Precise measurement of hadronic τ -decays in modes with η mesons
aa r X i v : . [ h e p - e x ] A ug BELLE-CONF-0714
Precise measurement of hadronic τ -decays in modes with η mesons K. Abe, I. Adachi, H. Aihara, K. Arinstein, T. Aso, V. Aulchenko, T. Aushev,
22, 16
T. Aziz, S. Bahinipati, A. M. Bakich, V. Balagura, Y. Ban, S. Banerjee, E. Barberio, A. Bay, I. Bedny, K. Belous, V. Bhardwaj, U. Bitenc, S. Blyth, A. Bondar, A. Bozek, M. Braˇcko,
24, 17
J. Brodzicka, T. E. Browder, M.-C. Chang, P. Chang, Y. Chao, A. Chen, K.-F. Chen, W. T. Chen, B. G. Cheon, C.-C. Chiang, R. Chistov, I.-S. Cho, S.-K. Choi, Y. Choi, Y. K. Choi, S. Cole, J. Dalseno, M. Danilov, A. Das, M. Dash, J. Dragic, A. Drutskoy, S. Eidelman, D. Epifanov, S. Fratina, H. Fujii, M. Fujikawa, N. Gabyshev, A. Garmash, A. Go, G. Gokhroo, P. Goldenzweig, B. Golob,
23, 17
M. Grosse Perdekamp,
12, 41
H. Guler, H. Ha, J. Haba, K. Hara, T. Hara, Y. Hasegawa, N. C. Hastings, K. Hayasaka, H. Hayashii, M. Hazumi, D. Heffernan, T. Higuchi, L. Hinz, H. Hoedlmoser, T. Hokuue, Y. Horii, Y. Hoshi, K. Hoshina, S. Hou, W.-S. Hou, Y. B. Hsiung, H. J. Hyun, Y. Igarashi, T. Iijima, K. Ikado, K. Inami, A. Ishikawa, H. Ishino, R. Itoh, M. Iwabuchi, M. Iwasaki, Y. Iwasaki, C. Jacoby, N. J. Joshi, M. Kaga, D. H. Kah, H. Kaji, S. Kajiwara, H. Kakuno, J. H. Kang, P. Kapusta, S. U. Kataoka, N. Katayama, H. Kawai, T. Kawasaki, A. Kibayashi, H. Kichimi, H. J. Kim, H. O. Kim, J. H. Kim, S. K. Kim, Y. J. Kim, K. Kinoshita, S. Korpar,
24, 17
Y. Kozakai, P. Kriˇzan,
23, 17
P. Krokovny, R. Kumar, E. Kurihara, A. Kusaka, A. Kuzmin, Y.-J. Kwon, J. S. Lange, G. Leder, J. Lee, J. S. Lee, M. J. Lee, S. E. Lee, T. Lesiak, J. Li, A. Limosani, S.-W. Lin, Y. Liu, D. Liventsev, J. MacNaughton, G. Majumder, F. Mandl, D. Marlow, T. Matsumura, A. Matyja, S. McOnie, T. Medvedeva, Y. Mikami, W. Mitaroff, K. Miyabayashi, H. Miyake, H. Miyata, Y. Miyazaki, R. Mizuk, G. R. Moloney, T. Mori, J. Mueller, A. Murakami, T. Nagamine, Y. Nagasaka, Y. Nakahama, I. Nakamura, E. Nakano, M. Nakao, H. Nakayama, H. Nakazawa, Z. Natkaniec, K. Neichi, S. Nishida, K. Nishimura, Y. Nishio, I. Nishizawa, O. Nitoh, S. Noguchi, T. Nozaki, A. Ogawa, S. Ogawa, T. Ohshima, S. Okuno, S. L. Olsen, S. Ono, W. Ostrowicz, H. Ozaki, P. Pakhlov, G. Pakhlova, H. Palka, C. W. Park, H. Park, K. S. Park, N. Parslow, L. S. Peak, M. Pernicka, R. Pestotnik, M. Peters, L. E. Piilonen, A. Poluektov, J. Rorie, M. Rozanska, H. Sahoo, Y. Sakai, H. Sakamoto, H. Sakaue, T. R. Sarangi, N. Satoyama, K. Sayeed, T. Schietinger, O. Schneider, P. Sch¨onmeier, J. Sch¨umann, C. Schwanda, A. J. Schwartz, R. Seidl,
12, 41
A. Sekiya, K. Senyo, M. E. Sevior, L. Shang, M. Shapkin, C. P. Shen, H. Shibuya, S. Shinomiya, J.-G. Shiu, B. Shwartz, J. B. Singh, A. Sokolov, E. Solovieva, A. Somov, S. Staniˇc, M. Stariˇc, J. Stypula, A. Sugiyama, K. Sumisawa, T. Sumiyoshi, S. Suzuki, S. Y. Suzuki, O. Tajima, F. Takasaki, K. Tamai, N. Tamura, M. Tanaka, N. Taniguchi, G. N. Taylor, Y. Teramoto, I. Tikhomirov, K. Trabelsi, Y. F. Tse, T. Tsuboyama, K. Uchida, Typeset by REVTEX 1. Uchida, S. Uehara, K. Ueno, T. Uglov, Y. Unno, S. Uno, P. Urquijo, Y. Ushiroda, Y. Usov, G. Varner, K. E. Varvell, K. Vervink, S. Villa, A. Vinokurova, C. C. Wang, C. H. Wang, J. Wang, M.-Z. Wang, P. Wang, X. L. Wang, M. Watanabe, Y. Watanabe, R. Wedd, J. Wicht, L. Widhalm, J. Wiechczynski, E. Won, B. D. Yabsley, A. Yamaguchi, H. Yamamoto, M. Yamaoka, Y. Yamashita, M. Yamauchi, C. Z. Yuan, Y. Yusa, C. C. Zhang, L. M. Zhang, Z. P. Zhang, V. Zhilich, V. Zhulanov, A. Zupanc, and N. Zwahlen (The Belle Collaboration) Budker Institute of Nuclear Physics, Novosibirsk Chiba University, Chiba University of Cincinnati, Cincinnati, Ohio 45221 Department of Physics, Fu Jen Catholic University, Taipei Justus-Liebig-Universit¨at Gießen, Gießen The Graduate University for Advanced Studies, Hayama Gyeongsang National University, Chinju Hanyang University, Seoul University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba Hiroshima Institute of Technology, Hiroshima University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Institute of High Energy Physics,Chinese Academy of Sciences, Beijing Institute of High Energy Physics, Vienna Institute of High Energy Physics, Protvino Institute for Theoretical and Experimental Physics, Moscow J. Stefan Institute, Ljubljana Kanagawa University, Yokohama Korea University, Seoul Kyoto University, Kyoto Kyungpook National University, Taegu Ecole Polyt´ecnique F´ed´erale Lausanne, EPFL, Lausanne University of Ljubljana, Ljubljana University of Maribor, Maribor University of Melbourne, School of Physics, Victoria 3010 Nagoya University, Nagoya Nara Women’s University, Nara National Central University, Chung-li National United University, Miao Li Department of Physics, National Taiwan University, Taipei H. Niewodniczanski Institute of Nuclear Physics, Krakow Nippon Dental University, Niigata Niigata University, Niigata University of Nova Gorica, Nova Gorica Osaka City University, Osaka Osaka University, Osaka Panjab University, Chandigarh Peking University, Beijing University of Pittsburgh, Pittsburgh, Pennsylvania 15260 Princeton University, Princeton, New Jersey 08544 RIKEN BNL Research Center, Upton, New York 11973 Saga University, Saga University of Science and Technology of China, Hefei Seoul National University, Seoul Shinshu University, Nagano Sungkyunkwan University, Suwon University of Sydney, Sydney, New South Wales Tata Institute of Fundamental Research, Mumbai Toho University, Funabashi Tohoku Gakuin University, Tagajo Tohoku University, Sendai Department of Physics, University of Tokyo, Tokyo Tokyo Institute of Technology, Tokyo Tokyo Metropolitan University, Tokyo Tokyo University of Agriculture and Technology, Tokyo Toyama National College of Maritime Technology, Toyama Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul
Abstract
We have measured branching fractions of hadronic τ decays involving an η meson using 485fb − of data collected with the Belle detector at the KEKB asymmetric-energy e + e − collider.We obtain the following branching fractions: B ( τ − → K − ην τ ) = (1 . ± . ± . × − , B ( τ − → K − π ην τ ) = (4 . ± . ± . × − , B ( τ − → π − π ην τ ) = (1 . ± . ± . × − ,and B ( τ − → K ∗− ην τ ) = (1 . ± . ± . × − improving the accuracy compared to the bestprevious measurements by factors of six, eight, four and four, respectively. PACS numbers: NTRODUCTION
Hadronic decays of τ lepton provide a useful tool for studying QCD phenomena at lowenergy. Various decay modes including η meson(s) are interesting for testing the Wess-Zumino-Witten (WZW) anomaly [1, 2], chiral theory [3, 4], and relations to e + e − crosssections following from the conservation of the vector current (CVC) [5].We measure the branching fractions of τ − → K − ην τ (unless specified otherwise, chargeconjugate decays are implied throughout the paper), K − π ην τ , and π − π ην τ decays, andthat of τ − → K ∗ − (892) ην τ ; the latter is evaluated from the corresponding K − π ην τ mea-surement. Studies of these modes have been reported by CLEO [6, 7, 8] and ALEPH [9],however, most of the results are based on rather low statistics, which do not allow one todiscriminate between different theoretical predictions. We use a data sample with an inte-grated luminosity of 485 fb − , corresponding to production of 430 million τ -pairs collectedwith the Belle detector at the KEKB asymmetric-energy e + e − collider [10].The 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) 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 identify muons(KLM). The detector is described in detail elsewhere [11]. Two inner detector configurationswere used. A 2.0 cm radius beampipe and a 3-layer silicon vertex detector were used forthe first sample of 144 fb − , while a 1.5 cm radius beampipe, a 4-layer silicon detector anda small-cell inner drift chamber were used to record the remaining 341 fb − [12].In this analysis, we use a data sample 100 times larger than any of the previous mea-surements. In addition, peaking backgrounds are estimated precisely to decrease systematicuncertainties.A study of resonance formation in the hadronic final states is in progress and will bereported later. EVENT SELECTION
Candidate e + e − → τ + τ − events are selected with the following common properties: e + e − → τ +tag τ − sig τ − sig → Xην τ and τ +tag → ( e/µ ) + ν l ¯ ν τ ,where X denotes K − , K − π , or π − π . Candidate η mesons are reconstructed through twodecay modes: γγ with a branching fraction of 39 . ± .
24% or π + π − π with a branchingfraction of 22 . ± .
35% with π → γγ . In order to remove qq contamination, the tag-side τ is required to decay leptonically i.e. τ − → ℓ − ν τ ¯ ν l ( ℓ = e/µ ) (with a branching fraction of35 . ± . τ − → K − ην τ selectionA candidate event is required to contain either two charged tracks with zero net chargeand at least two γ ’s in the η → γγ case, or four charged tracks with zero net charge and atleast two γ ’s in the η → π + π − π ( π → γγ ) case. A charged track should have transverse4 IG. 1: M γγ distributions for K − ην τ selection in (a) η → γγ and (b) η → π − π + π decays. Dataare fit with a Crystal Ball function plus a second-order polynomial for the background (BG). Thebest fit result is indicated by the solid curve with the BG shown by the dashed curve. momentum, p t > . − . < cos θ < .
956 ( θ is the polar angle within thedetector aperture) where p t and θ are measured relative to the direction opposite to that ofthe incident e + beam in the laboratory frame, and the γ should have energy E γ > .
05 GeVwithin the same polar angle fiducial region as above.To select a sample of τ -pairs, the thrust vector and total energy in the center-of-masssystem are required to satisfy | V thrust | > . . < E CMtotal < . qq contamination the effective mass of the particles on the tag sideshould satisfy the requirements, M tag < m τ (1.78 GeV/c ), while on the signal side themass, M sig , should satisfy 0 .
70 GeV / c < M sig < m τ .To reconstruct an η from 2 γ ’s, two γ ’s with E γ > . − . < cos θ < . γ with 0 . < E γ < . γ from a π decay (denoted hereafter as γ π ), the η -candidate γ ( γ η ) should not forma π mass with any other γ ( π veto selection). In this analysis the π mass window isdefined as 0.105 GeV/ c < M γγ < c (a ± σ range in the detector resolution).Particle identification (PID) uses a likelihood ratio, P x , for a charged particle of species x ( x = µ, e, K, or π ). P x is defined as P x = L x / Σ y L y (the sum runs over the relevant particlespecies), where L x is a likelihood based on the energy deposit and shower shape in the ECL,the momentum and dE/dX measured by the CDC, the particle range in the KLM, the lightyield in the ACC, and particle’s time-of-flight from the TOF counter [14]. For the trackon the tag side, P e > . e candidate and P µ > . µ candidate with p > . P K > .
9, butalso P e < . p > . γ ’s. The polar angle of the missing mo-mentum that must be attributed to neutrinos, should satisfy − . < cos θ ( P miss ) < . K − and η satisfies the requirement, cos θ ( P CM K ; P CM η ) > . γ η ’s should satisfy the following condition: 0 . < cos θ ( P CM γ ; P CM γ ) < .
96 and ( E CM γ − E CM γ ) / ( E CM γ + E CM γ ) < .
8, respectively.The γγ mass distribution obtained after these requirements is shown in Fig. 1 (a).5 IG. 2: Distribution of likelihood ratios for (a) K − π ην τ and (b) π − π ην τ candidates. The pointswith error bars are the data. The yellow, green hatched, and blue histograms indicate the signal, τ τ background, and qq background MC distributions, respectively. The MC histograms are normalizedto the integrated luminosity of the data. For demonstration purposes, the branching fractions ofsignal MC decays are set to 10 − and 10 − for (a) and (b), respectively. The dashed vertical lineshow the likelihood ratio requirement. In the case of η → π + π − π reconstruction, candidate events should have two additionalcharged tracks compared to the η → γγ sample, but two of the γ ’s have to form a π insteadof an η . While this mode provides one more constraint compared to those in the previous caseimproving the background rejection, the higher multiplicity reduces the detection efficiency.The selection criteria different from those in the previous case are indicated below. π + and π − candidates are required to have 0 . /c < p < . /c and to be inconsistentwith the e hypothesis ( P e < .
2) to reject the two-photon background. The photons used toform π -candidates are required to have E γ > . ω meson, the condition M π + π − π < . c is imposed. The condition on the polar angle of the missing momentum is the same as inthe previous case while the π momentum should be P CM π > . c .The resulting π + π − π mass distribution is shown in Fig.1 (b).Selection of τ − → K − π ην τ and π − π ην τ For these τ decay modes, we use only η → γγ to reconstruct the η , because of the smalldetection efficiency for η → π + π − π . Correspondingly, a candidate event should containtwo charged tracks and at least four γ ’s.The selection criteria different from those for K − ην τ are listed below. The total momen-tum on the signal side is required to satisfy P P CMsig > . c ; two additional γ ’s arerequired to lie in the barrel region on the signal side that form the π mass; a condition oncosine of the opening angle between the missing momentum and the direction of the thrustaxis pointing to the signal side is imposed: cos θ ( P CMmiss ; P CMthrust ) < − .
6. For the π − π ην τ mode, π − candidates should have P K < . P e < . | V thrust | , P CM η , M (missing mass squared), P CM π , E CM γ η , P P CMsig , andcos θ ( P CM K/π ; P CM η ). The τ τ background MC is used for the background likelihood while thedistributions from K − π ην and π − π ην MC are used for the signal likelihood in each case.6
IG. 3: M γγ distributions for (a) K − π ην τ and (b) π − π ην τ candidates. Data are fit with aCrystal Ball function plus a second-order polynomial for the background (BG). The result of thebest fit is indicated by the solid curve with the BG shown by the dashed curve. The resulting likelihood ratios defined for K − π ην τ and π − π ην τ are shown in Figs.2 (a)and (b), respectively. About half of the background is removed while 93% and 90% of thesignal is retained for each of the respective modes.The obtained M γγ distributions are shown in Figs. 3 (a) and (b) for the K − π ην τ and π − π ην τ modes, respectively. BRANCHING FRACTIONS FOR K − ην τ , K − π ην τ AND π − π ην τ DECAYS
To determine the signal yields we determine the number of η ’s and then subtract cross-feeds. In order to extract the number of η ’s from the resulting M γγ distributions, Figs. 1and 3, we use the Crystal Ball function [15] to represent the η signal and a second-orderpolynomial for the background distribution. The result of the fits is indicated by the solidcurve in the corresponding figures. The best fits give an η mass, m η , of 0 . ± .
001 GeV/ c ,in good agreement with the PDG value of 0 . ± . c , and a resolution σ m η = 0 . ± .
002 GeV/ c for the three different decay modes in the η → γγ case and m η = 0 . ± . c with σ m η = 0 . ± . for the K − ην τ mode inthe η → π + π − π case.The η yields obtained from the fits are N K − ην τ = 1387 ± N K − π ην τ = 270 ±
33, and N π − π ην τ = 5959 ±
105 events for the K − ην τ , K − π ην τ , and π − π ην τ modes, respectively,in the η → γγ case. The yield for the η → π + π − π case is N K − ην τ ; η → π = 241 ±
21 events.The η signal region is defined as 0 .
48 GeV /c < M γγ < .
58 GeV /c in the η → γγ case while it is 0 .
52 GeV /c < M π + π − π < .
58 GeV /c in the η → π + π − π case.The detection efficiencies are estimated with MC simulation in the same manner as thedetection of η yields. The corresponding efficiencies are ε = 0 .
94 %, 0 .
35 %, 0 .
47 %, and0 .
16 %, respectively, and include the intermediate branching fractions such as B ( η → γγ ), B ( η → π + π − π ), and B ( τ − → l − ν τ ¯ ν l ).These event yields include backgrounds classified into three categories. One is due tocross-feed effects between the three signal modes, which is taken into account by solving thefollowing system of equations: N K − ην τ = 2 N ττ ( B ( K − ην τ ) · ǫ + B ( K − π ην τ ) · ǫ + B ( π − π ην τ ) · ǫ ) , (1)7 ABLE I: Raw η yields for the four selected τ decay modes. N η is the total number of η eventsdetected, which include cross-feed from two other modes. The contributions of qq and ‘other’,mostly π − π π ην τ and π − π + π − ην τ , are also included.Mode N η Kην τ Kπ ην τ ππ ην τ Other q ¯ qK − ην τ ( η → γγ ) 1387 ± − . ± . . ± . . ± . . ± . K − π ην τ ±
33 16 . ± . − . ± . . ± . . ± . π − π ην τ ±
105 2 . ± . . ± . − . ±
20 212 ± K − ην τ ( η → π + π − π ) 241 ± − . ± . . ± . < .
18 9 . ± . N K − π ην τ = 2 N ττ ( B ( K − ην τ ) · ǫ + B ( K − π ην τ ) · ǫ + B ( π − π ην τ ) · ǫ ) , (2) N π − π ην τ = 2 N ττ ( B ( K − ην τ ) · ǫ + B ( K − π ην τ ) · ǫ + B ( π − π ην τ ) · ǫ ) , (3)where B ( K − ην τ ), B ( K − π ην τ ), and B ( π − π ην τ ) are the branching fractions of the respectivemodes and N ττ is the total number of τ pairs produced. Here ε ij is the detection efficiencyin each case and j ( i ) indicates the decay sample (selection criteria).The second type of background is from decay modes of the τ -lepton itself, such as π − π π ην τ and π − π + π − ην τ . These backgrounds are estimated by using a τ τ MC simu-lation with branching fractions taken from [16]. The estimated background is included inthe ‘other’ category in Table I. The contribution of this type of background is negligiblefor the K − ην τ and K − π ην τ modes, and is smaller than the statistical uncertainty in the η yield obtained above for the π − π ην τ mode. The contamination from π − ην τ decay shouldalso be considered. This decay is strongly suppressed since it violates G -parity and proceedsvia a second-class current. Its branching fraction is predicted to be 10 − . Therefore, itscontribution to each mode is negligible.The last background category is e + e − → q ¯ q , which is estimated from MC simulation. TheMC was tuned beforehand and validated with a q ¯ q enriched sample, which was produced withsome variations of the event selection criteria. The M sig cut is removed and the condition M tag > m τ is implemented on the tag side. In addition, the PID requirement for the chargedtrack on the tag side was reversed (i.e. P e < . P µ < . η yield of MC was thentuned to be consistent with that of data. The q ¯ q contributions are 2-4 % of the η yields forthe K − ην τ and π − π ην τ modes and 10% for the K − π ην τ . They also are summarized inTable I.After subtracting the ‘other’ and qq contributions from the individual η yields, we solvethe system of equations to obtain the branching fractions for three decay modes. They are(1 . ± . × − , (4 . ± . × − , and (1 . ± . × − for K − ην τ , K − π ην τ ,and π − π ην τ , respectively. The cross-feed yields obtained are also listed in Table I. Thenumber of cross-feed events for K − ην τ in the η → π + π − π case is evaluated using the abovebranching fractions, obtained in the η → γγ case. The branching fraction for K − ην τ in thiscase is (1 . ± . × − .The systematic uncertainties are estimated as follows: the estimation of peaking back-grounds provides sizable uncertainties only in case of the π − π ην τ (3.3 %) and qq (6.0 %)contributions to the K − π ην τ mode. As for the q ¯ q estimation, due to the finite statistics of q ¯ q enriched sample, the uncertainties of 26 %, 19 %, and 9.6 % for K − ην τ , K − π ην τ , and8 ABLE II: Summary of systematic uncertainties in each mode (%)Mode K − ην τ K − π ην τ π − π ην τ K − ην τ K ∗− ην τ η detection η → γγ η → γγ η → γγ η → π + π − π η → γγ Estimation of K − ην τ − . × − − − Estimation of K − π ην τ − . × − − Estimation of π − π ην τ . × − − − Estimation of π − π π ην τ − − − − Estimation of q ¯ q K/π ) 3.3 2.2 1.0 2.8 2.2Particle ID (Lepton) 2.3 2.8 2.6 2.6 2.6Track finding 1.3 1.3 1.3 3.3 1.3Luminosity measurement 1.6 1.6 1.6 1.6 1.6 π detection − π veto 2.8 2.8 2.8 − B ( η → π + π − π ) − − − − Total 5.6 8.9 5.0 6.3 6.0 π − π ην τ decays arise from tuning, respectively. The errors in the q ¯ q background estimationsin Table I come from this uncertainty and the statistical uncertainty in the q ¯ q MC, and aretreated as systematic uncertainties. The uncertainties in the peaking backgrounds in allother cases are rather small. Uncertainties in the PID efficiency and fake rate are evaluatedto be 2-3 % for kaon ID, 1 % for π ID and around 2.5 % for the lepton ID; these valuesare obtained by averaging the estimated uncertainties depending on momentum and polarangle of each charged track. For the π veto selection, the efficiency was compared betweendata and MC with a sample in which the PID of the charged track on the tag side wasreversed from the usual π − π ην τ selection. The efficiencies were consistent. Therefore, 2.8% of the statistical uncertainty from this comparison was counted as systematic uncertainty.Other systematic uncertainties are summarized in Table II. The total systematic uncertain-ties are 5.6 %, 8.9 %, 5.0 %, and 6.3 % for the K − ην τ ( η → γγ ), K − π ην τ , π − π ην τ , and K − ην τ ( η → π + π − π ) modes, respectively.Taking the systematic uncertainties into account we obtain the following branching frac-tions: B ( τ − → K − ην τ ) = (1 . ± . ± . × − for η → γγ, = (1 . ± . ± . × − for η → π + π − π , B ( τ − → K − π ην τ ) = (4 . ± . ± . × − , B ( τ − → π − π ην τ ) = (1 . ± . ± . × − . By combining two measurements for τ − → K − ην τ decay, we obtain: B ( τ − → K − ην τ ) = (1 . ± . ± . × − . IG. 4: The K − π invariant mass distribution for the K − π ην τ events. Data are fitted witha Breit-Wigner (BW) function in (a), and the best fit is indicated by the solid curve while thecontinuum component evaluated from sideband regions is shown by the dashed curve. The fitgives N K ∗− ην τ = 119 ±
19 events with χ / (d.o.f. = 27) = 1 .
15 (the probability to obtain thisresult is 0.265). (b) and (c) show the results of similar fit with a phase space distribution onlyand a BW plus a phase space distribution. In these cases the results are N K ∗− ην τ = 102 ± χ / (d.o.f. = 27) = 2 .
09 (the probability is 0.0008) for the phase-space distribution, or N K ∗− ην τ = 105 ±
20 and N K − π ην τ = 33 ±
30 events with χ / (d.o.f. = 26) = 1 .
13 (the probabilityis 0.294).
BRANCHING FRACTION FOR K ∗− (892) ην τ From the K − π ην τ samples within the η mass region,0 .
50 GeV /c < M γγ < .
58 GeV /c , we extract a branching fraction for τ − → K ∗− (892) ην τ decay through the K ∗− (892) → K − π mode ( B ( K ∗− (892) → K − π ) = 1 / K − π invariant mass, M K − π , for the selected samples is shown inFig. 4. The τ − → π − π ην τ background, which cannot be neglected as shown in TableI, is estimated by using MC simulation with the branching fraction measured in this pa-per. The other backgrounds are estimated from two sidebands of the M γγ distribution:0 .
43 GeV /c < M γγ < .
48 GeV /c and 0 .
60 GeV /c < M γγ < .
65 GeV /c . Thebackground distribution is indicated by the dashed curve. The peculiar shape of the ex-pected background is due to two components contributing to it: that of π − π ην τ at highmass and the one from all other τ decays at low mass. A clear excess above the backgroundis seen around 0.9 GeV/c , suggesting K ∗− (892) resonance formation. Three types of signal10 ABLE III: Comparison of our measurement with previous resultsMode B in this analysis Previous B Reference τ − → K − ην τ (1 . ± . ± . × − (2 . ± . ± . × − CLEO [7](2 . ± . ± . × − ALEPH [9] τ − → K − π ην τ (4 . ± . ± . × − (17 . ± . ± . × − CLEO [8] τ − → π − π ην τ (1 . ± . ± . × − (1 . ± . ± . × − CLEO [6](1 . ± . ± . × − ALEPH [9] τ − → K ∗− ην τ (1 . ± . ± . × − (2 . ± . ± . × − CLEO [8] functions have been tested. A Breit-Wigner (BW) function whose mass and width are setto those of the K ∗− (892) is fitted to data in Fig. 4 (a). A fit with the hypothesis that theexcess signal events are due to a non-resonant, but V − A pure phase space process is shownin Fig. 4 (b). Figure 4 (c) shows the result of a fit with a BW plus a phase space functionas a signal. In each case, the signal function is smeared to take into account the detectorresolution. The BW function describes the data well in Fig. 4 (a) and the resulting numberof K ∗− (892) events is N K ∗− ην τ = 119 ±
19. In contrast, the fit shown in Fig. 4 (b) is incomplete disagreement with the data. Although inclusion of a small phase space componentin addition to the dominant K ∗− resonance component also represents data well as shownin Fig. 4 (c), the resulting magnitude of the phase space component is consistent with zerowithin errors. Therefore, we conclude that all excess events are produced via the K ∗− (892)resonance.The detection efficiency is evaluated by MC simulation to be ε = 0 . B ( K ∗− (892) → K − π ), B ( η → γγ ), and B ( τ → ℓν τ ν ).Since the requirement of K ∗− (892) formation in this case is a rather strong constraint,no significant peaking background contribution from other τ decays is found. Therefore, thesystematic uncertainty in the K ∗− (892) ην τ mode is small as compared with the K − π ην τ analysis. Other sources of systematic uncertainties are the same as those of K − π ην τ , exceptfor the background contamination; a total systematic uncertainty of 6.0 % is obtained withdetails summarized in Table II. Finally, we obtain the following branching fraction: B ( τ − → K ∗− ην τ ) = (1 . ± . ± . × − . (4) RESULTS AND DISCUSSION
We have obtained branching fractions for four different decay modes based on a high-statistics data sample of 430 million τ -pairs collected with the Belle detector: B ( τ − → K − ην τ ) = (1 . ± . ± . × − , B ( τ − → K − π ην τ ) = (4 . ± . ± . × − , B ( τ − → π − π ην τ ) = (1 . ± . ± . × − , B ( τ − → K ∗− ην τ ) = (1 . ± . ± . × − , where the first error is statistical and the second is systematic.11 IG. 5: The invariant mass distributions of various combinations of final state particles for τ − → π − π ην τ decay. The points with error bars are the data. The yellow, green hatched, and bluehistograms indicate the signal, τ τ background, and qq background MC distributions, respectively.The dominant backgrounds come from τ τ events. The qq background is strongly suppressed andnegligible in our sample. Compared to previous experiments, we have improved not only the statistical uncertain-ties, but also evaluated reliably the background contamination. In Table III our results arecompared to those previously obtained by the CLEO [6, 7, 8] and ALEPH [9] collabora-tions. Our measurement improves the uncertainties in the branching fractions by a factorof six ( K − ην τ ), eight ( K − π ην τ ), four ( π − π ην τ ), and four ( K ∗− ην τ ) compared to the mostprecise determinations from CLEO. In addition, the high statistics of our experiment allowsmuch more reliable estimation of various backgrounds including the peaking one. The rela-tively poor statistics of previous measurements imposed some limitations on BG estimations[17]. It is also noteworthy that in all cases the central value of our measurement is lowerthan that of the other measurements. This may be due to the underestimation of back-grounds in the previous experiments. The improved accuracy in the branching fractions ofthe decay modes reported here is important for future searches for the second-class current τ − → π − ην τ decay.Our branching fraction for τ − → π − π ην τ decay is consistent with the prediction basedon CVC and experimentally measured e + e − → π + π − η cross sections [5]. In addition, theMonte Carlo code TAUOLA reproduces the observed hadronic mass distributions ratherwell as shown in Fig. 5 while more tuning is needed for τ ’s decay modes involving kaon(s).The values of the branching fractions obtained for τ − → K − ην τ and τ − → K − π ην τ decays12iffer slightly from the predictions by Li [4].Further studies of final state dynamics and resonance formation in the τ − → K − π ην τ and π − π ην τ decays, which may be important for understanding the WZW anomaly are inprogress. [1] J. Wess and B. Zumino, Phys. Lett. B (1971) 95.[2] E. Witten, Nucl. Phys. B (1983) 422.[3] A. Pich, Phys. Lett. B (1987) 561.[4] B. A. Li, Phys. Rev. D (1997) 1436.[5] S. Eidelman and V. Ivanchenko, Phys. Lett. B (1991) 437.[6] CLEO Collaboration, M. Artuso et al., Phys. Rev. Lett. (1992) 3278.[7] CLEO Collaboration, J. Bartelt et al., Phys. Rev. Lett. (1996) 4119.[8] CLEO Collaboration, M. Bishai et al., Phys. Rev. Lett. (1999) 281.[9] ALEPH Collaboration, D. Buskulic et al., Z. Phys. C (1997) 263.[10] S. Kurokawa and E. Kikutani, Nucl. Instr. and. Meth. A (2003) 1,and other papers included in this volume.[11] Belle Collaboration, A. Abashian et al., Nucl. Instr. and Meth. A (2002) 117.[12] Z. Natkaniec et al. (Belle SVD2 Group), Nucl. Instr. and Meth. A (2006) 1.[13] W.-M. Yao et al., J. Phys. G (2006) 1, and 2007 partial update for edition 2008.[14] K. Hanagaki et al., Nucl. Instr. and Meth. A (2002) 490;A. Abashian et al., Nucl. Instr. and Meth. A (2002) 69;E. Nakano et al., Nucl. Instr. and Meth. A (2002) 402.[15] J.E. Gaiser, Ph.D. thesis, SLAC-R-255 (1982).[16] CLEO Collaboration, A. Anastassov et al., Phys. Rev. Lett. (2001) 4467.[17] For instance, for the K − π ην τ measurement the cross-feed from π − π ην τ decay was notconsidered, although it gives the largest contribution as seen in Table I.decay was notconsidered, although it gives the largest contribution as seen in Table I.