Search for B⁺ → K⁺ т⁺ т⁻ at the BaBar Experiment

BABAR-PUB-16/001 SLAC-PUB-16526

Search for B

+

_{→ K}

+

τ

+

τ

−

at the B

A

B

AR

experiment

J. P. Lees,1 _{V. Poireau,}1 _{V. Tisserand,}1 _{E. Grauges,}2_{A. Palano,}3_{G. Eigen,}4 _{D. N. Brown,}5_{Yu. G. Kolomensky,}5

H. Koch,6 _{T. Schroeder,}6 _{C. Hearty,}7 _{T. S. Mattison,}7 _{J. A. McKenna,}7 _{R. Y. So,}7 _{V. E. Blinov}abc_,8

A. R. Buzykaeva_,8 _{V. P. Druzhinin}ab_,8 _{V. B. Golubev}ab_,8 _{E. A. Kravchenko}ab_,8 _{A. P. Onuchin}abc_,8

S. I. Serednyakovab,8 Yu. I. Skovpenab,8 E. P. Solodovab,8K. Yu. Todyshevab,8 A. J. Lankford,9 J. W. Gary,10 O. Long,10_{A. M. Eisner,}11_{W. S. Lockman,}11 _{W. Panduro Vazquez,}11 _{D. S. Chao,}12 _{C. H. Cheng,}12_{B. Echenard,}12

K. T. Flood,12 _{D. G. Hitlin,}12 _{J. Kim,}12 _{T. S. Miyashita,}12 _{P. Ongmongkolkul,}12 _{F. C. Porter,}12 _{M. R¨ohrken,}12

Z. Huard,13 _{B. T. Meadows,}13 _{B. G. Pushpawela,}13 _{M. D. Sokoloff,}13 _{L. Sun,}13,∗ _{J. G. Smith,}14 _{S. R. Wagner,}14

D. Bernard,15 _{M. Verderi,}15 _{D. Bettoni}a_,16 _{C. Bozzi}a_,16 _{R. Calabrese}ab_,16 _{G. Cibinetto}ab_,16 _{E. Fioravanti}ab_,16

I. Garziaab_,16 _{E. Luppi}ab_,16 _{V. Santoro}a_,16 _{A. Calcaterra,}17 _{R. de Sangro,}17 _{G. Finocchiaro,}17_{S. Martellotti,}17

P. Patteri,17 _{I. M. Peruzzi,}17 _{M. Piccolo,}17 _{A. Zallo,}17 _{S. Passaggio,}18 _{C. Patrignani,}18,† _{B. Bhuyan,}19

U. Mallik,20 _{C. Chen,}21 _{J. Cochran,}21 _{S. Prell,}21 _{H. Ahmed,}22 _{A. V. Gritsan,}23 _{N. Arnaud,}24 _{M. Davier,}24

F. Le Diberder,24 _{A. M. Lutz,}24_{G. Wormser,}24_{D. J. Lange,}25 _{D. M. Wright,}25 _{J. P. Coleman,}26 _{E. Gabathuler,}26

D. E. Hutchcroft,26 _{D. J. Payne,}26 _{C. Touramanis,}26 _{A. J. Bevan,}27 _{F. Di Lodovico,}27 _{R. Sacco,}27 _{G. Cowan,}28

Sw. Banerjee,29 _{D. N. Brown,}29 _{C. L. Davis,}29 _{A. G. Denig,}30 _{M. Fritsch,}30 _{W. Gradl,}30 _{K. Griessinger,}30

A. Hafner,30 _{K. R. Schubert,}30 _{R. J. Barlow,}31,‡ _{G. D. Lafferty,}31 _{R. Cenci,}32 _{A. Jawahery,}32 _{D. A. Roberts,}32

R. Cowan,33 _{R. Cheaib,}34_{S. H. Robertson,}34 _{B. Dey}a_,35_{N. Neri}a_,35 _{F. Palombo}ab_,35 _{L. Cremaldi,}36 _{R. Godang,}36,§

D. J. Summers,36 _{P. Taras,}37 _{G. De Nardo,}38 _{C. Sciacca,}38 _{G. Raven,}39 _{C. P. Jessop,}40 _{J. M. LoSecco,}40

K. Honscheid,41 _{R. Kass,}41 _{A. Gaz}a_,42 _{M. Margoni}ab_,42 _{M. Posocco}a_,42 _{M. Rotondo}a_,42 _{G. Simi}ab_,42

F. Simonettoab_,42 _{R. Stroili}ab_,42_{S. Akar,}43 _{E. Ben-Haim,}43 _{M. Bomben,}43 _{G. R. Bonneaud,}43 _{G. Calderini,}43

J. Chauveau,43 _{G. Marchiori,}43 _{J. Ocariz,}43 _{M. Biasini}ab_,44 _{E. Manoni}a_,44 _{A. Rossi}a_,44 _{G. Batignani}ab_,45

S. Bettariniab_,45 _{M. Carpinelli}ab_,45,¶ _{G. Casarosa}ab_,45 _{M. Chrzaszcz}a_,45 _{F. Forti}ab_,45 _{M. A. Giorgi}ab_,45

A. Lusianiac_,45 _{B. Oberhof}ab_,45 _{E. Paoloni}ab_,45 _{M. Rama}a_,45 _{G. Rizzo}ab_,45 _{J. J. Walsh}a_,45 _{A. J. S. Smith,}46

F. Anullia_,47 _{R. Faccini}ab_,47 _{F. Ferrarotto}a_,47 _{F. Ferroni}ab_,47 _{A. Pilloni}ab_,47 _{G. Piredda}a_,47 _{C. B¨unger,}48

S. Dittrich,48 _{O. Gr¨unberg,}48 _{M. Heß,}48 _{T. Leddig,}48 _{C. Voß,}48 _{R. Waldi,}48 _{T. Adye,}49 _{F. F. Wilson,}49 _{S. Emery,}50

G. Vasseur,50 _{D. Aston,}51 _{C. Cartaro,}51_{M. R. Convery,}51_{J. Dorfan,}51 _{W. Dunwoodie,}51 _{M. Ebert,}51 _{R. C. Field,}51

B. G. Fulsom,51 _{M. T. Graham,}51 _{C. Hast,}51 _{W. R. Innes,}51 _{P. Kim,}51 _{D. W. G. S. Leith,}51 _{S. Luitz,}51

V. Luth,51 _{D. B. MacFarlane,}51 _{D. R. Muller,}51 _{H. Neal,}51 _{B. N. Ratcliff,}51 _{A. Roodman,}51 _{M. K. Sullivan,}51

J. Va’vra,51_{W. J. Wisniewski,}51 _{M. V. Purohit,}52 _{J. R. Wilson,}52_{A. Randle-Conde,}53 _{S. J. Sekula,}53 _{M. Bellis,}54

P. R. Burchat,54 _{E. M. T. Puccio,}54_{M. S. Alam,}55 _{J. A. Ernst,}55 _{R. Gorodeisky,}56 _{N. Guttman,}56 _{D. R. Peimer,}56

A. Soffer,56_{S. M. Spanier,}57 _{J. L. Ritchie,}58 _{R. F. Schwitters,}58 _{J. M. Izen,}59 _{X. C. Lou,}59 _{F. Bianchi}ab_,60

F. De Moriab_,60 _{A. Filippi}a_,60 _{D. Gamba}ab_,60 _{L. Lanceri,}61 _{L. Vitale,}61 _{F. Martinez-Vidal,}62 _{A. Oyanguren,}62

J. Albert,63 _{A. Beaulieu,}63 _{F. U. Bernlochner,}63 _{G. J. King,}63 _{R. Kowalewski,}63 _{T. Lueck,}63 _{I. M. Nugent,}63

J. M. Roney,63 _{N. Tasneem,}63_{T. J. Gershon,}64_{P. F. Harrison,}64 _{T. E. Latham,}64 _{R. Prepost,}65 _{and S. L. Wu}65

(The BABAR Collaboration)

1_{Laboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP),}

Universit´e de Savoie, CNRS/IN2P3, F-74941 Annecy-Le-Vieux, France

2_{Universitat de Barcelona, Facultat de Fisica, Departament ECM, E-08028 Barcelona, Spain} 3_{INFN Sezione di Bari and Dipartimento di Fisica, Universit`a di Bari, I-70126 Bari, Italy}

4_{University of Bergen, Institute of Physics, N-5007 Bergen, Norway}

5_{Lawrence Berkeley National Laboratory and University of California, Berkeley, California 94720, USA} 6_{Ruhr Universit¨at Bochum, Institut f¨ur Experimentalphysik 1, D-44780 Bochum, Germany}

7_{University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1} 8_{Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090}a_,

Novosibirsk State University, Novosibirsk 630090b,

Novosibirsk State Technical University, Novosibirsk 630092c, Russia

9_{University of California at Irvine, Irvine, California 92697, USA} 10_{University of California at Riverside, Riverside, California 92521, USA}

11_{University of California at Santa Cruz, Institute for Particle Physics, Santa Cruz, California 95064, USA} 12_{California Institute of Technology, Pasadena, California 91125, USA}

13_{University of Cincinnati, Cincinnati, Ohio 45221, USA} 14_{University of Colorado, Boulder, Colorado 80309, USA}

15_{Laboratoire Leprince-Ringuet, Ecole Polytechnique, CNRS/IN2P3, F-91128 Palaiseau, France}

16_{INFN Sezione di Ferrara}a_{; Dipartimento di Fisica e Scienze della Terra, Universit`a di Ferrara}b_{, I-44122 Ferrara, Italy} 17_{INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy}

18_{INFN Sezione di Genova, I-16146 Genova, Italy}

19_{Indian Institute of Technology Guwahati, Guwahati, Assam, 781 039, India} 20_{University of Iowa, Iowa City, Iowa 52242, USA}

21_{Iowa State University, Ames, Iowa 50011, USA}

22_{Physics Department, Jazan University, Jazan 22822, Kingdom of Saudi Arabia} 23_{Johns Hopkins University, Baltimore, Maryland 21218, USA}

24_{Laboratoire de l’Acc´el´erateur Lin´eaire, IN2P3/CNRS et Universit´e Paris-Sud 11,}

Centre Scientifique d’Orsay, F-91898 Orsay Cedex, France

25_{Lawrence Livermore National Laboratory, Livermore, California 94550, USA} 26_{University of Liverpool, Liverpool L69 7ZE, United Kingdom} 27_{Queen Mary, University of London, London, E1 4NS, United Kingdom}

28_{University of London, Royal Holloway and Bedford New College, Egham, Surrey TW20 0EX, United Kingdom} 29_{University of Louisville, Louisville, Kentucky 40292, USA}

30_{Johannes Gutenberg-Universit¨at Mainz, Institut f¨ur Kernphysik, D-55099 Mainz, Germany} 31_{University of Manchester, Manchester M13 9PL, United Kingdom}

32_{University of Maryland, College Park, Maryland 20742, USA}

33_{Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, Massachusetts 02139, USA} 34_{McGill University, Montr´eal, Qu´ebec, Canada H3A 2T8}

35_{INFN Sezione di Milano}a_{; Dipartimento di Fisica, Universit`a di Milano}b_{, I-20133 Milano, Italy} 36_{University of Mississippi, University, Mississippi 38677, USA}

37_{Universit´e de Montr´eal, Physique des Particules, Montr´eal, Qu´ebec, Canada H3C 3J7} 38_{INFN Sezione di Napoli and Dipartimento di Scienze Fisiche,}

Universit`a di Napoli Federico II, I-80126 Napoli, Italy

39_{NIKHEF, National Institute for Nuclear Physics and High Energy Physics, NL-1009 DB Amsterdam, The Netherlands} 40_{University of Notre Dame, Notre Dame, Indiana 46556, USA}

41_{Ohio State University, Columbus, Ohio 43210, USA}

42_{INFN Sezione di Padova}a_{; Dipartimento di Fisica, Universit`a di Padova}b_{, I-35131 Padova, Italy} 43_{Laboratoire 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

44_{INFN Sezione di Perugia}a_{; Dipartimento di Fisica, Universit`a di Perugia}b_{, I-06123 Perugia, Italy} 45_{INFN Sezione di Pisa}a_{; Dipartimento di Fisica,}

Universit`a di Pisab_{; Scuola Normale Superiore di Pisa}c_{, I-56127 Pisa, Italy} 46_{Princeton University, Princeton, New Jersey 08544, USA}

47_{INFN Sezione di Roma}a_{; Dipartimento di Fisica,}

Universit`a di Roma La Sapienzab, I-00185 Roma, Italy

48_{Universit¨at Rostock, D-18051 Rostock, Germany}

49_{Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom} 50_{CEA, Irfu, SPP, Centre de Saclay, F-91191 Gif-sur-Yvette, France}

51_{SLAC National Accelerator Laboratory, Stanford, California 94309 USA} 52_{University of South Carolina, Columbia, South Carolina 29208, USA}

53_{Southern Methodist University, Dallas, Texas 75275, USA} 54_{Stanford University, Stanford, California 94305, USA} 55_{State University of New York, Albany, New York 12222, USA} 56_{Tel Aviv University, School of Physics and Astronomy, Tel Aviv, 69978, Israel}

57_{University of Tennessee, Knoxville, Tennessee 37996, USA} 58_{University of Texas at Austin, Austin, Texas 78712, USA} 59_{University of Texas at Dallas, Richardson, Texas 75083, USA}

60_{INFN Sezione di Torino}a_{; Dipartimento di Fisica, Universit`a di Torino</sub>b<sub>, I-10125 Torino, Italy</sub> 61<sub>INFN Sezione di Trieste and Dipartimento di Fisica, Universit`a di Trieste, I-34127 Trieste, Italy}

62_{IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain} 63_{University of Victoria, Victoria, British Columbia, Canada V8W 3P6} 64_{Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom}

65_{University of Wisconsin, Madison, Wisconsin 53706, USA}

We search for the rare flavor-changing neutral current process B+

→ K+_τ+_τ−_{using data from the}

BABARexperiment. The data sample, collected at the center-of-mass energy of the Υ (4S) resonance, corresponds to a total integrated luminosity of 424 fb−1and to 471 million BB pairs. We reconstruct one B meson, produced in the Υ (4S) _{→ B}+_B− _{decay, in one of many hadronic decay modes and}

search for activity compatible with a B+

→ K+_τ+_τ−_{decay in the rest of the event. Each τ lepton}

is required to decay leptonically into an electron or muon and neutrinos. Comparing the expected number of background events with the data sample after applying the selection criteria, we do not find evidence for a signal. The measured branching fraction is (1.31+0.66

−0.61(stat.)+0.35−0.25(sys.))× 10−3

with an upper limit, at the 90% confidence level, ofB(B+

→ K+_τ+_τ−_{)< 2.25× 10}−3_.

PACS numbers: 13.20.He, 12.38.Qk, 14.40.Nd

The flavor-changing neutral current process B+

→ K+ _τ+_τ−_{[1] is highly suppressed in the standard}

model (SM), with a predicted branching fraction in the range 1_{− 2 × 10}−7 _{[2, 3]. This decay is forbidden at}

tree level and only occurs, at lowest order, via one-loop diagrams. The SM contributions, shown in Fig. 1, include the electromagnetic penguin, the Z penguin, and the W+_W− _{box diagrams. Rare semi-leptonic B}

decays such as B+ _{→ K}+_τ+_τ− _{can provide a stringent}

test of the SM and a fertile ground for new physics searches. Virtual particles can enter in the loop and thus allow to probe, at relatively low energies, new physics at large mass scales. Measurements of the related decays, B+

→ K+_{`</sub>+<sub>`}− _{where ` = e or µ, have been previously}

published by BABAR [4] and other experiments [5], and exhibit some discrepancy with the SM expectation [6].

The decay B+ _{→ K}+_τ+_τ− _{is the third family}

equiv-alent of B+ → K+_{`</sub>+<sub>`}− _{and hence may provide}

addi-tional sensitivity to new physics due to third-generation couplings and the large mass of the τ lepton [7]. An important potential contribution to this decay is from neutral Higgs boson couplings, where the lepton-lepton-Higgs vertices are proportional to the mass squared of the lepton [8]. Thus, in the case of the τ , such contribu-tions can be significant and could alter the total decay rate. Additional sources of new physics and their effect on the B+

→ K+_τ+_τ− _{branching fraction and the}

kine-matic distributions of the τ+_τ− _{pair are also discussed}

in Refs. [9]-[17].

We report herein a search for B+

→ K+_τ+_τ− _with

data recorded by the BABAR detector [18] at the e+e− PEP-II collider at the SLAC National Accelerator Lab-oratory. This search is based on 424 fb−1 _{of data [19]}

collected at the center-of-mass (CM) energy of the Υ (4S)

5

J. L. Ritchie, A. M. Ruland, R. F. Schwitters, and B. C. Wray

University of Texas at Austin, Austin, Texas 78712, USA

J. M. Izen and X. C. Lou

University of Texas at Dallas, Richardson, Texas 75083, USA

F. Bianchi

ab

_{and D. Gamba}

ab

INFN Sezione di Torino

a

; Dipartimento di Fisica Sperimentale, Universit`a di Torino

b

, I-10125 Torino, Italy

L. Lanceri

ab

and L. Vitale

ab

INFN Sezione di Trieste

a

; Dipartimento di Fisica, Universit`a di Trieste

b

, I-34127 Trieste, Italy

F. Martinez-Vidal and A. Oyanguren

IFIC, Universitat de Valencia-CSIC, E-46071 Valencia, Spain

H. Ahmed, J. Albert, Sw. Banerjee, F. U. Bernlochner, H. H. F. Choi, G. J. King,

R. Kowalewski, M. J. Lewczuk, I. M. Nugent, J. M. Roney, R. J. Sobie, and N. Tasneem

University of Victoria, Victoria, British Columbia, Canada V8W 3P6

T. J. Gershon, P. F. Harrison, T. E. Latham, and E. M. T. Puccio

Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

H. R. Band, S. Dasu, Y. Pan, R. Prepost, and S. L. Wu

University of Wisconsin, Madison, Wisconsin 53706, USA

In a sample of 471 million BB events collected with the B

A

B

AR

detector at the PEP-II e

+

e

−

collider

we study the rare decays B

→ K

(∗)

_ℓ

+

_ℓ

−

_{, where ℓ}

+

_ℓ

−

_{is either e}

+

_e

−

_{or µ}

+

_µ

−

_{. We report results}

on partial branching fractions and isospin asymmetries in seven bins of di-lepton mass-squared. We

further present CP and lepton-flavor asymmetries for di-lepton masses below and above the J/ψ

resonance. We find no evidence for CP or lepton-flavor violation. The partial branching fractions

and isospin asymmetries are consistent with the Standard Model predictions and with results from

other experiments.

PACS numbers: 13.20.He

I. INTRODUCTION

The decays B

_{→ K}

(∗)

_ℓ

+

_ℓ

−

_{arise from flavor-changing}

neutral-current processes that are forbidden at tree level

in the Standard Model (SM). The lowest-order SM

pro-cesses contributing to these decays are the photon

pen-guin, the Z penguin and the W

+

W

−

box diagrams shown

in Fig. 1. Their amplitudes are expressed in terms of

hadronic form factors and perturbatively-calculable

ef-fective Wilson coefficients, C

eff

7

, C

9eff

and C

10eff

, which

represent the electromagnetic penguin diagram, and the

vector part and the axial-vector part of the linear

combi-nation of the Z penguin and W

+

_W

−

_{box diagrams,}

re-spectively [1]. In next-to-next-to-leading order (NNLO)

∗_{Now at the University of Tabuk, Tabuk 71491, Saudi Arabia} †_{Also with Universit`a di Perugia, Dipartimento di Fisica, Perugia,}

Italy

‡_{Now at the University of Huddersfield, Huddersfield HD1 3DH,}

UK

§_{Now at University of South Alabama, Mobile, Alabama 36688,}

USA

¶_{Also with Universit`a di Sassari, Sassari, Italy}

at a renormalization scale µ = 4.8 GeV, the effective

Wilson coefficients are C

₇eff

=

−0.304, C

eff

9

= 4.211, and

C

eff

10

=

−4.103 [2].

Non-SM physics may add new penguin and box

dia-grams, which can contribute at the same order as the SM

diagrams [3–5]. Examples of new physics loop processes

are depicted in Fig. 2. These contributions might modify

the Wilson coefficients from their SM expectations [5–8].

In addition, new contributions from scalar, pseudoscalar,

and tensor currents may arise that can modify, in

partic-ular, the lepton-flavor ratios [9, 10].

q q b t,c,u s W − γ , Z l + l − q q b t,c,u s W + W − ν l − l +

FIG. 1: Lowest-order Feynman diagrams for b

→ sℓ

+

_ℓ

−

_.

FIG. 1: Lowest order SM Feynman diagrams of→_¯ s `+`−.

resonance, where Υ (4S) decays into a BB pair. We use hadronic B meson tagging techniques, where one of the two B mesons, referred to as the Btag, is reconstructed

exclusively via its decay into one of several hadronic de-cay modes. The remaining tracks, clusters, and missing energy in the event are attributed to the signal B, de-noted as Bsig, on which the search for B+ → K+ τ+τ−

is performed. We consider only leptonic decays of the τ : τ+ _{→ e}+_ν

eντ and τ+ → µ+νµντ, which results in

three signal decay topologies with a charged K, multi-ple missing neutrinos, and either e+_e−_{, µ}+_µ− _{or e}+_µ−

in the final state. The neutrinos are accounted for as missing energy in any signal event where a charged kaon and lepton pair are identified and extra neutral activity, including π0 _{candidates, is excluded.}

Simulated Monte Carlo (MC) signal and background events, generated with EvtGen [20], are used to de-velop signal selection criteria and to study potential backgrounds. The detector response is simulated us-ing GEANT4 [21]. Signal MC events are generated as Υ (4S)_{→ B}+_B−_{, where one B decays according to its}

measured SM branching fractions [22] and the other B decays via B+ _{→ K}+_τ+_τ− _{according to the model}

de-scribed in Ref. [23]. Within this model, referred to as LCSR, a light-cone sum rule approach is used to deter-mine the form factors that enter into the parameteriza-tion of the matrix elements describing this decay. Signal events are also reweighted to a model based on the un-quenched lattice QCD calculations of the B_{→ K`</sub>+<sub>`}−

form factors [2] for the determination of the signal effi-ciency, and the two theoretical approaches are then com-pared to evaluate the model-dependence of our measure-ment. Because of the low efficiency of the hadronic Btag

reconstruction, “dedicated” signal MC samples are also generated for this analysis, where one B decays exclu-sively through B± _{→ D}0_π±_{, D}0

→ K−_π+ _{while the}

other B meson decays via the signal channel. This en-sures that more events pass the hadronic Btag

reconstruc-tion and allows for increased statistics in the distribureconstruc-tions of discriminating variables in the signal sample. Only variables that are independent of the Btag decay mode

are considered with the dedicated signal MC sample. To avoid potential bias, this dedicated sample is not used to evaluate the final signal selection efficiency. Back-ground MC samples consist of B+_B− _{and B}0_B0 _decays

and continuum events, e+_e− _{→ f ¯f , where f is a lepton}

or a quark. The BB and e+_e−_{→ cc MC-simulated}

that of data, whereas the remaining continuum samples have an integrated luminosity that is four times larger.

The signal selection of B+

→ K+_τ+_τ− _{events is}

pre-ceded by the full hadronic reconstruction of the Btag

meson, via B _{→ SX [24]. Here, S is a seed meson,} D(∗)0_{, D}(∗)±_{, D}∗±

s or J/ψ , and X is a combination of

at most five kaons and pions with a total charge of 0 or _{±1. The D seeds are reconstructed in the decay} modes D+ _{→ K}0 Sπ +_{, K}0 Sπ +_π0_{, K}0 Sπ +_π−_π+_{, K}−_π+_π+_, K−π+_π+_π0_{, K}+_K−_π+_{, K}+_K−_π+_π0_{; D}0 _{→ K}−_π+_, K−π+_π0_{, K}−_π+_π−_π+_{, K}0 Sπ +_π−_{, K}0 Sπ +_π−_π0_{, K}+_K−_, π+_π−_{, π}+_π−_π0_{, and K}0 Sπ 0_{; D}∗+ _{→ D}0_π+_{, D}+_π0_; D∗0 → D0_π0_{, D}0_{γ. The D}∗+

s and J/ψ seeds are

re-constructed as D∗+

s → D+sγ; Ds+ → φπ+, KS0K +_{; and}

J/ψ_{→ e}+_e−_{, µ}+_µ−_{, respectively. K}0

S and φ candidates

are reconstructed via their decay to π+_π− _{and K}+_K−_,

respectively.

We select Btag candidates using two kinematic

vari-ables: mES =

q (E∗

CM/2)2− ~p∗ 2

Btag and ∆E = E∗ CM 2 − E∗ Btag, where E ∗ Btag and ~p ∗

Btag are the CM energy and

three-momentum vector of the Btag, respectively, and E∗

CM

2 is the CM beam energy. A properly reconstructed

Btaghas mESconsistent with the mass of a B meson and

∆E consistent with 0 GeV. We require 5.20 < mES <

5.30 GeV/c2 _and

−0.12 < ∆E < 0.12 GeV, where the mES range includes a sideband region for background

studies. If more than one Btagcandidate per event

satis-fies these requirements, the Btagcandidate in the highest

purity mode is chosen. The purity of a Btagdecay mode

is determined from MC studies and is defined as the frac-tion of Btagcandidates with mES> 5.27 GeV/c2that are

properly reconstructed within the given mode. If more than one Btagcandidate with the same purity exists, the

one with the smallest|∆E| is chosen.

The hadronic Btag reconstruction results in both

charged and neutral B mesons. Since the Btagis fully

re-constructed, its four-vector is fully determined and thus that of the Bsigcan be calculated. The latter is obtained

using | ~p∗

Bsig| = p(E ∗

CM/2)2− m2B, where ~p∗Bsig is the

three momentum vector of Bsig in the CM frame and

mB is the mass of the B meson, with the direction of

~ p∗

Bsig opposite to that of ~p ∗

Btag. The missing momentum

four-vector, p∗

miss, is determined by subtracting the CM

four-momentum of all “signal-side” tracks and clusters from that of the Bsig.

B+ _{→ K}+_τ+_τ− _{signal events are required to have a}

charged Btag candidate with mES > 5.27 GeV/c2 and

a non-zero missing energy, Emiss, given by the energy

component of p∗miss. Furthermore, to reduce

contamina-tion from mis-reconstructed events with high-multiplicity Btagdecay modes, the purity of Btagcandidates is

recal-culated at this point after also requiring that there re-main only three charged tracks in the event not used in the Btagreconstruction (corresponding to the track

mul-tiplicity in signal events). This purity is more relevant to

the signal selection, since only charged Btagdecay modes

reconstructed with low multiplicity Bsig events are

con-sidered. Signal events with a purity greater than 40% are retained.

Continuum events are further suppressed using a multivariate likelihood selector, which consists of six event-shape variables. These include the magnitude of the Btag thrust, defined as the axis which maximizes

the sum of the longitudinal momenta of an event’s decay products, and its component along the beam axis and the ratio of the second-to-zeroth Fox-Wolfram moment [25]. The remaining variables are the angle of the missing momentum vector, ~p∗

miss, with the beam

axis, the angle between ~p∗

Btag and the beam axis, and

the angle between the thrust axis of the Btag and that

of the Bsig in the CM frame. The six event-shape

variables discriminate between BB events, where the spin-zero B mesons are produced almost at rest and the decay daughters consequently produce an isotropic distribution, and continuum events. In the latter, fermions are initially produced with higher momentum, resulting in a more collinear distribution of the final decay products. We require the likelihood ratio

L = Q iPB(xi) Q iPB(xi) + Q iPq(xi) > 0.50, (1)

where P (xi) are probability density functions,

deter-mined from MC samples, that describe the six event shape variables for BB, PB(xi), and continuum, Pq(xi),

events. This requirement removes more than 75% of the continuum events while retaining more than 80% of (sig-nal and background) BB MC events.

A signal selection is then applied on the charged tracks and neutral clusters that are not used in the Btag

re-construction. B+

→ K+_τ+_τ− _{candidates are required}

to possess exactly three charged tracks satisfying parti-cle identification (PID) requirements consistent with one charged K and an e+_e−_{, µ}+_µ−_{, or e}+_µ− _{pair. The}

PID selection algorithms for charged tracks are based on multivariate analysis techniques that use information from the BABAR detector subsystems [26]. The K± _is

required to have a charge opposite to that of Btag.

Fur-thermore, events with 3.00 < m`+<sub>`</sub>− < 3.19 GeV/c2 are

discarded to remove backgrounds with a J/ψ resonance. The invariant mass of the combination of the K with the oppositely charged lepton must also lie outside the region of the D0 _{mass, i.e. m}

K−_`+ < 1.80 GeV/c2 or

mK−_`+ > 1.90 GeV/c2, to remove events where a pion

coming from the D0 decay is misidentified as a muon. Moreover, events with γ_{→ e}+_e− _{are removed by}

requir-ing the invariant mass of each electron with any other oppositely charged track in the event to be greater than 50 MeV/c2_{. Background events with π}0 _candidates,

re-constructed from a pair of photons with individual en-ergies greater than 50 MeV, a total CM energy greater

than 100 MeV, and an invariant mass ranging between 100 and 160 MeV/c2_{, are rejected. Additional}

calorime-ter cluscalorime-ters not explicitly associated with Btag daughter

particles may originate from other low-energy particles in background events. We therefore define Eextra∗ to be

the energy sum of all neutral clusters with individual en-ergy greater than 50 MeV that are not used in the Btag

reconstruction.

The normalized squared mass of the τ+_τ−_{pair is given}

by sB = (pBsig− pK) 2_/m2

B, where pBsig and pK are the

four-momentum vectors of Bsig and of the kaon,

respec-tively, in the laboratory frame. The large mass of the τ leptons in signal events kinematically limits the sB

dis-tribution to large values. A requirement of sB > 0.45 is

applied.

At this point in the selection, remaining backgrounds are primarily BB events in which a properly recon-structed Btag is accompanied by Bsig → D(∗)`ν`, with

D(∗) _{→ K`}0_ν

`0 and thus have the same detected

final-state particles as signal events. A multi-layer perceptron (MLP) neural network [27], with seven input variables and one hidden layer, is employed to suppress this back-ground. The input variables are: the angle between the kaon and the oppositely charged lepton, the angle be-tween the two leptons, and the momentum of the lep-ton with charge opposite to the K, all in the τ+_τ−

rest frame, which is calculated as pBsig − pK; the

an-gle between the Bsig and the oppositely charged lepton,

the angle between the K and the low-momentum lep-ton, and the invariant mass of the K+_`− _{pair, all in the}

CM frame. Furthermore, the final input variables to the neural network are Eextra∗ and the residual energy, Eres,

which here is effectively the missing energy associated with the τ+_τ−_{pair and is calculated as the energy}

com-ponent of pτ

residual = pτBsig − p τ

K − pτ`+<sub>`</sub>−, where pτ_Bsig,

pτ

K and pτ`+<sub>`</sub>− are the four-momenta vectors in the τ+τ−

rest frame of the Bsig, K, and lepton pair in the event,

respectively. Eres has, in general, higher values for

sig-nal events than generic BB and continuum events due to the higher neutrino multiplicity. A neural network is trained and tested using randomly split dedicated signal MC and B+_B− _{background events, for each of the three}

channels: e+_e−_{, µ}+_µ−_{, and e}+_µ−_{. The results are shown}

in Fig. 2 for the three modes combined. The last step in the signal selection is to require that the output of the neural network is > 0.70 for the e+_e− _{and µ}+_µ−

chan-nels and > 0.75 for the e+_µ− _{channel. This requirement}

is optimized to yield the most stringent upper limit in the absence of a signal.

The branching fraction for each of the signal modes, i, is calculated as: Bi= Ni obs− Nbkgi i sigNBB , (2)

where N_BB= 471_{× 10}6 _{is the total number of BB pairs}

FIG. 2: (color online) MLP output distribution for the three signal channels combined. The B+

→ K+_τ+_τ− _{signal MC}

distribution is shown (dashed) with arbitrary normalization. The data (points) are overlaid on the expected combinatorial (shaded) plus mES-peaking (solid) background contributions.

in the data sample, assuming equal production of B+_B−

and B0_B0_{pairs in Υ (4S) decays, and N}i

obsis the number

of data events passing the signal selection. The signal ef-ficiency, i

sig, and the background estimate, Nbkgi , are

de-termined for each mode from the signal and background MC yields after all selection requirements.

For each mode, Nbkg consists of two components:

background events that have a properly reconstructed Btag and thus produce a distribution in mES which

peaks at the B mass, and combinatorial background events composed of continuum and BB events with mis-reconstructed Btag candidates which do not produce a

peaking structure in the mES signal region. After the

MLP output requirement, peaking background events comprise more than 92% of the total Nbkg for all three

modes. To reduce the dependence on MC simulation, the combinatorial background is extrapolated directly from the yield of data events in the mES “sideband” region

(5.20 < mES < 5.26 GeV/c2), after the full signal

selec-tion. Sideband data events are scaled to the correct nor-malization of the combinatorial background in the mES

signal region.

The peaking background is determined using B+_B−

background MC, while data in the final signal region is kept blinded to avoid experimentalist bias. Because of the large uncertainties on the branching fractions of many of the Btag decay modes as well as their

associ-ated reconstruction effects, there is a discrepancy in the Btagyield of approximately 10% between MC and data,

independent of the signal selection. A Btag yield

correc-tion is therefore determined by calculating the ratio of data to B+_B−_{MC events after the s}

B requirement. The

data sample after this requirement contains a sufficiently large background contribution after the sB requirement,

which consists mainly of B+_B−_{events (> 96%) according}

FIG. 3: (color online) Invariant-mass distribution of the K−_`+ _{pair in the B}+

→ D0_`+_ν

`, D0 → K−π+ samples

af-ter all signal selection criaf-teria are applied, except for the fi-nal requirement on the MLP output. The data (points) are overlaid on the expected combinatorial (shaded) plus mES

-peaking (solid) background contributions.

without unblinding the final signal-region. This correc-tion factor is determined to be 0.913_{± 0.020 and is} ap-plied to the MC reconstruction efficiency for both signal and background events.

The Btag yield is also cross-checked using a B+ →

D0_`+_ν

`, D0 → K−π+ control sample, which is selected

using the same signal selection discussed above, but with requiring one track to satisfy pion instead of lepton PID and reversing the D0 _{veto, such that 1.80 < m}

K−_π+ <

1.90 GeV/c2_{. These criteria are also applied to the full}

background MC and the resulting sample is found to con-sist mainly of peaking B+_B−_{events, which the MLP}

neu-ral network is trained to classify as background. Before the MLP requirement, good agreement between data and MC is found in all the distributions of the input variables of the B+

→ D0_`+_ν

`, D0 → K−π+ samples, as shown

in Fig. 3 for the mK−_π+ distribution. These samples are

then run through the MLP neural network and a detailed comparison of the MLP output and the input variables, after the full signal selection, is performed.

The results for each signal channel are then combined to determine _B(B+

→ K+_τ+_τ−_{). This is done using a}

frequentist approach by finding the value of_{B that} maxi-mizes the product of the Poisson likelihoods of observing Ni

obs in each of the signal channels. Branching fraction

uncertainties and limits are determined using the method described in Ref. [28], taking into account the statistical and systematic uncertainties on Nbkg and sig.

Systematic uncertainties associated with the level of data-MC agreement are determined for most of the vari-ables used in the signal selection. The determination of the Btag yield correction is anti-correlated with the

extrapolation of the combinatorial background from the mESsideband, as both use the combinatorial background

shape from MC. Therefore, only one systematic

uncer-e+_e− _µ+_µ− _e+_µ− Nbkgi 49.4±2.4±2.9 45.8±2.4 ±3.2 59.2±2.8 ±3.5 i sig(×10−5) 1.1±0.2±0.1 1.3±0.2±0.1 2.1±0.2±0.2 Ni obs 45 39 92 Significance (σ) -0.6 -0.9 3.7

TABLE I: Expected background yields, Ni

bkg, signal

efficien-cies, isig, number of observed data events, Nobsi , and signed

significance for each signal mode. Quoted uncertainties are statistical and systematic.

tainty on the Btag yield and combinatorial background

estimate is evaluated, using a simulated MC sample com-posed of background events with the same luminosity as the data sample. Accounting for the anti-correlation, the effect of varying the value of the Btagyield correction on

the final signal efficiency and background estimate is de-termined to be 1.2% and 1.6%, respectively. The uncer-tainty associated with the theoretical model is evaluated by reweighting the sB distribution of the dedicated

sig-nal MC sample to the LCSR [23] theoretical model and to that of Ref. [29] and determining the difference in sig-nal efficiency, which is calculated to be 3.0%. Additiosig-nal uncertainties on sig and Nbkg arise due to the

model-ing of PID selectors (4.8% for e+_e−_{, 7.0% for µ}+_µ−_,

and 5.0% for e+ µ−) and the π0 veto (3.0%). The level of agreement between data and MC is evaluated using the B+

→ D0_`+_ν

`, D0 → K−π+ control sample before

and after the MLP requirement. Comparison of both the overall yields as well as the distributions of the input and output variable results in a systematic uncertainty of 2.6%. Other potential sources of systematic uncertainties have been investigated, including those associated with the assumption that charged and neutral B candidates are produced at equal rates, the continuum likelihood suppression, Btagpurity, track multiplicity, Emissand sB

selection criteria, and are all implicitly accounted for in the Btag yield correction uncertainty. Correlations

be-tween the signal efficiency and the background estimate due to common systematic errors are included, but are found to have a negligible effect on the final branching fraction results.

The final signal efficiencies, background estimates and observed yields of each signal mode are shown in Ta-ble I, with the associated branching fraction significance. The yields in the e+_e− _{and µ}+_µ− _{channels show}

con-sistency with the expected background estimate. The yields in the e+ µ− channel consist of 40 e+ µ− and 52 e− _µ+ _{events, which corresponds to an excess of 3.7σ}

over the background expectation. Examination of kine-matic distributions in the e+ _µ− _{channel does not give}

any clear indication either of signal-like behavior or of systematic problems with background modeling. When combined with the e+_e− _{and µ}+_µ− _{modes, the overall}

significance of the B+_{→ K}+_τ+_τ− _{signal is less than 2σ,}

and hence we do not interpret this as evidence of signal. The branching fraction for the combined three modes is B(B+_{→ K}+_τ+_τ−_)=(1.31+0.66

−0.61(stat.)+0.35−0.25(sys.))× 10−3.

The upper limit at the 90% confidence level is B(B+

→ K+_τ+_τ−_{)< 2.25× 10}−3_.

In conclusion, this is the first search for the decay B+

→ K+_τ+_τ−_{, using the full BABARdataset collected}

at the CM energy of the Υ (4S) resonance. No signifi-cant signal is observed and the upper limit on the final branching fraction is determined to be 2.25_{× 10}−3_{at the}

90% confidence level.

ACKNOWLEDGMENTS

We are grateful for the excellent luminosity and ma-chine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the comput-ing organizations that support BABAR. The collaborat-ing 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), MINECO (Spain), STFC (United Kingdom), BSF (USA-Israel). Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foun-dation (USA).

∗ _{Now at: Wuhan University, Wuhan 43072, China} † _{Now at: Universit`a di Bologna and INFN Sezione di}

Bologna, I-47921 Rimini, Italy

‡ _{Now at: University of Huddersfield, Huddersfield HD1}

3DH, UK

§ _{Now at: University of South Alabama, Mobile, Alabama}

36688, USA

¶ _{Also at: Universit`a di Sassari, I-07100 Sassari, Italy}

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