Improved Limits on Lepton Flavor Violating Tau Decays to \ell\phi,\ell\rho,\ell K^{*}, and \ell\overline{K}^{*}

Improved Limits on Lepton Flavor Violating Tau Decays to , and

B. Aubert    Y. Karyotakis    J. P. Lees    V. Poireau    E. Prencipe    X. Prudent    V. Tisserand Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), Université de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France    J. Garra Tico    E. Grauges Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain    M. Martinelli    A. Palano    M. Pappagallo INFN Sezione di Bari; Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy    G. Eigen    B. Stugu    L. Sun University of Bergen, Institute of Physics, N-5007 Bergen, Norway    M. Battaglia    D. N. Brown    L. T. Kerth    Yu. G. Kolomensky    G. Lynch    I. L. Osipenkov    K. Tackmann    T. Tanabe Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA    C. M. Hawkes    N. Soni    A. T. Watson University of Birmingham, Birmingham, B15 2TT, United Kingdom    H. Koch    T. Schroeder Ruhr Universität Bochum, Institut für Experimentalphysik 1, D-44780 Bochum, Germany    D. J. Asgeirsson    B. G. Fulsom    C. Hearty    T. S. Mattison    J. A. McKenna University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1    M. Barrett    A. Khan    A. Randle-Conde Brunel University, Uxbridge, Middlesex UB8 3PH, United Kingdom    V. E. Blinov    A. D. Bukin    A. R. Buzykaev    V. P. Druzhinin    V. B. Golubev    A. P. Onuchin    S. I. Serednyakov    Yu. I. Skovpen    E. P. Solodov    K. Yu. Todyshev Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia    M. Bondioli    S. Curry    I. Eschrich    D. Kirkby    A. J. Lankford    P. Lund    M. Mandelkern    E. C. Martin    D. P. Stoker University of California at Irvine, Irvine, California 92697, USA    S. Abachi    C. Buchanan University of California at Los Angeles, Los Angeles, California 90024, USA    H. Atmacan    J. W. Gary    F. Liu    O. Long    G. M. Vitug    Z. Yasin    L. Zhang University of California at Riverside, Riverside, California 92521, USA    V. Sharma University of California at San Diego, La Jolla, California 92093, USA    C. Campagnari    T. M. Hong    D. Kovalskyi    M. A. Mazur    J. D. Richman University of California at Santa Barbara, Santa Barbara, California 93106, USA    T. W. Beck    A. M. Eisner    C. A. Heusch    J. Kroseberg    W. S. Lockman    A. J. Martinez    T. Schalk    B. A. Schumm    A. Seiden    L. O. Winstrom University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA    C. H. Cheng    D. A. Doll    B. Echenard    F. Fang    D. G. Hitlin    I. Narsky    T. Piatenko    F. C. Porter California Institute of Technology, Pasadena, California 91125, USA    R. Andreassen    G. Mancinelli    B. T. Meadows    K. Mishra    M. D. Sokoloff University of Cincinnati, Cincinnati, Ohio 45221, USA    P. C. Bloom    W. T. Ford    A. Gaz    J. F. Hirschauer    M. Nagel    U. Nauenberg    J. G. Smith    S. R. Wagner University of Colorado, Boulder, Colorado 80309, USA    R. Ayad Now at Temple University, Philadelphia, Pennsylvania 19122, USA    A. Soffer Now at Tel Aviv University, Tel Aviv, 69978, Israel    W. H. Toki    R. J. Wilson Colorado State University, Fort Collins, Colorado 80523, USA    E. Feltresi    A. Hauke    H. Jasper    T. M. Karbach    J. Merkel    A. Petzold    B. Spaan    K. Wacker Technische Universität Dortmund, Fakultät Physik, D-44221 Dortmund, Germany    M. J. Kobel    R. Nogowski    K. R. Schubert    R. Schwierz    A. Volk Technische Universität Dresden, Institut für Kern- und Teilchenphysik, D-01062 Dresden, Germany    D. Bernard    G. R. Bonneaud    E. Latour    M. Verderi Laboratoire Leprince-Ringuet, CNRS/IN2P3, Ecole Polytechnique, F-91128 Palaiseau, France    P. J. Clark    S. Playfer    J. E. Watson University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom    M. Andreotti    D. Bettoni    C. Bozzi    R. Calabrese    A. Cecchi    G. Cibinetto    E. Fioravanti    P. Franchini    E. Luppi    M. Munerato    M. Negrini    A. Petrella    L. Piemontese    V. Santoro INFN Sezione di Ferrara; Dipartimento di Fisica, Università di Ferrara, I-44100 Ferrara, Italy    R. Baldini-Ferroli    A. Calcaterra    R. de Sangro    G. Finocchiaro    S. Pacetti    P. Patteri    I. M. Peruzzi Also with Università di Perugia, Dipartimento di Fisica, Perugia, Italy    M. Piccolo    M. Rama    A. Zallo INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy    R. Contri    E. Guido    M. Lo Vetere    M. R. Monge    S. Passaggio    C. Patrignani    E. Robutti    S. Tosi INFN Sezione di Genova; Dipartimento di Fisica, Università di Genova, I-16146 Genova, Italy    K. S. Chaisanguanthum    M. Morii Harvard University, Cambridge, Massachusetts 02138, USA    A. Adametz    J. Marks    S. Schenk    U. Uwer Universität Heidelberg, Physikalisches Institut, Philosophenweg 12, D-69120 Heidelberg, Germany    F. U. Bernlochner    V. Klose    H. M. Lacker Humboldt-Universität zu Berlin, Institut für Physik, Newtonstr. 15, D-12489 Berlin, Germany    D. J. Bard    P. D. Dauncey    M. Tibbetts Imperial College London, London, SW7 2AZ, United Kingdom    P. K. Behera    M. J. Charles    U. Mallik University of Iowa, Iowa City, Iowa 52242, USA    J. Cochran    H. B. Crawley    L. Dong    V. Eyges    W. T. Meyer    S. Prell    E. I. Rosenberg    A. E. Rubin Iowa State University, Ames, Iowa 50011-3160, USA    Y. Y. Gao    A. V. Gritsan    Z. J. Guo Johns Hopkins University, Baltimore, Maryland 21218, USA    N. Arnaud    J. Béquilleux    A. D’Orazio    M. Davier    D. Derkach    J. Firmino da Costa    G. Grosdidier    F. Le Diberder    V. Lepeltier    A. M. Lutz    B. Malaescu    S. Pruvot    P. Roudeau    M. H. Schune    J. Serrano    V. Sordini Also with Università di Roma La Sapienza, I-00185 Roma, Italy    A. Stocchi    G. Wormser Laboratoire de l’Accélérateur Linéaire, IN2P3/CNRS et Université Paris-Sud 11, Centre Scientifique d’Orsay, B. P. 34, F-91898 Orsay Cedex, France    D. J. Lange    D. M. Wright Lawrence Livermore National Laboratory, Livermore, California 94550, USA    I. Bingham    J. P. Burke    C. A. Chavez    J. R. Fry    E. Gabathuler    R. Gamet    D. E. Hutchcroft    D. J. Payne    C. Touramanis University of Liverpool, Liverpool L69 7ZE, United Kingdom    A. J. Bevan    C. K. Clarke    F. Di Lodovico    R. Sacco    M. Sigamani Queen Mary, University of London, London, E1 4NS, United Kingdom    G. Cowan    S. Paramesvaran    A. C. Wren University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom    D. N. Brown    C. L. Davis University of Louisville, Louisville, Kentucky 40292, USA    A. G. Denig    M. Fritsch    W. Gradl    A. Hafner Johannes Gutenberg-Universität Mainz, Institut für Kernphysik, D-55099 Mainz, Germany    K. E. Alwyn    D. Bailey    R. J. Barlow    G. Jackson    G. D. Lafferty    T. J. West    J. I. Yi University of Manchester, Manchester M13 9PL, United Kingdom    J. Anderson    C. Chen    A. Jawahery    D. A. Roberts    G. Simi    J. M. Tuggle University of Maryland, College Park, Maryland 20742, USA    C. Dallapiccola    E. Salvati    S. Saremi University of Massachusetts, Amherst, Massachusetts 01003, USA    R. Cowan    D. Dujmic    P. H. Fisher    S. W. Henderson    G. Sciolla    M. Spitznagel    R. K. Yamamoto    M. Zhao Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA    P. M. Patel    S. H. Robertson    M. Schram McGill University, Montréal, Québec, Canada H3A 2T8    A. Lazzaro    V. Lombardo    F. Palombo    S. Stracka INFN Sezione di Milano; Dipartimento di Fisica, Università di Milano, I-20133 Milano, Italy    J. M. Bauer    L. Cremaldi    R. Godang Now at University of South Alabama, Mobile, Alabama 36688, USA    R. Kroeger    D. J. Summers    H. W. Zhao University of Mississippi, University, Mississippi 38677, USA    M. Simard    P. Taras Université de Montréal, Physique des Particules, Montréal, Québec, Canada H3C 3J7    H. Nicholson Mount Holyoke College, South Hadley, Massachusetts 01075, USA    G. De Nardo    L. Lista    D. Monorchio    G. Onorato    C. Sciacca INFN Sezione di Napoli; Dipartimento di Scienze Fisiche, Università di Napoli Federico II, I-80126 Napoli, Italy    G. Raven    H. L. Snoek NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands    C. P. Jessop    K. J. Knoepfel    J. M. LoSecco    W. F. Wang University of Notre Dame, Notre Dame, Indiana 46556, USA    L. A. Corwin    K. Honscheid    H. Kagan    R. Kass    J. P. Morris    A. M. Rahimi    J. J. Regensburger    S. J. Sekula    Q. K. Wong Ohio State University, Columbus, Ohio 43210, USA    N. L. Blount    J. Brau    R. Frey    O. Igonkina    J. A. Kolb    M. Lu    R. Rahmat    N. B. Sinev    D. Strom    J. Strube    E. Torrence University of Oregon, Eugene, Oregon 97403, USA    G. Castelli    N. Gagliardi    M. Margoni    M. Morandin    M. Posocco    M. Rotondo    F. Simonetto    R. Stroili    C. Voci INFN Sezione di Padova; Dipartimento di Fisica, Università di Padova, I-35131 Padova, Italy    P. del Amo Sanchez    E. Ben-Haim    H. Briand    J. Chauveau    O. Hamon    Ph. Leruste    G. Marchiori    J. Ocariz    A. Perez    J. Prendki    S. Sitt Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France    L. Gladney University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA    M. Biasini    E. Manoni INFN Sezione di Perugia; Dipartimento di Fisica, Università di Perugia, I-06100 Perugia, Italy    C. Angelini    G. Batignani    S. Bettarini    G. Calderini Also with Laboratoire de Physique Nucléaire et de Hautes Energies, IN2P3/CNRS, Université Pierre et Marie Curie-Paris6, Université Denis Diderot-Paris7, F-75252 Paris, France    M. Carpinelli Also with Università di Sassari, Sassari, Italy    A. Cervelli    F. Forti    M. A. Giorgi    A. Lusiani    M. Morganti    N. Neri    E. Paoloni    G. Rizzo    J. J. Walsh INFN Sezione di Pisa; Dipartimento di Fisica, Università di Pisa; Scuola Normale Superiore di Pisa, I-56127 Pisa, Italy    D. Lopes Pegna    C. Lu    J. Olsen    A. J. S. Smith    A. V. Telnov Princeton University, Princeton, New Jersey 08544, USA    F. Anulli    E. Baracchini    G. Cavoto    R. Faccini    F. Ferrarotto    F. Ferroni    M. Gaspero    P. D. Jackson    L. Li Gioi    M. A. Mazzoni    S. Morganti    G. Piredda    F. Renga    C. Voena INFN Sezione di Roma; Dipartimento di Fisica, Università di Roma La Sapienza, I-00185 Roma, Italy    M. Ebert    T. Hartmann    H. Schröder    R. Waldi Universität Rostock, D-18051 Rostock, Germany    T. Adye    B. Franek    E. O. Olaiya    F. F. Wilson Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom    S. Emery    L. Esteve    G. Hamel de Monchenault    W. Kozanecki    G. Vasseur    Ch. Yèche    M. Zito CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France    M. T. Allen    D. Aston    R. Bartoldus    J. F. Benitez    R. Cenci    J. P. Coleman    M. R. Convery    J. C. Dingfelder    J. Dorfan    G. P. Dubois-Felsmann    W. Dunwoodie    R. C. Field    A. M. Gabareen    M. T. Graham    P. Grenier    C. Hast    W. R. Innes    J. Kaminski    M. H. Kelsey    H. Kim    P. Kim    M. L. Kocian    D. W. G. S. Leith    S. Li    B. Lindquist    S. Luitz    V. Luth    H. L. Lynch    D. B. MacFarlane    H. Marsiske    R. Messner    D. R. Muller    H. Neal    S. Nelson    C. P. O’Grady    I. Ofte    M. Perl    B. N. Ratcliff    A. Roodman    A. A. Salnikov    R. H. Schindler    J. Schwiening    A. Snyder    D. Su    M. K. Sullivan    K. Suzuki    S. K. Swain    J. M. Thompson    J. Va’vra    A. P. Wagner    M. Weaver    C. A. West    W. J. Wisniewski    M. Wittgen    D. H. Wright    H. W. Wulsin    A. K. Yarritu    K. Yi    C. C. Young    V. Ziegler SLAC National Accelerator Laboratory, Stanford, California 94309 USA    X. R. Chen    H. Liu    W. Park    M. V. Purohit    R. M. White    J. R. Wilson University of South Carolina, Columbia, South Carolina 29208, USA    P. R. Burchat    A. J. Edwards    T. S. Miyashita Stanford University, Stanford, California 94305-4060, USA    S. Ahmed    M. S. Alam    J. A. Ernst    B. Pan    M. A. Saeed    S. B. Zain State University of New York, Albany, New York 12222, USA    S. M. Spanier    B. J. Wogsland University of Tennessee, Knoxville, Tennessee 37996, USA    R. Eckmann    J. L. Ritchie    A. M. Ruland    C. J. Schilling    R. F. Schwitters    B. C. Wray University of Texas at Austin, Austin, Texas 78712, USA    B. W. Drummond    J. M. Izen    X. C. Lou University of Texas at Dallas, Richardson, Texas 75083, USA    F. Bianchi    D. Gamba    M. Pelliccioni INFN Sezione di Torino; Dipartimento di Fisica Sperimentale, Università di Torino, I-10125 Torino, Italy    M. Bomben    L. Bosisio    C. Cartaro    G. Della Ricca    L. Lanceri    L. Vitale INFN Sezione di Trieste; Dipartimento di Fisica, Università di Trieste, I-34127 Trieste, Italy    V. Azzolini    N. Lopez-March    F. Martinez-Vidal    D. A. Milanes    A. Oyanguren IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain    J. Albert    Sw. Banerjee    B. Bhuyan    H. H. F. Choi    K. Hamano    G. J. King    R. Kowalewski    M. J. Lewczuk    I. M. Nugent    J. M. Roney    R. J. Sobie University of Victoria, Victoria, British Columbia, Canada V8W 3P6    T. J. Gershon    P. F. Harrison    J. Ilic    T. E. Latham    G. B. Mohanty    E. M. T. Puccio Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom    H. R. Band    X. Chen    S. Dasu    K. T. Flood    Y. Pan    R. Prepost    C. O. Vuosalo    S. L. Wu University of Wisconsin, Madison, Wisconsin 53706, USA
Abstract

We search for the neutrinoless, lepton-flavor-violating tau decays , where is an electron or muon and is a vector meson reconstructed as . The analysis has been performed using 451 of data collected at an  center-of-mass energy near 10.58 with the BABAR detector at the PEP-II storage rings. The number of events found in the data is compatible with the background expectation, and upper limits on the branching fractions are set in the range at the 90% confidence level.

pacs:
13.35.Dx, 14.60.Fg, 11.30.Hv
preprint: BABAR-PUB-09/002preprint: SLAC-PUB-13559

BABAR-PUB-09/002

SLAC-PUB-13559

thanks: Deceasedthanks: Deceased

The BABAR Collaboration

Lepton-flavor violation (LFV) involving tau leptons has never been observed, and recent experimental results have placed stringent limits on the branching fractions for 2- and 3-body neutrinoless tau decays taulll (); taulhh (); belle08 (). Many descriptions of physics beyond the Standard Model (SM) predict such decays paradisi05 (); brignole03 (); and certain models brignole04 (); arganda08 () specifically predict semileptonic tau decays such as (), with rates as high as the current experimental limits belle08 (). An observation of these decays would be a clear signature of physics beyond the SM, while improved limits will further constrain models of new physics.

This paper presents a search for LFV in a set of eight neutrinoless decay modes cc (), where is an electron or muon and is a neutral vector meson decaying to two charged hadrons () via one of the following four decay modes: , , , . This analysis is based on data recorded by the BABAR detector at the PEP-II asymmetric-energy  storage rings operated at the SLAC National Accelerator Laboratory. The BABAR detector is described in detail in Ref. detector (). The data sample consists of 410 recorded at an  center-of-mass (c.m.) energy , and 40.8 recorded at . With a calculated cross section for tau pairs of nb tautau (); kk () at the stated luminosity-weighted , this data set corresponds to the production of about 830 million tau decays.

We use a Monte Carlo (MC) simulation of lepton-flavor-violating tau decays to optimize the search. Tau-pair events including higher-order radiative corrections are generated using KK2f kk (). One tau decays via two-body phase space to a lepton and a vector meson, with the meson decaying according to the measured branching fractions PDG (). The other tau decays via SM processes simulated with TAUOLA tauola (). Final state radiative effects are simulated for all decays using PHOTOS photos (). The detector response is modeled with GEANT4 geant (), and the simulated events are then reconstructed in the same manner as data. SM background processes are modeled with a similar software framework.

We search for the signal decay by reconstructing candidates in which three charged particles, each identified as the appropriate lepton or hadron, have an invariant mass and energy close to that of the parent tau lepton. Candidate signal events are first required to have a “3-1 topology,” where one tau decay yields three charged particles, while the second tau decay yields one charged particle. This requirement on the second tau decay greatly reduces the background from continuum multi-hadron events. Events with four well-reconstructed tracks and zero net charge are selected, and the tracks are required to point toward a common region consistent with production and decay. The polar angle of all four tracks in the laboratory frame is required to be within the calorimeter acceptance. Pairs of oppositely-charged tracks are ignored if their invariant mass, assuming electron mass hypotheses, is less than 30. Such tracks are likely to be from photon conversions in the traversed material. The event is divided into hemispheres in the  c.m. frame using the plane perpendicular to the thrust axis, as calculated from the observed tracks and neutral energy deposits. The signal (3-prong) hemisphere must contain exactly three tracks while the other (1-prong) hemisphere must contain exactly one. Each of the charged particles found in the 3-prong hemisphere must be identified as a lepton or hadron candidate appropriate to the search channel. The relevant particle identification capabilities of the BABAR detector are described in Ref. taulhh ().

To further suppress backgrounds from quark pair production, Bhabha scattering events, and SM tau pair production, we apply additional selection criteria separately in the eight different search channels. Specific cut values are shown in Tab. 1. All selection criteria are optimized to provide the smallest expected upper limit on the branching fraction in the background-only hypothesis. Resonant decays are selected with cuts on the invariant mass of the two hadrons in the 3-prong hemisphere (). The invariant mass of the 1-prong hemisphere () is calculated from the charged and neutral particles in that hemisphere and the total missing momentum in the event. As the missing momentum in signal events results from one or more neutrinos in the 1-prong hemisphere, this mass is required to be near the tau mass. Background events from quark pair production are suppressed with cuts on the missing transverse momentum in the event (), the scalar sum of all transverse momenta in the c.m. frame (), and the number of photons in the 1-prong and 3-prong hemispheres (). To reduce the background contribution from radiative Bhabha and di-muon events, the 1-prong and 3-prong momentum vectors must not be collinear in the c.m. frame. For the same reason, the 1-prong track must not be identified as an electron for the  search.

Channel
min 1.000 1.005 0.6 0.6 0.8 0.82 0.80 0.78
max 1.040 1.035 0.92 0.96 1.0 0.98 1.04 1.00
min 0.3 0.4 0.3 0.3 0.3 0.2 0.3 -
max 2.5 2.5 2.5 2.5 2.5 2.5 2.5 -
min 0.4 0.3 0.4 0.4 0.4 0.4 0.4 0.4
min 0.5 - - - 0.6 - 0.3 -
max 4 3 3 1 - 3 - 2
max 3 1 2 1 - 2 - 1
Table 1: Values of the cuts on the selection variables described in the text. Masses are in units of GeV/c, and momenta in units of GeV/c.

As a final discriminant, we require candidate signal events to have an invariant mass and total energy in the 3-prong hemisphere consistent with a parent tau lepton. These quantities are calculated from the measured track momenta, assuming lepton and hadron masses that correspond to the neutrinoless tau decay in each search channel. The energy difference is defined as , where is the total energy of the tracks observed in the 3-prong hemisphere and is the beam energy, with both quantities calculated in the c.m. frame. The mass difference is defined as where is calculated from a kinematic fit to the 3-prong track momenta with the energy constrained to be in the c.m. frame, and is the tau mass PDG (). While the energy constraint significantly reduces the spread of  values, it also introduces a correlation between  and , which must be taken into account when fitting distributions in this 2-dimensional space.

Detector resolution and radiative effects broaden the signal distributions in the  plane. Because of the correlation between  and , the radiation of photons from the incoming  particles produces a tail at positive values of  and negative values of . Radiation from the final-state leptons, which is more likely for electrons than muons, leads to a tail at low values of . Rectangular signal boxes (SB) in the  plane are defined separately for each search channel. As with previous selection criteria, the SB boundaries are chosen to provide the smallest expected upper limit on the branching fraction. The expected upper limit is estimated using only MC simulations and data events in the sideband region, as described below. Figure 1 shows the observed data in the Large Box (LB) of the  plane, along with the SB boundaries and the expected signal distributions. Table 2 lists the channel-specific dimensions of the SB. While a small fraction of the signal events lie outside the SB, the effect on the final result is negligible. To avoid bias, we use a blinded analysis procedure with the number of data events in the SB remaining unknown until the selection criteria are finalized and all crosschecks are performed.

Mode
-0.02 -0.02 -0.02 -0.015 -0.008 -0.01 -0.01 -0.008
0.015 0.02 0.02 0.02 0.01 0.015 0.01 0.01
-0.13 -0.10 -0.15 -0.125 -0.09 -0.06 -0.08 -0.08
0.10 0.06 0.08 0.06 0.06 0.04 0.04 0.06
Table 2: Signal Box boundaries; is in units of  and in units of .

There are three main classes of background events remaining after the selection criteria are applied: charm quark production (), low-multiplicity continuum events (), and SM pair events. The background from two-photon production is negligible. These three background classes have distinctive distributions in the  plane. The  events tend to populate the plane evenly, with a fall-off at positive values of . Events in the  sample exhibit peaks at positive values of  due to and mesons, and are generally restricted to negative values of . The background events are restricted to negative values of both and .

The expected background rates in the SB are determined by fitting a set of 2-dimensional probability density functions (PDFs) to the observed data in the grand sideband (GS) region of the  plane. The GS region is defined as the LB minus the SB. The shapes of the PDFs are determined by fits to the  distributions of background MC samples in the LB, as described in Ref. taulll (). The present analysis makes use of the same parameterization as Ref. taulll () for the  spectra, except for the case of the  spectrum in some search channels. In these cases, combinations of polynomial and Gaussian functions are used. The choice of PDF for the  spectrum of the  samples is the same as used in Ref. taulll (), while the  and   spectra are modeled with Gaussian and polynomial functions, or the Crystal Ball function CBF (). All shape parameters, including a rotation angle accounting for the correlation between  and , are determined from the fits to MC samples.

Once the shapes of the three background PDFs are determined, an unbinned extended maximum likelihood fit to the data in the GS region is used to find the expected background count in the SB. The fits to the background MC samples and to data are performed separately for each of the eight search channels.

Figure 1: Observed data shown as dots in the Large Box of the  plane and the boundaries of the Signal Box. The dark and light shading indicates contours containing 50% and 90% of the selected MC signal events, respectively.

We estimate the signal event selection efficiency with a MC simulation of lepton-flavor violating tau decays. Between and of the MC signal events pass the 3-1 topology requirement. The efficiency for identification of the three final-state particles ranges from for to for . The total efficiency for signal events to be found in the SB is shown in Table 3, and ranges from 4.1% to 8.0%. This efficiency includes the branching fraction for the vector meson decay to charged daughters, as well as the branching fraction for 1-prong tau decays.

The particle identification efficiencies and misidentification probabilities have been measured with control samples both for data and MC events, as a function of particle momentum, polar angle, and azimuthal angle in the laboratory frame. The systematic uncertainties related to the particle identification have been estimated from the statistical uncertainty of the efficiency measurements and from the difference between data and MC efficiencies. These uncertainties range from 1.7% for  to 9.0% for uncertain (). The modeling of the tracking efficiency and the uncertainty from the 1-prong tau branching fraction each contribute an additional 1% uncertainty. Furthermore, the uncertainty on the intermediate branching fractions contributes a uncertainty. All other sources of uncertainty in the signal efficiency are found to be negligible, including the statistical limitations of the MC signal samples, modeling of radiative effects by the generator, track momentum resolution, trigger performance, and the choice of observables used for event selection.

Since the background levels are extracted directly from the data, systematic uncertainties on the background estimation are directly related to the background parameterization and the fit technique used. Uncertainties related to the fits to the background samples are estimated by varying the background shape parameters according to the covariance matrix and repeating the fits, and range from to . Uncertainties related to the fits for the background yields in the GS are estimated by varying the yields within their errors, and range from to . The total uncertainty on the background estimates is shown in Table 3. Crosschecks of the background estimation are performed by comparing the number of events expected and observed in sideband regions immediately neighboring the SB for each search channel. No major discrepancies are observed.

Mode [%]          
Table 3: Efficiency estimate, number of expected background events (), number of observed events (), observed upper limit at 90% CL on the number of signal events (), expected branching fraction upper limit at 90% CL (), and observed branching fraction upper limit at 90% CL ().  and  are in units of .

The number of events observed () and the number of background events expected () are shown in Table 3. The POLE calculator pole (), based on the method of Feldman and Cousins feldmanCousins (), is used to place CL upper limits on the number of signal events (), which include uncertainties on  and on the selection efficiency (). For the  search, the POLE calculation results in a two-sided interval at 90% CL for the number of signal events: . Upper limits on the branching fractions are calculated according to , where the values and are the integrated luminosity and cross section, respectively. The uncertainty on the product is 1.0%. Table 3 lists the upper limits on the branching fractions, as well as the expected upper limit , defined as the mean upper limit expected in the background-only hypothesis. The 90% CL upper limits on the branching fractions are in the range , and these limits represent improvements over the previous experimental bounds belle08 () in almost all search channels.

We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality. This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MEC (Spain), and STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

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