! , respectively. We require that the K K , ,K and masses be within 8 MeV/c , 10 MeV/c , 50 MeV/c and 12 MeV/c of the nominal , K , K and masses, respectively. For the KS candidates, the vertex must be separated from the beam position. For combinations which satisfy the invariant mass cut, a mass-constrained t is performed to improve the momentum resolution. We require that each photon candidate be found in a single isolated neutral energy cluster with a minimum energy of 30 MeV for j cos j < 0:71 and 50 MeV for 0:71 < j cos j < 0:95, where is the angle of the shower with respect to the beam-line. At least one photon must lie in the region j cos j < 0:71 and both candidates must have lateral shower shapes consistent with those of photons. Angular cuts are also used to reduce the combinatoric background. Pseudoscalar to vector-pseudoscalar decays, Ds ! and Ds ! K K , follow a cos H distribution, where H is the angle between either of daughters of the vector particle and the Ds direction, both evaluated in the rest-frame of the vector particle. The combinatoric background is at in cos H . Therefore, the requirement j cos H j > 0:4 is imposed on these decays. The decay-angle, D , is the angle between the evaluated in the Ds rest frame and the Ds lab direction; for signal events the cos D distribution is at, while the background from random pions is peaked toward cos D =1. A cos D < 0:9 cut is imposed for the Ds ! decay candidates. Ds and D candidates are formed by combining Ds and D candidates with soft photons and soft pions. These combinations must satisfy the requirement that the massdi erences, MDs = MDs MDs and MD = MD0 + MD0, be within 2.5 of the measured mean values. The typical standard deviations are about 5.3 MeV/c for MDs and 1.0 MeV/c for MD . More stringent requirements are placed on these photons. They are restricted to the barrel region of the detector (jcos j < 0:71), their energies are required to be greater than 110 MeV, and a stricter lateral shape cut is used. In addition, a photon is rejected if it forms a candidate with any other photon in the event. When the D ! mode is used, the D signal to background ratio is improved by exploiting the K resonant sub-structure of the nal state. Candidates are selected from high probability regions of the Dalitz plot. D candidates are rejected if they are consistent with coming from B ! D ` decay. When the Ds is fully reconstructed, we consider two kinds of backgrounds, fake Ds 's combined with either true or random pions, and random pions combined with the true Ds 's. We use a Monte Carlo simulation, which includes both BB and continuum events, to obtain the cos D distribution for both backgrounds. We use data to obtain the normalization the for fake Ds contribution. 0 + 0 + + + 2 2 2 2 0 0 0 0 + 0 0 2 + 0 2 2 0 0 + 0 + + + 5 To obtain the normalization for the fake Ds background in the Ds signal region, we use MDs sidebands (60 < MDs < 90; 170 < MDs < 220 MeV/c ) from the Monte Carlo and the data as control samples. First, we divide the Monte Carlo sideband into two samples, one with true pions from D decay and the one with random pions. The rst sample tends to peak in the signal region of the cos D distribution, when the soft photon is fake and the Ds is true. Since the Monte Carlo does not necessarily produce the two contributions with the correct ratio, the ratio of these two is obtained from data. We t the data sideband distribution using these two Monte Carlo sideband distributions with both normalizations oated as shown in gure 2. This procedure gives the absolute normalization as well as the ratio of the normalizations for the two fake Ds backgrounds. When the D is fully reconstructed, we also consider two kinds of backgrounds, fake D 's and random photons with the true D 's. We use the Monte Carlo simulation to obtain cos Ds distribution for the backgrounds. For the fake D background, we use the same procedure to obtain the normalization as was used for the fake Ds background. Since the random photon background is a dominant background source and is rising in the signal region, we pay particular attention to its shape. Since the background shape depends on the photon energy spectrum and on the D momentum spectrum, we compare these distributions between the data and Monte Carlo. In particular, we study the E and PD + distributions, for photons and D 's used in a candidate combination, but after reversing the direction of all soft photon candidates. The reversed photon distribution provides a good approximation for the isotropically distributed random photon background; the majority (75%) of the random photon background is due to photons from the decay of the other B meson in the event, and is therefore isotropic. We compare the data and Monte Carlo distributions by calculating their ratio in each bin. The points in gure 3 show this ratio as a function of E ; we observe a systematic trend. We t the shape to a second order polynomial function to obtain a correction function. The solid line in gure 3 shows the t. When lling the cos D and cos Ds histograms, we weight each event according to this correction function with a given E . To evaluate the systematic error due to this correction procedure, we vary the correction parameters by one standard deviation obtained from the t. The maximum di erence in the nal result is 8%, for which the correction function is shown by the dotted line in gure 3. As a systematic check, we use an exponential function, instead of a polynomial function, as a correction function; this correction function changes the nal result by 2%. We also study the PD + distribution, and use the same procedure to correct it as E , however, the e ect is negligible. We also study the random pion background in the same manner. We use wrong sign combinations from the data and the Monte Carlo as control samples. The e ect on the nal 2 + + + + + + + 6 result is negligible because the random pion background contribution is small (14% of the total background). In addition to the above backgrounds, we also take into account feed down from the following decays, B ! D (2420) Ds , D (2420) ! D ; B ! D (2420) Ds , D (2420) ! D ; B ! D Ds ; B ! D Ds ; B ! D Ds1(2536) , Ds1(2536) ! D K , D ! D ; B ! D Ds , Ds ! Ds 5], ! . This contribution is quite small ( 1{2]% of the total background), and is estimated as follows. From the measurement of the inclusive B(B ! DsX) and the exclusive B(B ! D Ds ), the sum of the branching fractions for the rest of B ! DsX is constrained to be (2:73 0:54) B(B ! D Ds ) 6]. The estimate for the branching fractions for the unknown higher order mode B decays is based on this constraint. We have assumed that the total rate for these higher modes is (1:1 1:0) B(B ! D Ds ). Even if we make the extreme assumption that the rest of the modes making up B ! DsX all (or none of them) feed down to the signal mode, the nal result changes by less than 2%. The result is very insensitive to the feed-down background because it does not peak in the signal region. We assign large errors ( 90%) for the unknown branching fractions. In the t, the ratio of these feed down backgrounds relative to the signal is xed, since their branching fractions are estimated relative to the B ! D Ds decay. Figures 4(a) and (b) show the t results when Ds and D are fully reconstructed, respectively. The data is represented by data points and the t is represented by the solid histogram. The dashed histogram shows the sum of all backgrounds, and the dotted and hatched histograms show the fake Ds (D ) background and the feed down, respectively. The ts yield NDs = 76 11 and ND = 188 30. The normalization of the fake Ds (D ) background is xed in the t. The normalization of the other backgrounds are allowed to oat. The normalization of the random pion (photon) background obtained from the t is consistent with the Monte Carlo prediction. This agreement gives further con dence in the Monte Carlo predictions. To explicitly display the signal, we show the cos D and cos Ds distributions after the all backgrounds are subtracted in gures 4 (c) and (d), respectively. The points are background subtracted data and the solid histogram is the signal function. They are in good agreement. We do not observe any systematic trend outside the signal region. modes, we Table I gives the R( B) for each mode. For the D ! K and K use the following substitution, Rj ( B)j = (Nj =NK )( B)K , where Nj is the number of reconstructed D 's in the appropriate momentum region in our data sample when the D decay mode j (= K , K or K ) is used. In this way only the D ! K detection e ciency need to be determined from Monte Carlo. We do not use this substitution for 1 0 1 0 + 0 1 + 1 0 + 0 0 + 0 + 0 0 + 0 0 0 + 0 0 () () 0 + 0 + 0 + + + 0 0 + 0 0 + + 0 0 0 0 + 7 the Ds decay modes due to lack of statistics. Substituting all the relevant quantities into equation (1) we obtain, B(Ds ! ) = 0:92 0:20 0:11; (3) B(D ! K ) where the rst error is statistical and the second is systematic. This systematic error includes the uncertainty in the random photon background shape (8%), the uncertainty in the fake D and Ds background normalization (4%), the uncertainty in the feed down background normalization (2%), the uncertainty in the Ri ( B)i for Ds modes (6%), the uncertainty in the Rj ( B)j for D modes (3%), the uncertainty in the tracking e ciency (2%), the error associated with mass cuts (3%), and the uncertainty in the K reconstruction e ciency (1%). Using our measurement of B(D ! K ) = (3:91 0:19)% 7] we obtain, 0 + 0 0 0 + B(Ds ! + ) = (3:59 0:77 0:48)%: 0 + (4) We take into account the correlation of the systematic errors. When the D is fully reconstructed, we calculate the B ! D Ds branching fraction independent of the B(Ds ! ) to be B(B ! D Ds ) = (1:85 0:30 0:49)%. As a systematic check, we compare this with the measured branching fraction when the B ! D Ds is fully reconstructed; (2:11 0:52 0:37)% 6,8]. They are in good agreement. As a systematic check, we have generated 3 sets of 3 million BB Monte Carlo events with B(Ds ! ) = 3:7%, and analyzed them as if they were data. The results come out as B(Ds ! ) = (3:67 0:64), (4:00 0:92) and (4:00 0:69)%. They are consistent with the generated value. We have also looked at other kinematic variables in the partial reconstruction. Using these variables to extract yields, we obtain consistent results for B(Ds ! ). In conclusion, we have made the rst statistically signi cant measurement of B(Ds ! ). This result is free of assumptions about the production and decay of charm and bottom mesons, and is B(Ds ! ) = (3:59 0:77 0:48)%. 0 + 0 + We gratefully acknowledge the e ort of the CESR sta in providing us with excellent luminosity and running conditions. J.P.A., J.R.P., and I.P.J.S. thank the NYI program of the NSF, M.S thanks the PFF program of the NSF, G.E. thanks the Heisenberg Foundation, K.K.G., M.S., H.N.N., T.S., and H.Y. thank the OJI program of DOE, J.R.P, K.H., and M.S. thank the A.P. Sloan Foundation, and A.W., and R.W. thank the Alexander von Humboldt Stiftung for support. This work was supported by the National Science Foundation, the U.S. Department of Energy, and the Natural Sciences and Engineering Research Council of Canada. 8 ACKNOWLEDGEMENTS REFERENCES 1] Particle Data Group, L. Montanet et al., Review of Particle Properties, Phys. Rev. D 50, 1(1994). 3] TASSO Collaboration, W. Braunschweig et al., Z. Phys. C 35, 317(1987), NA14 Collaboration, M. P. Alvarez et al., Phys. Lett. B 246, 261(1990), ARGUS Collaboration, H. Albrecht et al., Phys. Lett. B 255, 634(1991), E687 Collaboration, P.L. Frabetti et al., Phys. Lett. B 313, 253(1993), F. Muheim and S. Stone, Phys. Rev. D 49, 3767(1994). The reference 1] lists all estimates for B(Ds ! ) and describes assumptions made. 2] BES Collaboration, J.Z. Bai et al., Phys. Rev. D 52, 3781(1995). 4] CLEO Collaboration, J. Alexander et al., Phys. Rev. Lett. 65, 1531(1990), F. Butler et al., Phys. Lett. B 324, 255(1994), M .Battle et al., Preprint CLEO CONF 94-18. 5] CLEO Collaboration, J. Gronberg et al., Phys. Rev. Lett. B(Ds ! Ds )=B(Ds ! Ds ) = 0:06 0:03. 0 75, 3232(1995), this gives 6] CLEO Collaboration, D. Gibaut et al., Preprint, CLNS 95/1354. Accepted by Phys. Rev. D. 7] CLEO Collaboration, D. S. Akerib et al., Phys. Rev. Lett. 71, 3070(1993). 8] The value is corrected upward by 4% since this measurement assumed B(Ds ! Ds ) = 100% and B(Ds ! ) = 3:5 0:4%. The systematic error does not include the error due to B(Ds ! ). 9 FIGURES 3281295-016 (a) D* D * D* S D* D* S D * D* S 0.25 (b) 3281295-017 3281295-018 0.25 Monte Carlo 0.20 (c) Monte Carlo 0.20 Arbitrary Units 0.15 Arbitrary Units 2.5 0 cos * D 2.5 5.0 0.15 0.10 0.10 0.05 0.05 0 5.0 0 5.0 2.5 0 cos * DS 2.5 5.0 I I I decay when the Ds is fully reconstructed. (b) The signal Monte Carlo cos distribution for events in which the Ds is fully FIG. 1. (a) Partial Reconstruction of the B 0 ! D + Ds reconstructed and (c) for events in which the D + is fully reconstructed. 10 I 50 3281295-019 Events / 0.4 25 0 0 5 cos * DS 10 FIG. 2. cos D distribution in MDs sidebands. The points with errors indicate data and the solid histogram indicates the sum of two Monte Carlo backgrounds. The dashed histogram indicates the contribution from signal pion{fake Ds . 11 0.20 3281295-020 0.15 Ratio (Data / MC) 0.10 0.05 0 0.10 0.15 0.20 E (GeV) 0.25 0.30 FIG. 3. The ratio of the data to the Monte Carlo in each E bin for random photon background and t to a second order polynomial function. The dotted line is explained in the text. 12 50 (a) 40 3281295-021 200 (b) 3281295-022 150 Events / 0.2 30 Events / 0.4 100 20 50 10 0 0 5 cos * D 10 0 10 5 0 cos 5 D S* 10 3281295-023 I I 3281295-024 (c) 30 (d) 40 20 Events / 0.2 Events / 0.4 0 0 0 5 cos * D 10 40 10 I I 10 10 5 0 cos * DS 5 10 I FIG. 4. Fit used to extract the number of B 0 candidates when (a) the Ds and (b) the D + are fully reconstructed. The data is represented by data points and the t is represented by the solid histogram. The dashed line show the sums of all backgrounds, whereas the dotted and hatched lines represent the fake Ds (D + ) background and the feed down, respectively. Background subtracted data when (c) the Ds and (d) the D + are fully reconstructed. Solid histograms are signal functions. 13 I TABLES decay mode Ds Ds Ds D0 D0 D0 ! R( B) (%) 2:34 0:06 K 0K K K K K 0 0 ! 1:85 0:30 2:50 0:27 7:42 0:13 0 ! K + + + ! ! 6:13 0:35 1:61 0:14 ! TABLE I. R( B) when each of the Ds and D0 decay modes is used to fully reconstruct either the Ds or D + , respectively. 14

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