Search for Lepton Flavor and Lepton Number Violating tau Decays into a Lepton and Two Charged Mesons
aa r X i v : . [ h e p - e x ] A ug KEK Preprint 2009-20Belle Preprint 2009-20NTLP Preprint 2009-02
Search for Lepton Flavor and Lepton Number Violating τ Decaysinto a Lepton and Two Charged Mesons
Y. Miyazaki, H. Aihara, K. Arinstein,
1, 33
V. Aulchenko,
1, 33
T. Aushev,
19, 13
A. M. Bakich, V. Balagura, E. Barberio, A. Bay, K. Belous, V. Bhardwaj, M. Bischofberger, A. Bondar,
1, 33
M. Braˇcko,
21, 14
T. E. Browder, P. Chang, A. Chen, B. G. Cheon, I.-S. Cho, Y. Choi, J. Dalseno,
22, 41
M. Dash, W. Dungel, S. Eidelman,
1, 33
D. Epifanov,
1, 33
M. Feindt, N. Gabyshev,
1, 33
A. Garmash,
1, 33
P. Goldenzweig, H. Ha, J. Haba, K. Hara, Y. Hasegawa, K. Hayasaka, H. Hayashii, Y. Horii, Y. Hoshi, W.-S. Hou, H. J. Hyun, T. Iijima, K. Inami, R. Itoh, M. Iwasaki, Y. Iwasaki, T. Julius, D. H. Kah, J. H. Kang, H. Kawai, T. Kawasaki, H. O. Kim, J. H. Kim, S. K. Kim, Y. I. Kim, Y. J. Kim, B. R. Ko, S. Korpar,
21, 14
P. Kriˇzan,
20, 14
P. Krokovny, R. Kumar, T. Kumita, A. Kuzmin,
1, 33
Y.-J. Kwon, S.-H. Kyeong, S.-H. Lee, T. Lesiak,
29, 4
J. Li, C. Liu, D. Liventsev, R. Louvot, A. Matyja, S. McOnie, K. Miyabayashi, H. Miyata, T. Nagamine, Y. Nagasaka, E. Nakano, M. Nakao, S. Nishida, K. Nishimura, O. Nitoh, T. Ohshima, S. Okuno, S. L. Olsen, P. Pakhlov, G. Pakhlova, H. Palka, C. W. Park, H. Park, H. K. Park, R. Pestotnik, L. E. Piilonen, A. Poluektov,
1, 33
Y. Sakai, O. Schneider, C. Schwanda, K. Senyo, M. Shapkin, V. Shebalin,
1, 33
J.-G. Shiu, B. Shwartz,
1, 33
A. Sokolov, E. Solovieva, S. Staniˇc, M. Stariˇc, T. Sumiyoshi, G. N. Taylor, Y. Teramoto, I. Tikhomirov, S. Uehara, Y. Unno, S. Uno, P. Urquijo, Y. Usov,
1, 33
G. Varner, A. Vinokurova,
1, 33
C. H. Wang, P. Wang, Y. Watanabe, R. Wedd, E. Won, B. D. Yabsley, Y. Yamashita, Y. Yusa, Z. P. Zhang, V. Zhilich,
1, 33
V. Zhulanov,
1, 33
T. Zivko, A. Zupanc, and O. Zyukova
1, 33 (The Belle Collaboration) Budker Institute of Nuclear Physics, Novosibirsk, Russian Federation Chiba University, Chiba, Japan University of Cincinnati, Cincinnati, OH, USA T. Ko´sciuszko Cracow University of Technology, Krakow, Poland The Graduate University for Advanced Studies, Hayama, Japan Hanyang University, Seoul, South Korea University of Hawaii, Honolulu, HI, USA High Energy Accelerator Research Organization (KEK), Tsukuba, Japan
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Hiroshima Institute of Technology, Hiroshima, Japan Institute of High Energy Physics,Chinese Academy of Sciences, Beijing, PR China Institute for High Energy Physics, Protvino, Russian Federation Institute of High Energy Physics, Vienna, Austria Institute for Theoretical and Experimental Physics, Moscow, Russian Federation J. Stefan Institute, Ljubljana, Slovenia Kanagawa University, Yokohama, Japan Institut f¨ur Experimentelle Kernphysik,Universit¨at Karlsruhe, Karlsruhe, Germany Korea University, Seoul, South Korea Kyungpook National University, Taegu, South Korea ´Ecole Polytechnique F´ed´erale de Lausanne, EPFL, Lausanne, Switzerland Faculty of Mathematics and Physics,University of Ljubljana, Ljubljana, Slovenia University of Maribor, Maribor, Slovenia Max-Planck-Institut f¨ur Physik, M¨unchen, Germany University of Melbourne, Victoria, Australia Nagoya University, Nagoya, Japan Nara Women’s University, Nara, Japan National Central University, Chung-li, Taiwan National United University, Miao Li, Taiwan Department of Physics, National Taiwan University, Taipei, Taiwan H. Niewodniczanski Institute of Nuclear Physics, Krakow, Poland Nippon Dental University, Niigata, Japan Niigata University, Niigata, Japan University of Nova Gorica, Nova Gorica, Slovenia Novosibirsk State University, Novosibirsk, Russian Federation Osaka City University, Osaka, Japan Panjab University, Chandigarh, India University of Science and Technology of China, Hefei, PR China Seoul National University, Seoul, South Korea Shinshu University, Nagano, Japan Sungkyunkwan University, Suwon, South Korea School of Physics, University of Sydney, NSW 2006, Australia Excellence Cluster Universe, Technische Universit¨at M¨unchen, Garching, Germany Tohoku Gakuin University, Tagajo, Japan Tohoku University, Sendai, Japan Department of Physics, University of Tokyo, Tokyo, Japan Tokyo Metropolitan University, Tokyo, Japan Tokyo University of Agriculture and Technology, Tokyo, Japan IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA Yonsei University, Seoul, South Korea bstract We search for lepton flavor and lepton number violating τ decays into a lepton ( ℓ = electron ormuon) and two charged mesons ( h, h ′ = π ± or K ± ), τ − → ℓ − h + h ′− and τ − → ℓ + h − h ′− , using671 fb − of data collected with the Belle detector at the KEKB asymmetric-energy e + e − collider.We obtain 90% C.L. upper limits on the branching fractions in the range (4 . − . × − for τ → ehh ′ , and (3 . − × − for τ → µhh ′ processes. These results improve upon previouslypublished upper limits by factors between 1.6 to 8.8. PACS numbers: 11.30.Fs; 13.35.Dx; 14.60.Fg NTRODUCTION
Lepton flavor violation (LFV) in charged lepton decays is forbidden or highly suppressedeven if neutrino mixing is included. However, LFV appears in various extensions of theStandard Model (SM), such as supersymmetry, leptoquark and many other models [1, 2, 3, 4,5, 6, 7, 8]. Some of these models predict branching fractions which, for certain combinationsof model parameters, can be as high as 10 − ; these rates are already accessible in high-statistics B -factory experiments. Here, we search for τ decays [ † ] into one lepton ( ℓ =electron or muon) and two charged mesons ( h, h ′ = π ± or K ± ) including lepton flavor andlepton number violation ( τ − → ℓ − h − h ′ + and τ − → ℓ + h − h ′− ) [ ‡ ], with a data sample of 671fb − collected at the Υ(4 S ) resonance and 60 MeV below with the Belle detector at theKEKB asymmetric-energy e + e − collider [9]. Previously, we reported 90% confidence level(C.L.) upper limits on these LFV branching fractions using 158 fb − of data; the resultswere in the range (1.6 − × − [10]. The BaBar collaboration has also obtained 90%C.L. upper limits in the range (0.7 − × − [11]. using 221 fb − of dataThe Belle detector is a large-solid-angle magnetic spectrometer that consists of a siliconvertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aerogel thresholdCherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters(TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL), all locatedinside a superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside the coil is instrumented to detect K L mesons and to identify muons(KLM). The detector is described in detail elsewhere [12].Particle identification is very important for this measurement. We use hadron identi-fication likelihood variables based on the ratio of the energy deposited in the ECL to themomentum measured in the SVD and CDC, the shower shape in the ECL, the particle rangein the KLM, the hit information from the ACC, the dE/dx information in the CDC, andthe particle time-of-flight from the TOF. To distinguish hadron species, we use likelihoodratios, P ( i/j ) = L i / ( L i + L j ), where L i ( L j ) is the likelihood for the detector responseto a track with flavor hypothesis i ( j ). For lepton identification, we form likelihood ratios P ( e ) [13] and P ( µ ) [14] based on the electron and muon probabilities, respectively, whichare determined by the responses of the appropriate subdetectors.In order to estimate the signal efficiency and optimize the event selection, we use MonteCarlo (MC) simulated event samples. The signal and background events from generic τ + τ − decays are generated by KKMC/TAUOLA [15]. For the signal MC sample, we generate τ + τ − pairs, where one τ decays into a lepton and two charged mesons, using a three-body phase space model, and the other τ decays generically. Other backgrounds, including B ¯ B and continuum e + e − → q ¯ q ( q = u, d, s, c ) events, Bhabha events, and two-photonprocesses are generated by EvtGen [16], BHLUMI [17], and AAFH [18], respectively. Theevent selection is optimized mode-by-mode since the backgrounds are mode dependent. Allkinematic variables are calculated in the laboratory frame unless otherwise specified. In [ † ] Throughout this paper, charge-conjugate modes are implied unless stated otherwise.[ ‡ ] The notation “ τ → ℓhh ′ “ indicates both τ − → ℓ − h + h ′− and τ − → ℓ + h − h ′− modes. e + e − center-of-mass (CM) system are indicated bythe superscript “CM”. EVENT SELECTION
Since the majority of τ decays produce one-prong final states [19], we search for τ + τ − events in which one τ (the signal τ ) decays into a lepton and two charged mesons ( π ± or K ± )and the other τ (the tag τ ) decays into one charged track with any number of additionalphotons and neutrinos. Candidate τ -pair events are required to have four tracks with zeronet charge.We start by reconstructing four charged tracks and any number of photons within thefiducial volume defined by − . < cos θ < . θ is the polar angle relative to thedirection opposite to that of the incident e + beam in the laboratory frame. The transversemomentum ( p t ) of each charged track and the energy of each photon ( E γ ) are required tosatisfy p t > c and E γ > . P ( ℓ ) > . τ + τ − and q ¯ q background events, we veto events that have a photon on the signal side.To ensure that the missing particles are neutrinos rather than photons or charged particlesthat pass outside the detector acceptance, we impose requirements on the missing momentum ~p miss , which is calculated by subtracting the vector sum of the momenta of all tracks andphotons from the sum of the e + and e − beam momenta. We require that the magnitudeof ~p miss be greater than 1.0 GeV/ c , and that its direction point into the fiducial volume ofthe detector. Furthermore, we reject the event if the direction of the missing momentumtraverses the gap between the barrel and endcap of the ECL. Since neutrinos are emittedonly on the tag side, the direction of ~p miss should lie within the tag side of the event. Thecosine of the opening angle between ~p miss and the charged track on the tag side in the CMsystem, cos θ CM tag − miss , should be in the range 0 . < cos θ CM tag − miss < . K ± ( π ± ) if they satisfy thecondition P ( K/π ) > . < . . < P ( K/π ) < .
8, the event is rejected. The kaon (pion) identification efficiency is 80% (88%)while the probability to misidentify a pion (kaon) as a kaon (a pion) is below 10% (12%).In order to reduce background from mesons reconstructed from photon conversions (i.e.5
ABLE I: Selection criteria for lepton momentum ( p ℓ ) and magnitude of thrust ( T ).Mode p ℓ (GeV/ c ) Tτ → µππ p µ > . . < T < . τ → µKπ p µ > . . < T < . τ → µKK p µ > . . < T < . τ → eππ p e > . . < T < . τ → eKπ p e > . . < T < . τ → eKK p e > . . < T < . γ → e + e − ), we require that two charged meson candidates have P ( e ) < .
1. Furthermore,we require P ( µ ) < . e + e − → e + e − µ + µ − .To reject q ¯ q background, we require the magnitude of the thrust ( T ) to be in the rangesgiven in Table I (see Fig. 1 (a) and Fig. 2 (a)). We also require 5 . < E CM vis < . E CM vis is the total visible energy in the CM system, defined as the sum of the energiesof the lepton, two charged mesons, the charged track on the tag side (with a pion masshypothesis) and all photon candidates (see Fig. 1 (b)). The invariant mass reconstructedfrom the charged track and any photons on the tag side m tag , is required to be less than1.00 GeV/ c (see Fig.2 (b)). In order to reduce q ¯ q background, a kaon veto P ( K/π ) < . µπK and µKK modes.We remove events if K S candidates are reconstructed from two oppositely-charged trackson the signal side with an invariant mass 0.470 GeV/ c < M π + π − < .
525 GeV/ c , assumingthe pion mass for both tracks, and the π + π − vertex is displaced from the interaction point(IP) in the direction of the pion pair momentum [21]. Events including a K L meson alsoconstitute background since the undetected K L results in fake missing momentum. There-fore, we veto events with K L candidates, which are selected from hit clusters in the KLMthat are not associated with either an ECL cluster or with a charged track [22], for the µhh ′ modes.To suppress the B ¯ B and q ¯ q background, we require that the number of photons on thetag side n TAG γ be n TAG γ ≤ n TAG γ ≤ P ( e ) < . eππ and eπK modes. Furthermore, we require that the momentum ofthe electron and track on the tag side in the CM system be less than 4.5 GeV/ c to reduceBhabha background in the eππ modes.Finally, to suppress backgrounds from generic τ + τ − and q ¯ q events, we apply a selectionbased on the magnitude of the missing momentum p miss and the missing mass squared m . We apply different selection criteria depending on the lepton identification of thecharged track on the tag side; two neutrinos are emitted if the track is an electron or muon(leptonic tag) while only one is emitted if the track is a hadron (hadronic tag). For the ehh ′ , µππ and µKK modes, we require the following relation between p miss and m : p miss > − . × m − p miss > . × m − . p miss > − . × m +0 . IG. 1: Distribution of (a) the magnitude of thrust and (b) the total visible energy in the CMsystem. While the signal MC ( τ − → µ − K + K − ) distribution is normalized arbitrarily, the dataand background MC are normalized to the same luminosity. The selected regions are indicated bythe arrows.FIG. 2: Distribution of (a) the magnitude of thrust and (b) invariant mass using particles on thetag side. While the signal MC ( τ − → µ − π + π − ) distribution is normalized arbitrarily, the dataand background MC are normalized to the same luminosity. The selected regions are indicated bythe arrows. and p miss > . × m − . p miss is in GeV/ c and m miss is inGeV/ c (see Fig. 4). For the µπK modes, we require the following relation between p miss and m : p miss > − . × m − . p miss > . × m − . p miss > − . × m + 0 . p miss > . × m − . IG. 3: Distributions of the number of photons on the tag side for (left) hadronic and (right)leptonic tags. While the signal MC ( τ − → µ − π + π − ) distribution is normalized arbitrarily, the dataand background MC are normalized to the same luminosity. The selected regions are indicated bythe arrows. SIGNAL AND BACKGROUND ESTIMATION
The signal candidates are examined in the two-dimensional plot of the ℓhh ′ invariantmass ( M ℓhh ′ ) versus the difference of their energy from the beam energy in the CM sys-tem (∆ E ). A signal event should have M ℓhh ′ close to the τ -lepton mass ( m τ ) and ∆ E close to zero. For all modes, the M ℓhh ′ and ∆ E resolutions are parameterized from fits tothe signal MC distributions, with an asymmetric Gaussian function that takes into accountinitial-state radiation. The resolutions in M ℓhh ′ and ∆ E are listed in Table II.To evaluate the branching fractions, we use elliptical signal regions that contain 90% ofthe MC signal events satisfying all selection criteria. We blind the data in the signal regionuntil all selection criteria are finalized so as not to bias our choice of selection criteria.For the ehh ′ modes the dominant background is from two-photon processes; the fractionof q ¯ q and generic τ + τ − events is small due to the low electron fake rate. For the µππ modethe dominant background is from q ¯ q processes and a smaller background is from generic τ + τ − events in the ∆ E < M µππ < m τ region, which are combinations of afake muon and two pions. For the µπK mode, the dominant background is from generic τ + τ − events that are combinations of a fake muon, a fake kaon and a true pion. If a pionis misidentified as a kaon, the reconstructed mass from generic τ + τ − background can begreater than the τ lepton mass because of the larger kaon mass. For the µKK mode, thedominant background originates from q ¯ q events and τ + τ − events.The number of background events in the signal region is estimated from the data remain-ing after event selection in the sideband region. For the ehh ′ and µKK modes, since thenumber of remaining data events is small, the number of background events in the signalregion is estimated by interpolating the number of observed events in the sideband region8 IG. 4: Scatter-plots of p miss vs. m : (a) and (b) show the signal MC ( τ − → µ − π + π − ) andgeneric τ + τ − MC distributions, respectively, for the hadronic tags while (c) and (d) are the samedistributions for the leptonic tags. The selected regions are indicated by lines. defined as the range ± σ M ℓhh ′ and ± σ ∆ E excluding the signal region, assuming that thebackground distribution is uniform in the sideband region. For the µππ and µπK modes,we estimate the number of background events in the signal region by fitting to observeddata in the sideband region using a probability density function (PDF) that describes theshapes of the background distributions along the M µππ axis within ± σ ∆ E . For the µππ mode, the PDFs of generic τ τ and q ¯ q events are determined using MC samples, assumingexponential and first-order polynomial distributions, respectively (see Fig. 5). For the µπK modes, we parameterize the PDF by a 3rd-order polynomial function that is fitted to thedata remaining in the sideband region. The signal efficiency and the number of expectedbackground events in the signal region for each mode are summarized in Table III.The dominant systematic uncertainties for this analysis come from tracking efficienciesand particle identification. The uncertainty due to the charged track finding is estimated tobe 1.0% per charged track; the total uncertainty due to the charged track finding is 4.0%.The uncertainties due to lepton identification are 2.2% and 1.9% for electron and muon,respectively. The uncertainty due to pion and kaon identification is 1.3% and 1.8% per pionand kaon, respectively. The uncertainty due to the e -veto on the tag side applied for the τ → eππ and τ → eπK modes is estimated as the uncertainty in the electron identification9 ABLE II: Summary of M ℓ hh ′ and ∆ E resolutions ( σ high / low M ℓ hh ′ (MeV/ c ) and σ high / low∆ E (MeV)). Here σ high ( σ low ) means the standard deviation on the higher (lower) side of the peak.Mode σ high M ℓ hh ′ σ low M ℓ hh ′ σ high∆ E σ low∆ E τ − → µ − π + π − τ − → µ + π − π − τ − → e − π + π − τ − → e + π − π − τ − → µ − K + K − τ − → µ + K − K − τ − → e − K + K − τ − → e + K − K − τ − → µ − π + K − τ − → e − π + K − τ − → µ − K + π − τ − → e − K + π − τ − → µ + K − π − τ − → e + K − π − times the branching fraction of τ − → e − ¯ ν e ν τ (0.4%). The uncertainties due to MC statisticsand luminosity are estimated to be (2.5 − − UPPER LIMITS ON THE BRANCHING FRACTIONS
Finally, we examine the data in the signal region and observe two candidate events for the µ − π + K − mode, one candidate event for each of the µ − K + π − , µ + π − K − and e + π − π − modes,and no candidate events for the other modes. These numbers of events are consistent withthe expected numbers of background events. Since no statistically significant excess of dataover the expected background is observed, we set the following upper limits on the branchingfractions of τ → ℓhh ′ based on the Feldman-Cousins method [23]. The 90% C.L. upper limiton the number of signal events including a systematic uncertainty ( s ) is obtained usingthe POLE program without conditioning [24] based on the number of expected backgroundevents, the number of observed events and the systematic uncertainty. The upper limit onthe branching fraction ( B ) is then given by B ( τ → ℓhh ′ ) < s N ττ ε , (1)10 ABLE III: The signal efficiency ( ε ), the number of expected background events ( N BG ) estimatedfrom the sideband data, the total systematic uncertainty ( σ syst ), the number of observed events inthe signal region ( N obs ), 90% C.L. upper limit on the number of signal events including systematicuncertainties ( s ) and 90% C.L. upper limit on the branching fraction for each individual mode.Mode ε (%) N BG σ syst (%) N obs s B (10 − ) τ − → µ − π + π − . ± .
38 5.9 0 1.53 3.3 τ − → µ + π − π − . ± .
25 5.9 0 1.77 3.7 τ − → e − π + π − . ± .
15 6.0 0 2.15 4.4 τ − → e + π − π − . ± .
07 6.0 1 4.21 8.8 τ − → µ − K + K − . ± .
23 6.7 0 1.92 6.8 τ − → µ + K − K − . ± .
06 6.8 0 2.46 9.6 τ − → e − K + K − . ± .
08 6.5 0 2.35 5.4 τ − → e + K − K − . ± .
05 6.6 0 2.43 6.0 τ − → µ − π + K − . ± .
14 6.3 2 5.05 16 τ − → e − π + K − . ± .
19 6.4 0 2.12 5.8 τ − → µ − K + π − . ± .
32 6.3 1 3.34 10 τ − → e − K + π − . ± .
19 6.4 0 1.90 5.2 τ − → µ + K − π − . ± .
21 6.3 1 3.16 9.4 τ − → e + K − π − . ± .
07 6.4 0 2.40 6.7 where N ττ is the number of τ + τ − pairs, and ε is the signal efficiency. The value N ττ = 616 . × is obtained from the integrated luminosity times the cross section for τ -pair production,which is calculated in the updated version of KKMC [25] to be σ ττ = 0 . ± .
003 nb.Table III summarizes information about the upper limits for all modes. We obtain thefollowing 90% C.L. upper limits on the branching fractions: B ( τ → ehh ′ ) < (4 . − . × − and B ( τ → µhh ′ ) < (3 . − × − . These results improve upon previously publishedupper limits by factors of 1.6 to 8.8 [10]. SUMMARY
We have searched for lepton-flavor and lepton-number-violating τ decays into a leptonand two charged mesons ( h, h ′ = π ± or K ± ) using 671 fb − of data. We found no excess ofsignal in any of the modes. The resulting 90% C.L. upper limits on the branching fractions, B ( τ → ehh ′ ) < (4 . − . × − and B ( τ → µhh ′ ) < (3 . − × − , improve uponpreviously published results by factors of 1.6 to 8.8. These more stringent upper limits canbe used to constrain the parameter spaces in various models of new physics.11 IG. 5: Mass distribution of µ − π + π − within the ± σ ∆ E region after event selection. While thesignal MC ( τ − → µ − π + π − ) distribution is normalized arbitrarily, the data and background MCare normalized to the same luminosity. The expected background is shown as the solid histogram. Acknowledgments
We are grateful to M.J. Herrero for stimulating discussions. We thank the KEKB groupfor the excellent operation of the accelerator, the KEK cryogenics group for the efficientoperation of the solenoid, and the KEK computer group and the National Institute of In-formatics for valuable computing and SINET3 network support. We acknowledge supportfrom the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan,the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Re-search Center of Nagoya University; the Australian Research Council and the AustralianDepartment of Industry, Innovation, Science and Research; the National Natural ScienceFoundation of China under contract No. 10575109, 10775142, 10875115 and 10825524; theDepartment of Science and Technology of India; the BK21 and WCU program of the MinistryEducation Science and Technology, the CHEP SRC program and Basic Research program(grant No. R01-2008-000-10477-0) of the Korea Science and Engineering Foundation, Ko-rea Research Foundation (KRF-2008-313-C00177), and the Korea Institute of Science andTechnology Information; the Polish Ministry of Science and Higher Education; the Ministryof Education and Science of the Russian Federation and the Russian Federal Agency forAtomic Energy; the Slovenian Research Agency; the Swiss National Science Foundation;the National Science Council and the Ministry of Education of Taiwan; and the U.S. De-partment of Energy. This work is supported by a Grant-in-Aid from MEXT for ScienceResearch in a Priority Area (”New Development of Flavor Physics”), and from JSPS forCreative Scientific Research (”Evolution of Tau-lepton Physics”).12
IG. 6: Scatter-plots in the M ℓhh ′ – ∆ E plane within the ± σ area for the (a) τ − → µ − π + π − , (b) τ − → µ + π − π − , (c) τ − → µ − K + K − , (d) τ − → µ + K − K − , (e) τ − → µ − π + K − , (f) τ − → µ − K + π − ,and (g) τ − → µ + π − K − modes. The data are indicated by the solid circles. The filled boxes showthe MC signal distribution with arbitrary normalization. The elliptical signal regions shown bythe solid curves are used for evaluating the signal yield. IG. 7: Scatter-plots in the M ℓhh ′ – ∆ E plane within the ± σ area for the (a) τ − → e − π + π − , (b) τ − → e + π − π − , (c) τ − → e − K + K − , (d) τ − → e + K − K − , (e) τ − → e − π + K − , (f) τ − → e − K + π − ,and (g) τ − → e + π − K − modes. The data are indicated by the solid circles. The filled boxes showthe MC signal distribution with arbitrary normalization. The elliptical signal regions shown bythe solid curves are used for evaluating the signal yield.
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