BABAR-PUB-10/024 SLAC-PUB-14229 hep-ex/1008.4080 Measurement of the Absolute Branching Fractions for D− → ℓ−ν¯ and Extraction of s ℓ the Decay Constant f Ds P. del Amo Sanchez,1 J. P. Lees,1 V. Poireau,1 E. Prencipe,1 V. Tisserand,1 J. Garra Tico,2 E. Grauges,2 M. Martinelliab,3 A. Palanoab,3 M. Pappagalloab,3 G. Eigen,4 B. Stugu,4 L. Sun,4 M. Battaglia,5 D. N. Brown,5 B. Hooberman,5 L. T. Kerth,5 Yu. G. Kolomensky,5 G. Lynch,5 I. L. Osipenkov,5 T. Tanabe,5 C. M. Hawkes,6 A. T. Watson,6 H. Koch,7 T. Schroeder,7 D. J. Asgeirsson,8 C. Hearty,8 T. S. Mattison,8 J. A. McKenna,8 1 A. Khan,9 A. Randle-Conde,9 V. E. Blinov,10 A. R. Buzykaev,10 V. P. Druzhinin,10 V. B. Golubev,10 1 A. P. Onuchin,10 S. I. Serednyakov,10 Yu. I. Skovpen,10 E. P. Solodov,10 K. Yu. Todyshev,10 A. N. Yushkov,10 0 M. Bondioli,11 S. Curry,11 D. Kirkby,11 A. J. Lankford,11 M. Mandelkern,11 E. C. Martin,11 D. P. Stoker,11 2 H. Atmacan,12 J. W. Gary,12 F. Liu,12 O. Long,12 G. M. Vitug,12 C. Campagnari,13 T. M. Hong,13 D. Kovalskyi,13 n J. D. Richman,13 C. West,13 A. M. Eisner,14 C. A. Heusch,14 J. Kroseberg,14 W. S. Lockman,14 A. J. Martinez,14 a T. Schalk,14 B. A. Schumm,14 A. Seiden,14 L. O. Winstrom,14 C. H. Cheng,15 D. A. Doll,15 B. Echenard,15 J D. G. Hitlin,15 P. Ongmongkolkul,15 F. C. Porter,15 A. Y. Rakitin,15 R. Andreassen,16 M. S. Dubrovin,16 7 G. Mancinelli,16 B. T. Meadows,16 M. D. Sokoloff,16 P. C. Bloom,17 W. T. Ford,17 A. Gaz,17 M. Nagel,17 ] U. Nauenberg,17 J. G. Smith,17 S. R. Wagner,17 R. Ayad,18,∗ W. H. Toki,18 H. Jasper,19 T. M. Karbach,19 x e J. Merkel,19 A. Petzold,19 B. Spaan,19 K. Wacker,19 M. J. Kobel,20 K. R. Schubert,20 R. Schwierz,20 - D. Bernard,21 M. Verderi,21 P. J. Clark,22 S. Playfer,22 J. E. Watson,22 M. Andreottiab,23 D. Bettonia,23 p C. Bozzia,23 R. Calabreseab,23 A. Cecchiab,23 G. Cibinettoab,23 E. Fioravantiab,23 P. Franchiniab,23 E. Luppiab,23 e h M. Muneratoab,23 M. Negriniab,23 A. Petrellaab,23 L. Piemontesea,23 R. Baldini-Ferroli,24 A. Calcaterra,24 [ R. de Sangro,24 G. Finocchiaro,24 M. Nicolaci,24 S. Pacetti,24 P. Patteri,24 I. M. Peruzzi,24,† M. Piccolo,24 3 M. Rama,24 A. Zallo,24 R. Contriab,25 E. Guidoab,25 M. Lo Vetereab,25 M. R. Mongeab,25 S. Passaggioa,25 v C. Patrignaniab,25 E. Robuttia,25 S. Tosiab,25 B. Bhuyan,26 V. Prasad,26 C. L. Lee,27 M. Morii,27 A. Adametz,28 0 J. Marks,28 U. Uwer,28 F. U. Bernlochner,29 M. Ebert,29 H. M. Lacker,29 T. Lueck,29 A. Volk,29 P. D. Dauncey,30 8 M. Tibbetts,30 P. K. Behera,31 U. Mallik,31 C. Chen,32 J. Cochran,32 H. B. Crawley,32 L. Dong,32 0 4 W. T. Meyer,32 S. Prell,32 E. I. Rosenberg,32 A. E. Rubin,32 A. V. Gritsan,33 Z. J. Guo,33 N. Arnaud,34 . M. Davier,34 D. Derkach,34 J. Firmino da Costa,34 G. Grosdidier,34 F. Le Diberder,34 A. M. Lutz,34 B. Malaescu,34 8 0 A. Perez,34 P. Roudeau,34 M. H. Schune,34 J. Serrano,34 V. Sordini,34,‡ A. Stocchi,34 L. Wang,34 G. Wormser,34 0 D. J. Lange,35 D. M. Wright,35 I. Bingham,36 C. A. Chavez,36 J. P. Coleman,36 J. R. Fry,36 E. Gabathuler,36 1 R. Gamet,36 D. E. Hutchcroft,36 D. J. Payne,36 C. Touramanis,36 A. J. Bevan,37 F. Di Lodovico,37 R. Sacco,37 : v M. Sigamani,37 G. Cowan,38 S. Paramesvaran,38 A. C. Wren,38 D. N. Brown,39 C. L. Davis,39 A. G. Denig,40 i M. Fritsch,40 W. Gradl,40 A. Hafner,40 K. E. Alwyn,41 D. Bailey,41 R. J. Barlow,41 G. Jackson,41 G. D. Lafferty,41 X J. Anderson,42 R. Cenci,42 A. Jawahery,42 D. A. Roberts,42 G. Simi,42 J. M. Tuggle,42 C. Dallapiccola,43 r a E. Salvati,43 R. Cowan,44 D. Dujmic,44 G. Sciolla,44 M. Zhao,44 D. Lindemann,45 P. M. Patel,45 S. H. Robertson,45 M. Schram,45 P. Biassoniab,46 A. Lazzaroab,46 V. Lombardoa,46 F. Palomboab,46 S. Strackaab,46 L. Cremaldi,47 R. Godang,47,§ R. Kroeger,47 P. Sonnek,47 D. J. Summers,47 X. Nguyen,48 M. Simard,48 P. Taras,48 G. De Nardoab,49 D. Monorchioab,49 G. Onoratoab,49 C. Sciaccaab,49 G. Raven,50 H. L. Snoek,50 C. P. Jessop,51 K. J. Knoepfel,51 J. M. LoSecco,51 W. F. Wang,51 L. A. Corwin,52 K. Honscheid,52 R. Kass,52 J. P. Morris,52 N. L. Blount,53 J. Brau,53 R. Frey,53 O. Igonkina,53 J. A. Kolb,53 R. Rahmat,53 N. B. Sinev,53 D. Strom,53 J. Strube,53 E. Torrence,53 G. Castelliab,54 E. Feltresiab,54 N. Gagliardiab,54 M. Margoniab,54 M. Morandina,54 M. Posoccoa,54 M. Rotondoa,54 F. Simonettoab,54 R. Stroiliab,54 E. Ben-Haim,55 G. R. Bonneaud,55 H. Briand,55 G. Calderini,55 J. Chauveau,55 O. Hamon,55 Ph. Leruste,55 G. Marchiori,55 J. Ocariz,55 J. Prendki,55 S. Sitt,55 M. Biasiniab,56 E. Manoniab,56 A. Rossiab,56 C. Angeliniab,57 G. Batignaniab,57 S. Bettariniab,57 M. Carpinelliab,57,¶ G. Casarosaab,57 A. Cervelliab,57 F. Fortiab,57 M. A. Giorgiab,57 A. Lusianiac,57 N. Neriab,57 E. Paoloniab,57 G. Rizzoab,57 J. J. Walsha,57 D. Lopes Pegna,58 C. Lu,58 J. Olsen,58 A. J. S. Smith,58 A. V. Telnov,58 F. Anullia,59 E. Baracchiniab,59 G. Cavotoa,59 R. Facciniab,59 F. Ferrarottoa,59 F. Ferroniab,59 M. Gasperoab,59 L. Li Gioia,59 M. A. Mazzonia,59 G. Pireddaa,59 F. Rengaab,59 T. Hartmann,60 T. Leddig,60 H. Schr¨oder,60 R. Waldi,60 T. Adye,61 B. Franek,61 E. O. Olaiya,61 F. F. Wilson,61 S. Emery,62 G. Hamel de Monchenault,62 G. Vasseur,62 Ch. Y`eche,62 2 M. Zito,62 M. T. Allen,63 D. Aston,63 D. J. Bard,63 R. Bartoldus,63 J. F. Benitez,63 C. Cartaro,63 M. R. Convery,63 J. Dorfan,63 G. P. Dubois-Felsmann,63 W. Dunwoodie,63 R. C. Field,63 M. Franco Sevilla,63 B. G. Fulsom,63 A. M. Gabareen,63 M. T. Graham,63 P. Grenier,63 C. Hast,63 W. R. Innes,63 M. H. Kelsey,63 H. Kim,63 P. Kim,63 M. L. Kocian,63 D. W. G. S. Leith,63 S. Li,63 B. Lindquist,63 S. Luitz,63 V. Luth,63 H. L. Lynch,63 D. B. MacFarlane,63 H. Marsiske,63 D. R. Muller,63 H. Neal,63 S. Nelson,63 C. P. O’Grady,63 I. Ofte,63 M. Perl,63 T. Pulliam,63 B. N. Ratcliff,63 A. Roodman,63 A. A. Salnikov,63 V. Santoro,63 R. H. Schindler,63 J. Schwiening,63 A. Snyder,63 D. Su,63 M. K. Sullivan,63 S. Sun,63 K. Suzuki,63 J. M. Thompson,63 J. Va’vra,63 A. P. Wagner,63 M. Weaver,63 C. A. West,63 W. J. Wisniewski,63 M. Wittgen,63 D. H. Wright,63 H. W. Wulsin,63 A. K. Yarritu,63 C. C. Young,63 V. Ziegler,63 X. R. Chen,64 W. Park,64 M. V. Purohit,64 R. M. White,64 J. R. Wilson,64 S. J. Sekula,65 M. Bellis,66 P. R. Burchat,66 A. J. Edwards,66 T. S. Miyashita,66 S. Ahmed,67 M. S. Alam,67 J. A. Ernst,67 B. Pan,67 M. A. Saeed,67 S. B. Zain,67 N. Guttman,68 A. Soffer,68 P. Lund,69 S. M. Spanier,69 R. Eckmann,70 J. L. Ritchie,70 A. M. Ruland,70 C. J. Schilling,70 R. F. Schwitters,70 B. C. Wray,70 J. M. Izen,71 X. C. Lou,71 F. Bianchiab,72 D. Gambaab,72 M. Pelliccioniab,72 M. Bombenab,73 L. Lanceriab,73 L. Vitaleab,73 N. Lopez-March,74 F. Martinez-Vidal,74 D. A. Milanes,74 A. Oyanguren,74 J. Albert,75 Sw. Banerjee,75 H. H. F. Choi,75 K. Hamano,75 G. J. King,75 R. Kowalewski,75 M. J. Lewczuk,75 I. M. Nugent,75 J. M. Roney,75 R. J. Sobie,75 T. J. Gershon,76 P. F. Harrison,76 T. E. Latham,76 E. M. T. Puccio,76 H. R. Band,77 S. Dasu,77 K. T. Flood,77 Y. Pan,77 R. Prepost,77 C. O. Vuosalo,77 and S. L. Wu77 (The BABAR Collaboration) 1Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Universit´e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France 2Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain 3INFN Sezione di Baria; Dipartimento di Fisica, Universita` di Barib, I-70126 Bari, Italy 4University of Bergen, Institute of Physics, N-5007 Bergen, Norway 5Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA 6University of Birmingham, Birmingham, B15 2TT, United Kingdom 7Ruhr Universita¨t Bochum, Institut fu¨r Experimentalphysik 1, D-44780 Bochum, Germany 8University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1 9Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom 10Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia 11University of California at Irvine, Irvine, California 92697, USA 12University of California at Riverside, Riverside, California 92521, USA 13University of California at Santa Barbara, Santa Barbara, California 93106, USA 14University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA 15California Institute of Technology, Pasadena, California 91125, USA 16University of Cincinnati, Cincinnati, Ohio 45221, USA 17University of Colorado, Boulder, Colorado 80309, USA 18Colorado State University, Fort Collins, Colorado 80523, USA 19Technische Universita¨t Dortmund, Fakult¨at Physik, D-44221 Dortmund, Germany 20Technische Universita¨t Dresden, Institut fu¨r Kern- und Teilchenphysik, D-01062 Dresden, Germany 21Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France 22University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 23INFN Sezione di Ferraraa; Dipartimento di Fisica, Universita` di Ferrarab, I-44100 Ferrara, Italy 24INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy 25INFN Sezione di Genovaa; Dipartimento di Fisica, Universita` di Genovab, I-16146 Genova, Italy 26Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India 27Harvard University, Cambridge, Massachusetts 02138, USA 28Universita¨t Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany 29Humboldt-Universita¨t zu Berlin, Institut fu¨r Physik, Newtonstr. 15, D-12489 Berlin, Germany 30Imperial College London, London, SW7 2AZ, United Kingdom 31University of Iowa, Iowa City, Iowa 52242, USA 32Iowa State University, Ames, Iowa 50011-3160, USA 33Johns Hopkins University, Baltimore, Maryland 21218, USA 34Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11, Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France 35Lawrence Livermore National Laboratory, Livermore, California 94550, USA 36University of Liverpool, Liverpool L69 7ZE, United Kingdom 37Queen Mary, University of London, London, E1 4NS, United Kingdom 38University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom 39University of Louisville, Louisville, Kentucky 40292, USA 40Johannes Gutenberg-Universit¨at Mainz, Institut fu¨r Kernphysik, D-55099 Mainz, Germany 3 41University of Manchester, Manchester M13 9PL, United Kingdom 42University of Maryland, College Park, Maryland 20742, USA 43University of Massachusetts, Amherst, Massachusetts 01003, USA 44Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA 45McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8 46INFN Sezione di Milanoa; Dipartimento di Fisica, Universita` di Milanob, I-20133 Milano, Italy 47University of Mississippi, University, Mississippi 38677, USA 48Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7 49INFN Sezione di Napolia; Dipartimento di Scienze Fisiche, Universita` di Napoli Federico IIb, I-80126 Napoli, Italy 50NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands 51University of Notre Dame, Notre Dame, Indiana 46556, USA 52Ohio State University, Columbus, Ohio 43210, USA 53University of Oregon, Eugene, Oregon 97403, USA 54INFN Sezione di Padovaa; Dipartimento di Fisica, Universita` di Padovab, I-35131 Padova, Italy 55Laboratoire de Physique Nucl´eaire et de Hautes Energies, IN2P3/CNRS, Universit´e Pierre et Marie Curie-Paris6, Universit´e Denis Diderot-Paris7, F-75252 Paris, France 56INFN Sezione di Perugiaa; Dipartimento di Fisica, Universita` di Perugiab, I-06100 Perugia, Italy 57INFN Sezione di Pisaa; Dipartimento di Fisica, Universita` di Pisab; Scuola Normale Superiore di Pisac, I-56127 Pisa, Italy 58Princeton University, Princeton, New Jersey 08544, USA 59INFN Sezione di Romaa; Dipartimento di Fisica, Universita` di Roma La Sapienzab, I-00185 Roma, Italy 60Universita¨t Rostock, D-18051 Rostock, Germany 61Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom 62CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France 63SLAC National Accelerator Laboratory, Stanford, California 94309 USA 64University of South Carolina, Columbia, South Carolina 29208, USA 65Southern Methodist University, Dallas, Texas 75275, USA 66Stanford University, Stanford, California 94305-4060, USA 67State University of New York, Albany, New York 12222, USA 68Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel 69University of Tennessee, Knoxville, Tennessee 37996, USA 70University of Texas at Austin, Austin, Texas 78712, USA 71University of Texas at Dallas, Richardson, Texas 75083, USA 72INFN Sezione di Torinoa; Dipartimento di Fisica Sperimentale, Universita` di Torinob, I-10125 Torino, Italy 73INFN Sezione di Triestea; Dipartimento di Fisica, Universita` di Triesteb, I-34127 Trieste, Italy 74IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain 75University of Victoria, Victoria, British Columbia, Canada V8W 3P6 76Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom 77University of Wisconsin, Madison, Wisconsin 53706, USA (Dated: January 10, 2011) The absolute branching fractions for the decays D−→ℓ−ν¯ (ℓ = e, µ, or τ) are measured using s ℓ a data sample corresponding to an integrated luminosity of 521 fb−1 collected at center of mass energiesnear10.58GeVwiththeBABARdetectoratthePEP-IIe+e−collideratSLAC.Thenumber of D− mesons is determined by reconstructing the recoiling system DKXγ in events of the type s e+e−→DKXD∗−,whereD∗− →D−γ andX representsadditionalpionsfrom fragmentation. The s s s D− → ℓ−ν events are detected by full or partial reconstruction of the recoiling system DKXγℓ. s ℓ The branching fraction measurements are combined to determine the Ds− decay constant fDs = (258.6±6.4±7.5) MeV, where thefirst uncertaintyis statistical and thesecond is systematic. PACSnumbers: 13.20.Fc,12.38.Gc The D− meson can decay purely leptonically via an- s nihilation of the c¯ and s quarks into a W− boson [1]. In the Standard Model (SM), the leptonic partial width ∗†ANloswowatitTheUmnpilveerUsniti`avedrisiPtye,ruPghiial,adPeelrpuhgiiaa,,PItAal1y9122,USA Γ(Ds−→ℓ−ν¯ℓ) is given by ‡AlsowithUniversit`adiRomaLaSapienza, I-00185Roma,Italy §NowatUniversityofSouthAlabama,Mobile,AL36688, USA G2M3 m 2 m2 2 ¶AlsowithUniversit`adiSassari,Sassari,Italy Γ= F8πDs (cid:18)M ℓ (cid:19) (cid:18)1− M2ℓ (cid:19) |Vcs|2fD2s, (1) Ds Ds 4 where M and m are the D− and lepton masses, re- fication (PID) of charged hadrons. Muons are mainly Ds ℓ s spectively, G is the Fermi coupling constant, and V identified by the instrumented magnetic flux return,and F cs is an element of the Cabibbo-Kobayashi-Maskawaquark electrons are identified using EMC and dE/dx informa- mixing matrix. These decays provide a clean probe of tion. The analysis uses Monte Carlo (MC) events gen- the pseudoscalar meson decay constant f . erated with EvtGen and JETSET [10, 11] and passed Ds Within the SM, f has been predicted using sev- throughadetailedGEANT4[12]simulationofthedetec- Ds eral methods [2]; the most precise value by Follana torresponse. Finalstateradiationfromchargedparticles etal. uses unquenched LQCD calculations and gives is modeled by PHOTOS [13]. Samples of MC events for f =(241 3) MeV. Currently, the experimental values e+e−annihilationtoqq¯(q =u,d,s,c,b)(genericMC)are aDressignific±antly larger than this theoretical prediction. used to develop methods to separate signal events from TheHeavyFlavorAveragingGroupcombinestheCLEO- backgrounds. In addition, we use dedicated samples for c, Belle and BABAR measurements and reports fDs= Ds− production and leptonic decays (signal MC) to de- (254.6 5.9) MeV [3]. Models of new physics (NP), in- termine reconstruction efficiencies and the distributions cluding±atwo-Higgsdoublet [4]andleptoquarks[5], may needed for the extraction of the signal decays. explain this difference. In addition, f measurements We reconstruct D candidates using the following Ds provide a cross-check of QCD calculations which predict 15 modes: D0 K−π+(π0), K−π+π−π+(π0), or the impact of NP on B and B meson decay rates and K0π+π−(π0); D+→ K−π+π+(π0), K0π+(π0), or mixing. Highprecisiondeterminsationsoff ,bothfrom KS0π+π−π+;andΛ+ →pK−π+(π0),pK0,oSrpK0π−π+. experimentandtheory,arenecessaryinordDesrtodiscover AlSl π0’s and K0’s ucse→d in this analysis arSe reconsStructed S or constrain effects of NP. from two photons or two oppositely charged pions, re- We present absolute measurements of the branching spectively, and are kinematically constrained to their fractions of leptonic D− decays with a method simi- nominalmassvalues[14]. TheK0 inaDcandidatemust s S lar to the one used by the Belle Collaboration [6, 7]. have a flight distance from the e+e− interaction point An inclusive sample of D−’s is obtained by recon- (IP) greater than 10 times its uncertainty. For each D s structing the rest of the event in reactions of the kind candidate we fit the tracks to a common vertex, and for e+e− cc¯ DKXD∗−, where D∗− D−γ. Here, D each mode, we determine the mean and σ of the recon- repres→ents→a charmeds hadron (D0s, D→+, Ds∗, or Λ+), K structed signal mass distribution from a fit to data. We c representstheK0 orK+ requiredtobalancestrangeness thensimultaneouslyoptimizeasetofselectioncriteriato intheevent,andSX representsadditionalpionsproduced maximizeS/√S+B, whereS referstothe number ofD in the cc¯ fragmentation process. When the charmed candidates after subtractionofthe backgroundB within hadron is a Λ+ an additional anti-proton is required to a mass window defined about the signal peak. Where B c assure baryon number conservation. No requirements is estimated from the sideband regions of the mass dis- are placed on the decay products of the D− so that tribution. In addition to the size of the mass window, s the selected events correspond to an inclusive sample. several other properties of the D candidate are used in The4-momentumofeachD− candidate, p ,ismeasured the optimization: the center-of-mass (CM) momentum s r as the difference between the momenta of the colliding of the D, PID requirements on the tracks, the probabil- beam particles and the fully reconstructed DKXγ sys- ity of the D vertex fit, and the minimum lab energy of tem: pr = pe+ + pe− pD pK pX pγ. π0 photons. The CM momentum must be at least 2.35 The inclusive D− yield is −obtained−from a−binned−fit to GeV/c in order to remove B meson backgrounds. After s the distribution in the recoil mass m (DKXγ) p2. the optimization the relative contributions to the total r ≡ r signal sample are 74.0% D0, 22.6% D+, and 3.4% Λ+. Within this inclusive sample, we determine the frapction c of events corresponding to D− µ−ν¯ , D− e−ν¯ , and Multiple candidates per event are accepted. D− τ−ν¯ decays. In the SsM→, ratioµs ofsth→e braneching To identify D mesons originating from D∗ decays we frasct→ionsfoτrthesedecaysaree−ν¯ :µ−ν¯ :τ−ν¯ =2 10−5: reconstruct the following decays: D∗+ D0π+, D∗0 1 : 10, due to helicity and phase-espaceµsupprτessio×n. D0π0, D∗+ D+π0, and D∗0 D→0γ. The photo→n → → The analysis is based on a data sample of 521 fb−1, energy in the laboratory frame is required to exceed 30 which corresponds to about 677 million e+e− cc¯ MeV for π0 γγ and 250 MeV for D∗0 D0γ decays. → → events, recorded near √s = 10.58 GeV by the B→ABAR The γγ invariant mass must be within 3 sigma of the π0 peak. ForallD∗ decays,themassdifferencem(D∗) detector at the SLAC PEP-II asymmetric-energy col- − m(D)isrequiredtobewithin2.5sigmaofthepeakvalue. lider. The detector is described in detail in Refs. [8, 9]. Charged-particle momenta are measured with a 5 layer, A K candidate is selected from tracksnot overlapping double-sided silicon vertex tracker (SVT) and a 40 layer with the D candidate. PID requirements are applied to drift chamber (DCH) inside a 1.5 T superconducting each K+ candidate, and a K0 candidate must have a S solenoidal magnet. A calorimeter consisting of 6580 flight distance greater than 5 times its uncertainty. CsI(Tl) crystals (EMC) is used to measure electro- An X candidate is reconstructed from the remaining magnetic energy. Measurements from a ring-imaging π±’s and π0s not overlapping with the DK candidate. Cherenkov radiation detector, and of specific ionization In the laboratory frame, a π± must have a momentum (dE/dx) in the SVT and DCH, provide particle identi- greaterthan100MeV/candeachphotonfromaπ0decay 5 musthaveenergygreaterthan100 MeV. Wereconstruct inaccuracies, we extract the D− signal yields from a fit s Xmodeswithoutπ0’swithuptothreechargedpions,and to the two-dimensional histogram of m (DKXγ) versus r modes with one π0 with up to two charged pions. The nR. The PDF for the signal distribution is written as a X total charge of the X candidate is not checked at this weighted sum of the MC distributions for j =nT, X stage. Finally,weselectaγ candidateforthesignalD∗− de- 6 s S(m,nR)= w S (m,nR). (2) cay by requiring a minimum energy of 120 MeV in the X j j X laboratory frame, and an angle with respect to the di- Xj=0 rection of the D candidate momentum in the CM frame The weights w have to be extracted from this fit. To greaterthan90degrees. Thisphotoncannotformaπ0or j constraintheshapeoftheweightsdistribution,weintro- ηcandidatewhencombinedwithanyotherphotoninthe duce the parameterization w (j α)βe−γj together j event. In addition, the cluster must pass tight require- ∝ − with the condition w = 1. This parametrization is j j ments onthe showershapeinthe EMCandaseparation motivatedby the diPstributionof weights inthe MC. The ofatleast15cmfromtheimpactofanychargedparticle value α = 1.32 is taken from a fit to MC, whereas β or the position of any other energy cluster in the EMC. − and γ are determined from the fit to data. Only DKXγ candidates with a total charge of +1 are The RS and WS samples are fitted simultaneously to selected to form a right-sign (RS) sample, from which determine the background. The fit to the WS sample we extract the Ds− signal yield. The charm and strange uses a signal component similar to that used in the RS quark content of the DKX must be consistent with re- fit, except that due to the small signal component, the coiling from a Ds−. The RS sample includes candidates weightsarefixedtotheMCvaluesandthesignalyieldis for which consistency cannot be determined due to the determinedfromsignalMC tobe 11.8%ofthe RSsignal presence of a K0. We define a wrong-sign (WS) sample yield. The shapes remaining after the signal component S withthesamechargerequirementabove,butbyrequiring is removed from the WS sample, B (m) (i = nR), are i X that the charm and strange quark content of the DKX used to model the RS backgrounds. A shape correction be consistent with a recoil from a Ds+. The WS sam- isappliedtoB0toaccountforadifferenceobservedinthe ple contains a small fraction of signal events due mainly MC. We addthese components with free coefficients (b ) i to DKX candidates for which the total charge is misre- toconstructthetotalRSbackgroundshape: B(m,nR)= X constructed. The generic MC shows that the WS sam- 3 b B (m)δ(i nR). Thusinadditiontoβ,γ,andthe ple,aftersubtractionofthesignalcontribution,correctly i=0 i i − X Ptotal signal yield, there are 3 additional free parameters models the backgrounds in the RS sample. b (i=0,1,2) in the RS fit. i A kinematic fit to each DKX candidate is per- Figure 1 shows the data and the results of the fit, and formed in which the particles are required to originate Fig.2 shows the totalRS andWS samples. The fit finds from a common point inside the IP region, and the D a mininum χ2/ndf = 216/182 and the fitted parameter mass is constrained to the nominal value [14]. The 4- values are β = 0.27 0.17 and γ = 0.28 0.07. These momentum ofthe signal Ds∗− is extractedas the missing are different from th±e MC values β = 3.38±and γ = 1.15 4-momentumintheevent. WerequirethattheDs∗− can- since there are more events at low values of nTX than in didate mass be within 2.5σ of the signal peak. For MC the MC. signalevents,themeanisfoundtobeconsistentwiththe Having constructed the inclusive D− sample, we pro- nominal value and σ varies between 37 and 64 MeV/c2 ceed to the selection of D− µ−ν¯ esvents within that depending on the number of pions in X. sample. We use the m (DsK→Xγ) µrange between 1.934 r We perform a similar kinematic fit with the signal γ and 2.012 GeV/c2, which contains an inclusive D− yield s included and with the mass recoiling against the DKX (N ) of(67.2 1.5) 103. We requirethatthere be ex- constrained to the nominal D∗− mass [14] in order to actDlys one more±charg×ed particle in the remainder of the s determine the D− 4-momentum. We require that the event, and that it be identified as a µ−. In addition, we s D− CMmomentumexceed3.0GeV/c,andthatitsmass requirethattheextraneutralenergyintheevent,E , s extra be greater than 1.82 GeV/c2. After the final selections, belessthan1.0GeV;E isdefinedasthetotalenergy extra there remain on average 1.7 D− candidates per event, of EMC clusters with individual energy greater than 30 s due mainly to multiple photons that can be associated MeV and not overlapping with the DKXγ candidate. with the D∗− decay. In order to properly count events Sincetheonlymissingparticleintheeventshouldbethe s in the fits described below, we assignweight 1/n to each neutrino we expectthe distribution ofE to peak at extra D− candidate, where n is the number of D− candidates zero for signal events. We determine the 4-momentum s s in the event. of the ν¯ candidate through a kinematic fit similar to µ We define nR and nT to be the number of recon- that described earlier in the determination of the D− X X s structed and true pions in the X system, respectively. 4-momentum,butwiththeµ− includedintherecoilsys- The efficiency for reconstructing signal events depends tem. In this fit we constrain the mass recoiling against on nT. However, the nT distribution is expected to dif- the DKXγ system to the nominal value for the D− X X s fer from the MC simulation due to inaccurate fragmen- [14]. To extract the signal yield, we perform a binned tation functions used by JETSET. To correct for these maximum likelihood fit to the m2(DKXγµ) distribu- r 6 2MeV/c 6×1n0XR00=0 2MeV/c 8×1n0XR00=1 42 /cGeV100 a) 42 /cGeV4600 b) 6 4 6 6 5 5 Events / 2 Events / 24 vents / 0.050 vents / 0.020 E E 0 0 1.85 1.9 m1.r9(5DKX2γ) 2 . 0(G5eV2/.c12) 1.85 1.9 m1.r9(D5KX2γ) 2 .0(G5eV2/.c12) -0.5 0mr2(D0.K5Xγµ1) (G1.e5V2/c42) -0.5 0mr2(0D.5KXγe1) (G1.e5V2/c42) ×1000 ×1000 2MeV/c10 nXR=2 2MeV/c 8 nXR=3 5 GeV100 c) 5 GeV100 d) nts / 6 5 nts / 6 46 nts / 0.0 nts / 0.0 Eve Eve 2 Eve50 Eve50 0 0 1.85 1.9 1.95 2 2.05 2.1 1.85 1.9 1.95 2 2.05 2.1 mr(DKXγ) (GeV/c2) mr(DKXγ) (GeV/c2) 0 1 2 3 0 1 2 3 E (GeV) E (GeV) extra extra FIG. 1: (color online) mr(DKXγ) distributions for each nRX value. The points are the data. The open histogram is 2V/c e) from thefit described in thetext. Thesolid histogram is the Me600 8 bthaeckrgergoiounndusceodmipnotnheentℓ−frν¯oℓmsetlhecetfiiotn.sT.heverticallinesdefine vents / 400 E200 ×1000 ×1000 2.05 2.1 2.15 2.2 2V/c 8 2V/c30 m(K+K-π+γ) (GeV/c2) e e M 6 M nts / 6 4 nts / 6 20 FmI2rG(D. K3X: γµ)(,c(oblo)rm2ro(nDliKneX)γeF)i,t(tce)dEedxitsrtaribfourtiDons−s→oτfe−νν(ν¯aτ), Eve 2 Eve10 (d) Eextra for Ds−→τµ−ννν¯τ candidates, and (e) m(KKπγ). In each figure, the points represent the data with statistical 0 0 1.85 1.9 m1.9(5DKX2γ) 2 . 0(G5eV2/.c12) 1.85 1.9 m1.9(D5KX2γ) 2 .0(G5eV2/.c12) errorbars,theopenhistogramisfromthefitdescribedinthe r r text, and the solid histogram is the background component from the fit. FIG. 2: (color online) mr(DKXγ) distribution for thetotal WS (left) and RS(right) samples. the resolutiononthe D− signalPDF(for bothmassand s tion using a signal PDF determined from reconstructed nR), and by estimating how well the MC models the X signal MC events that contain the signal decay chain non-peaking component of the signal PDF observed in Ds∗− → Ds−γ with Ds−→µ−ν¯µ. The background PDF Figs. 1 and 2. The non-peaking signal component in the is determined from the reconstructed generic MC events m (DKXγ) distribution arises from DKXγ candidates r withsignaleventsremoved. ThefitisshowninFig.3(a), ineventsthatcontainthesignaldecayD∗− D−γ,but s → s and the number of signalevents extracted, Nµν, is listed for which the photon candidate is mis-identified and is in Table I. due to other sources such as π0 or η decays, or tracks The Ds−→µ−ν¯µ branching fraction is obtained from: or KL0 interacting in the calorimeter. Uncertainties are assigned for possible mismodeling of the signal or back- (D− µ−ν¯ )= Nµν = Nµν , (3) ground m2r(DKXγµ) distributions due to possible dif- B s → µ NDsP6j=0wjεεjDjµνs NDsε¯µν fbeurteinocne,soirnmthisempoodseitliinongsoorfrdeisffoeluretniotnDos−f tdheecamyass.sUdniscterri-- tainties in the efficiencies due to tracking and µ− identi- where the Ds−→µ−ν¯µ reconstruction efficiency, εjµν, is fication are included. This measurement supersedes our determinedusingthesignalMCsamplewithj =nT,and previous result [15]. X εfijDciseniscyt.heThcoererffiescpioenndcyinrgatiniocsluεsjiv/eεDj s−dreeccroenassterfurcotmion87e%f- weUssienagrcha pforrocDed−ure sime−ilν¯ar teovetnhtas.t foTrhDes−fit→toµ−tνh¯µe to 33% as j increases from 0 µtoν 6.DsThe weighted aver- m2(DKXγe) disstrib→ution,eshown in Fig. 3(b), gives a r age, ε¯ , and the value determined for (D− µ−ν¯ ) signal yield N consistent with 0. We obtain an upper are listµeνdin Table I. The statistical unceBrtainsty→includµes limit on (D−eν e−ν¯ ) by integrating a likelihood func- contributionsfromN , ε¯ ,andN (with correlations tion fromB0 tso→the vaelue of (D− e−ν¯ ) correspond- Ds µν µν B s → e takenintoaccounted). Thesystematicuncertaintyis de- ing to 90% of the integral from 0 to infinity. The like- termined by varying the parameter values in the inclu- lihood function consists of a Gaussian function written sive D− fit which were fixed to MC values, by varying in terms of the variable N ε¯ with mean and sigma s B Ds eν 7 TABLE I: Average efficiency ratios, signal yields, branching fractions, and decay constants for the leptonic D− decays. The s first uncertainty is statistical and the second is systematic. Decay ε¯ Signal Yield B(Ds−→ℓ−ν¯ℓ) fDs (MeV) Ds−→e−ν¯e 70.5% 6.1 ± 2.2 ± 5.2 <2.3×10−4 at 90% C.L. Ds−→µ−ν¯µ 67.7% 275 ± 17 (6.02 ± 0.38 ± 0.34)×10−3 265.7 ± 8.4 ± 7.7 Ds−→τ−ν¯τ (τ− →e−ν¯eντ) 61.6% 408 ± 42 (5.07 ± 0.52 ± 0.68)×10−2 247 ± 13 ± 17 Ds−→τ−ν¯τ (τ− →µ−ν¯µντ) 59.5% 340 ± 32 (4.91 ± 0.47 ± 0.54)×10−2 243 ± 12 ± 14 set to N and its total uncertainty, respectively. To struction was not applied) the background was found to eν accountforthe uncertaintiesonN ε¯ ,the mainGaus- belinearinm(KKπγ). Fromafittothem(KKπγ) dis- Ds eν sian is convolved with another Gaussian function cen- tribution,showninFig.3(e),wedetermine asignalyield tered atthe measuredvalue of N ε¯ with sigma set to of N =1866 40 events. Ds eν KKπ ± tuhpepNerDlsimε¯eiνttisotlaisltuedncienrtTaainbtlye.IT. hevalueobtainedforthe tioWneuscinogmEpuqt.e(3t)h.eTDhes−effi→cieKnc−yKfo+rπr−ecbonrasntrcuhcitnigngfrsaigc-- We find D− τ−ν¯ decays within the sample of in- nal events is determined from the signal MC in three clusively recosns→tructedτ D− events by requiring exactly regions of the K−K+π− Dalitz plot, corresponding to s one more track identified as an e− or µ−, from the φπ−, K−K∗0, and the rest. A variation of 8% is ob- ∼ decay τ− e−ν¯ ν or τ− µ−ν¯ ν . We remove served across the Dalitz plot, leading to a correction e τ µ τ events asso→ciated with D− →µ−ν¯ decays by requiring factor of 1.016 on εj . The weighted efficiency ratio mco2rn(tDaiKnXmγoµre) t>h0a.n5 oGneeVn2se/uc→4tr.inSoinwcµee Duss−e→Eτ−ν¯τ etovenexts- Kis−foKun+dπ−t)o=be(5ε¯.7K8KKπ0=K.22π09(.5s%ta,t)an0d.3w0e(soybstt)a)i%n.BT(Dhes−fir→st extra ± ± tract the yield of signal events; these are expected to uncertainty accounts for the statistical uncertainties as- peak towards zero, while the backgrounds extend over a sociated with the inclusive Ds− sample and NKKπ. The wide range. The signal and backgroundPDFs are deter- secondaccountsforsystematicuncertaintiesinthesignal minedfromreconstructedMCeventsamples. Thefitsare and background models, and the inclusive Ds− sample, shown in Figs. 3(c) and 3(d); the signal yields are listed as well as the reconstruction and PID selection of the inTableI. Wedetermine (D− τ−ν¯ )fromthee−and K−K+π− candidates. This result is consistent with the µ− samples using Eq. (3)Bands a→ccounτting for the decay value (5.50 0.23 0.16)% measured by CLEO-c [18]. ± ± fractionsoftheτ− [14]. Thevaluesobtainedarelistedin Using the leptonic branching fractions measured Table I and are consistent with the previous BABAR re- above,wedeterminetheD−decayconstantusingEq.(1) s sult [16]. The error-weightedaverage [17] of the branch- and the known values for m , m , V (we assume ing fractions is (D− τ−ν¯ ) = (5.00 0.35(stat) V = V ), and the D−ℓ lifDetsim|euodb|tained from 0.49(syst)) 10B−2. sT→he weiτghts used i±n the averag±e |Recfs.|[14].|Tuhde| f values arse listed in Table I; the sys- × Ds are computed from the total error matrix and account tematic uncertainty includes the uncertainties on these for correlations. As a test of lepton flavor universality parameters (1.9 MeV). Finally, we obtain the error- wedeterminetheratio (D− τ−ν¯ )/ (D− µ−ν¯ )= weighted average f = (258.6 6.4(stat) 7.5(syst)) B s → τ B s → µ Ds ± ± (8.27 0.77(stat) 0.85(syst)), which is consistent with MeV. ± ± the SM value of 9.76. In conclusion, we use the full dataset collected by the As a cross-check of this analysis method, we measure BABAR experiment to measure the branching fractions tKh−eKbr+aπn−ch.ingWfirtahcintiotnheforincthluesihveadDros−nicsadmecpaley, Dws−e r→e- vfoarluteheoflefpDtosniisc1d.e8casytsanofdathrde Ddes−viamteiosnons.laTrgheermtheaasnutrhede quire exactly three additional charged particle tracks theoretical value [2], consistent with the measurements that do not overlap with the DKXγ candidate. PID by Belle and CLEO-c [6, 19]. Further work on this sub- requirements are applied to the kaon candidates. The ject is necessary to validate the theoretical calculations mass ofthe K−K+π− systemmust be between 1.93and or to shed light on possible NP processes. 2.00 GeV/c2, and the CM momentum above 3.0 GeV/c. We are grateful for the excellent luminosity and ma- We combine the K−K+π− system with the signal γ chine conditions providedby our PEP-II colleagues,and and extract the signal yield from the m(KKπγ) dis- for the substantial dedicated effort from the comput- tribution. For this mode we choose the loose selection ing organizations that support BABAR. The collaborat- m (DKXγ) > 1.82 GeV/c2, because this variable is ing institutions wish to thank SLAC for its support and r correlated with m(KKπγ); this corresponds to an in- kind hospitality. This work is supported by DOE and clusive D− yield of N = (108.9 2.4) 103. We NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 s Ds ± × model the signal distribution using reconstructed MC (France), BMBF and DFG (Germany), INFN (Italy), events that contain the decay chain D∗− D−γ and FOM(TheNetherlands),NFR(Norway),MES(Russia), D− K−K+π−. In the generic MC ansd a→highsstatis- MICIIN (Spain), STFC (United Kingdom). 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