Observation of D + → K + η (′) and Search for CP Violation in D + → π + η (′) Decays
aa r X i v : . [ h e p - e x ] N ov Observation of D + → K + η ( ′ ) and Search for CP Violation in D + → π + η ( ′ ) Decays
E. Won, B. R. Ko, I. Adachi, H. Aihara, K. Arinstein, D. M. Asner, T. Aushev, A. M. Bakich, E. Barberio, A. Bay, V. Bhardwaj, B. Bhuyan, M. Bischofberger, A. Bondar, A. Bozek, M. Braˇcko,
J. Brodzicka, T. E. Browder, P. Chang, A. Chen, P. Chen, B. G. Cheon, K. Chilikin, I.-S. Cho, K. Cho, S.-K. Choi, Y. Choi, J. Dalseno,
26, 47
M. Danilov, Z. Doleˇzal, Z. Dr´asal, A. Drutskoy, S. Eidelman, J. E. Fast, V. Gaur, N. Gabyshev, A. Garmash, Y. M. Goh, B. Golob,
24, 17
J. Haba, T. Hara, K. Hayasaka, H. Hayashii, Y. Horii, Y. Hoshi, W.-S. Hou, Y. B. Hsiung, H. J. Hyun, T. Iijima, K. Inami, A. Ishikawa, R. Itoh, M. Iwabuchi, Y. Iwasaki, T. Iwashita, N. J. Joshi, T. Julius, J. H. Kang, N. Katayama, T. Kawasaki, H. Kichimi, H. J. Kim, H. O. Kim, J. B. Kim, J. H. Kim, K. T. Kim, M. J. Kim, S. K. Kim, Y. J. Kim, K. Kinoshita, N. Kobayashi,
S. Koblitz, P. Kodyˇs, S. Korpar,
P. Kriˇzan,
24, 17
T. Kumita, A. Kuzmin, Y.-J. Kwon, J. S. Lange, M. J. Lee, S.-H. Lee, J. Li, Y. Li, J. Libby, C.-L. Lim, C. Liu, Y. Liu, D. Liventsev, R. Louvot, S. McOnie, K. Miyabayashi, H. Miyata, Y. Miyazaki, R. Mizuk, G. B. Mohanty, Y. Nagasaka, E. Nakano, M. Nakao, H. Nakazawa, Z. Natkaniec, S. Neubauer, S. Nishida, K. Nishimura, O. Nitoh, S. Ogawa, T. Ohshima, S. Okuno, S. L. Olsen,
43, 8
Y. Onuki, P. Pakhlov, G. Pakhlova, H. Park, H. K. Park, K. S. Park, R. Pestotnik, M. Petriˇc, L. E. Piilonen, M. R¨ohrken, S. Ryu, H. Sahoo, K. Sakai, Y. Sakai, T. Sanuki, O. Schneider, C. Schwanda, A. J. Schwartz, K. Senyo, O. Seon, M. E. Sevior, C. P. Shen, T.-A. Shibata,
40, 52
J.-G. Shiu, F. Simon,
26, 47
J. B. Singh, P. Smerkol, Y.-S. Sohn, A. Sokolov, E. Solovieva, S. Staniˇc, M. Stariˇc, M. Sumihama,
40, 5
T. Sumiyoshi, S. Suzuki, G. Tatishvili, Y. Teramoto, K. Trabelsi, M. Uchida,
40, 52
S. Uehara, T. Uglov, Y. Unno, S. Uno, Y. Usov, S. E. Vahsen, G. Varner, A. Vinokurova, C. H. Wang, M.-Z. Wang, P. Wang, M. Watanabe, Y. Watanabe, K. M. Williams, B. D. Yabsley, Y. Yamashita, M. Yamauchi, Z. P. Zhang, V. Zhilich, V. Zhulanov, A. Zupanc, and O. Zyukova (The Belle Collaboration) Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630090 Faculty of Mathematics and Physics, Charles University, Prague University of Cincinnati, Cincinnati, Ohio 45221 Justus-Liebig-Universit¨at Gießen, Gießen Gifu University, Gifu 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 Indian Institute of Technology Guwahati, Guwahati Indian Institute of Technology Madras, Madras 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 Institut f¨ur Experimentelle Kernphysik, Karlsruher Institut f¨ur Technologie, Karlsruhe Korea Institute of Science and Technology Information, Daejeon Korea University, Seoul Kyungpook National University, Taegu ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana University of Maribor, Maribor Max-Planck-Institut f¨ur Physik, M¨unchen 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 Pacific Northwest National Laboratory, Richland, Washington 99352 Panjab University, Chandigarh Research Center for Nuclear Physics, Osaka Saga University, Saga University of Science and Technology of China, Hefei Seoul National University, Seoul Sungkyunkwan University, Suwon School of Physics, University of Sydney, NSW 2006 Tata Institute of Fundamental Research, Mumbai Excellence Cluster Universe, Technische Universit¨at M¨unchen, Garching 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 CNP, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul
We report the first observation of the doubly Cabibbo-suppressed decays D + → K + η ( ′ ) using a791 fb − data sample collected with the Belle detector at the KEKB asymmetric-energy e + e − col-lider. The ratio of the branching fractions of doubly Cabibbo-suppressed relative to singly Cabibbo-suppressed D + → π + η ( ′ ) decays are B ( D + → K + η )/ B ( D + → π + η ) = (3.06 ± ± B ( D + → K + η ′ )/ B ( D + → π + η ′ ) = (3.77 ± ± D + decays, δ TA , is (72 ± ◦ or (288 ± ◦ . We also report the most precise measurements of CP asymmetries to date: A D + → π + ηCP = (+1.74 ± ± A D + → π + η ′ CP = ( − ± ± PACS numbers: 11.30.Hv, 11.30.Er, 13.25.Ft, 14.40.Lb
Decays of charmed mesons play an important rolein understanding the sources of SU(3) flavor symme-try breaking structure [1, 2] and can also be sensi-tive probes of the violation of the combined charge-conjugation and parity symmetries ( CP ) produced bythe irreducible complex phase in the Cabibbo-Kobayashi-Maskawa flavor-mixing matrix [3] in the standard model(SM). This SU(3) flavor symmetry structure is not wellstudied in D + meson decays into two-body final stateswith an η ( ′ ) , since they are all Cabibbo-suppressed de-cays. Examples of two-body decays with an η ( ′ ) in thefinal state are the doubly Cabibbo-suppressed (DCS) de-cays D + → K + η ( ′ ) and the singly Cabibbo-suppressed(SCS) decays D + → π + η ( ′ ) . The DCS decays D + → K + η ( ′ ) have not yet been observed. The observation ofsuch modes is not only intrinsically important to illu-minate the meson decay process but also there is gen-eral interest in the experimental technique of measuringan extremely rare decay processes with neutral particles.Observation of D + → K + η ( ′ ) would complete the picture of DCS decays for D + mesons decaying to pairs of lightpseudoscalar mesons.In this Letter, we report the first observation of D + → K + η ( ′ ) decays. The DCS decays D + → K + η ( ′ ) togetherwith D + → K + π can be used to measure the relativephase difference between the tree and annihilation am-plitudes ( δ T A ), which is an important piece of informa-tion relevant to final-state interactions in D meson de-cays. Note that experimentally one is able to determineonly the tree and annihilation amplitudes and the relativephase difference between them since all decays involving K will be overwhelmed by Cabibbo-favored decays in-volving a ¯ K , with no way to distinguish between thembecause one detects only a K S [4]. In addition, the mostsensitive search for CP violation in D + → π + η ( ′ ) decaysis reported. Observation of CP violation in D + → π + η ( ′ ) decays with current experimental sensitivity would rep-resent strong evidence for processes involving physics be-yond the SM [5].The data used in this analysis were recorded at or nearthe Υ(4 S ) resonance with the Belle detector [6] at the e + e − asymmetric-energy collider KEKB [7]. The samplecorresponds to an integrated luminosity of 791 fb − .We apply the same charged track selection criteriathat were used in Ref. [8]. Charged kaons and pionsare identified by requiring the ratio of particle identifi-cation (PID) likelihoods [8] to be greater or less than0.6, respectively. For kaons (pions) used in this analy-sis, the efficiencies and misidentification probabilities areapproximately 87% (88%) and 9% (10%), respectively.For the reconstruction of the η meson in the D + → h + η decay, where h + refers to either π + or K + , we use the η → π + π − π mode instead of the frequently used η → γγ ( η γγ ) mode since our event selection will include stringentrequirements on the vertex formed from charged tracks inthe η decay. We find that the η → γγ mode has a smallsignal to background ratio and poor η invariant mass res-olution that prohibit the final signal extraction from ourdata. To reconstruct the η ′ meson in D + → h + η ′ decay,we use the η ′ → π + π − η γγ decay. The minimum energy ofthe γ from the π or η is chosen to be 60 MeV for the bar-rel and 100 MeV for the forward region of the calorime-ter [9]. The decay vertex of the D + is formed by fittingthe three charged tracks ( h + π + π − ) to a common ver-tex and requiring a confidence level (C.L.) greater than0.1%. For π reconstruction in D + → h + η , we requirethe invariant mass of the γγ pair to be within [0.12,0.15]GeV/ c and for the η we require the invariant mass ofthe π + π − π system to be within [0.538,0.558] GeV/ c .In the D + → h + η ′ mode, to reconstruct the daughter η γγ , we require the invariant mass of the γγ pair to bewithin [0.50,0.58] GeV/ c . Furthermore, in order to re-move a significant π contribution under the η γγ signalpeak, we reject γ candidates as described in Ref. [10].The π + π − η γγ invariant mass is required to be within therange [0.945,0.970] GeV/ c . The momenta of photonsfrom the π and the η γγ combination are recalculatedwith π and η mass [11] constraints, respectively. Theinvariant mass distributions of the h + η ( ′ ) system afterthe initial selection described above are shown in Fig. 1where there is little indication of signal for either of theDCS modes.In order to search for D + → K + η ( ′ ) decays, the follow-ing four variables are considered. The first is the angle( ξ ) between the charmed meson momentum vector, asreconstructed from the daughter particles, and the vec-tor joining its production and decay vertices [12]. Thesecond variable is the isolation χ ( χ ) normalized bythe number of degrees of freedom (d.o.f) for the hypoth-esis that the candidate tracks forming the charmed me-son arise from the primary vertex, where the primaryvertex is the most probable point of intersection of thecharmed meson momentum vector and the e + e − inter-action region [12]. Because of the finite lifetime of D + mesons their daughter tracks are not likely to be compat-ible with the primary vertex. The third and the fourth ) c ) (GeV/ η + M(h1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / x10 ) c ) (GeV/ η + M(h1.85 1.9100150200 x10 ) c ’) (GeV/ η + M(h1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / x10 ) c ’) (GeV/ η + M(h1.85 1.920304050 x10 FIG. 1: The invariant mass distributions of h + η ( h + η ′ )in the left (right) plot after the initial selection. The solidhistograms show π + η ( ′ ) while the dashed histograms show K + η ( ′ ) final states. The two inset histograms are K + η ( ′ ) de-cays with enlarged vertical scales. variables are the momentum of the η ( ′ ) ( p η ( ′ ) ) in the lab-oratory system, and the momentum of the D + in thecenter-of-mass system ( p ∗ D + ). To optimize the selection,we maximize ǫ sig / √N B where ǫ sig and N B are the signalefficiency and the background yield in the invariant massdistribution of D + candidates. A uniform grid of 10,000points in four dimensions spanned by the four kinematicvariables described above is used to select an optimal setof selection requirements using Monte Carlo (MC) sim-ulation samples [13]. Since we use MC samples, this issimilar to the importance-sampled grid search techniquein Ref. [14]. The optimal selection for the D + → K + η mode is found to be: ξ < ◦ , χ > p η > c ,and p ∗ D + > c , and for D + → K + η ′ is : ξ < ◦ , χ > p η ′ > c , and p ∗ D + > c . Thesame selection criteria are applied to the normalizationmodes, D + → π + η ( ′ ) . Figure 2 shows the π + η ( ′ ) and K + η ( ′ ) invariant mass distributions after the final selec-tions used for the branching fraction measurements. Pos-sible structures, for example from D + s → K + π − π + π or D + s → K + K − π + π due to particle misidentification orcross-feed between η and η ′ are studied using MC sam-ples; we find no indication of such background.A fit is then performed for D + → π + η ( ′ ) candidatesand the results are shown as the top two plots in Fig. 2.The signal probability density function (PDF) is mod-eled as the sum of a Gaussian and a bifurcated Gaussianwhile the combinatorial background is modeled as a lin-ear background. The χ /d.o.f of fits are 0.7 and 1.4, re-spectively. For fits to these DCS decays, we fix the widthof the Gaussian, the two widths of the bifurcated Gaus-sian, and then ratio of the normalizations of the Gaussianand the bifurcated Gaussian to the values obtained fromthe fits to the SCS modes in order to obtain stable fits.The fixed widths are scaled according to the differenceof widths observed in the signal MC samples. We ex-amine possible systematic uncertainties due to this later.The statistical significance of the signal based on the log- TABLE I: Yields from the data and the signal efficiencies forthe branching fraction measurements. Errors are statisticalonly.Mode yield Signal Efficiency (%) D + → K + η ±
23 1.35 ± D + → K + η ′ ±
19 1.20 ± D + → π + η ±
110 1.68 ± D + → π + η ′ ±
93 1.59 ± likelihood ratio is 9 σ and more than 10 σ ( σ represents onestandard deviation from the background-only hypothe-sis) for D + → K + η and D + → K + η ′ , respectively; thecorresponding invariant mass distributions and fits areshown in the lower panel of Fig. 2. The χ /d.o.f offits to the K + η and K + η ′ final states are 0.8 and 0.9,respectively. In order to compute the ratio of branch-ing fractions of DCS modes with respect to SCS modes,the signal efficiencies for the selection criteria describedabove are estimated with our signal MC samples. Table Ilists all the information used for the branching fractionmeasurements. ) c ) (GeV/ η + π M(1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / c ’) (GeV/ η + π M(1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / c ) (GeV/ η + M(K1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / c ’) (GeV/ η + M(K1.82 1.84 1.86 1.88 1.9 1.92 ) c E v en t s / ( M e V / FIG. 2: The invariant mass distributions used for the branch-ing fraction measurements. The top two plots are for the π + η (left) and π + η ′ (right) final states while the bottom two plotsare for the K + η (left) and K + η ′ (right) final states. Pointswith error bars and histograms correspond to the data andthe fit, respectively. The dominant sources of the systematic uncertainty inthe branching fraction measurements are the uncertain-ties of the parameters that are fixed in the fits to DCSdecays, and are estimated to be 3.4% (2.1%) for the η ( η ′ )mode. These uncertainties are determined by refittingthe data with the fit parameters varied by one standarddeviation. Other sources include the choice of the fitting functions, estimated to be 2.7% (1.0%) for the η ( η ′ )mode, and the uncertainty in the PID, estimated to be1.1% for the both modes. A summary of the systematicuncertainties for the ratio of branching fraction measure-ments can be found in Table II. The ratios of branchingfractions are B ( D + → K + η )/ B ( D + → π + η ) = (3.06 ± ± B ( D + → K + η ′ )/ B ( D + → π + η ′ ) =(3.77 ± ± K + η mode is in agreement with the SU(3) based expec-tations [1, 2], the K + η ′ mode is measured to be larger,by approximately three standard deviations. TABLE II: Summary of all relative systematic uncertaintiesfor the measurements of ratios of branching fractions.Source σ (cid:16) B ( D + → K + η ) B ( D + → π + η ) (cid:17) (%) σ (cid:16) B ( D + → K + η ′ ) B ( D + → π + η ′ ) (cid:17) (%)PID 1.1 1.1Signal PDF 3.4 2.1Fit method 2.7 1.0Total 4.5 2.6 Using the relations in Ref. [4], which give | T | = 3 |A ( K + η ) | | A | = 12 " |A ( K + π ) | + |A ( K + η ′ ) | − |A ( K + η ) | cos δ T A = 12 | T || A | " |A ( K + η ) | + 12 |A ( K + η ′ ) | − |A ( K + π ) | (1)where T ( A ) is the tree (annihilation) amplitude and A is the specified decay amplitude, and from the recentbranching fraction measurement of B ( D + → K + π ) =(1 . ± . × − [15], we find that the relative final-state phase difference between the tree and annihilationin D + decays, δ T A , is (72 ± ◦ or (288 ± ◦ . TABLE III: Comparison of our branching fraction results tothe present best upper limit (90% C.L.) from Ref. [15]. Thefirst and second uncertainties are statistical and systematic,respectively.Measurement Belle Ref. [15] B ( D + → K + η ) (1.08 ± ± × − < × − B ( D + → K + η ′ ) (1.76 ± ± × − < × − For our A CP measurement in the D + → π + η ( ′ ) modes,we re-optimize our selection by maximizing N S /σ S where σ S is the statistical error on the signal yield N S in thesimulated sample. The re-optimized requirements for D + → π + η decays are: ξ < ◦ , χ > p η > c ,and p ∗ D + > c , and for D + → π + η ′ are: ξ < ◦ , χ > p η ′ > c , and p ∗ D + > c , respec-tively. These requirements are slightly less stringent thanthe selection criteria used for the branching fraction mea-surements of DCS modes. This improves the statisticalsensitivity on A CP by around 15%.We determine the quantities A D + → π + η ( ′ ) CP [16] by mea-suring the asymmetry in signal yield A D + → π + η ( ′ ) rec ≡ N D + → π + η ( ′ ) rec − N D − → π − η ( ′ ) rec N D + → π + η ( ′ ) rec + N D − → π − η ( ′ ) rec ∼ = A D + → π + η ( ′ ) CP + A D + F B + A π + ǫ , (2)where N rec is the number of reconstructed decays. Notethat we neglect the terms involving the product of asym-metries and the approximation is valid for small asym-metries. The measured asymmetry in Eq. (2) includestwo contributions other than A CP . One is the forward-backward asymmetry ( A D + F B ) due to γ ∗ − Z interfer-ence in e + e − → c ¯ c and the other is the detection ef-ficiency asymmetry between positively and negativelycharged pions ( A π + ǫ ). To correct for the asymmetriesother than A CP , we use a sample of Cabibbo-favored D + s → φπ + decays, in which the expected CP asym-metry from the SM is negligible. Assuming that A F B is the same for all charmed mesons, the difference be-tween A D + → π + η ( ′ ) rec and A D + s → φπ + rec yields the CP viola-tion asymmetry A D + → π + η ( ′ ) CP . We reconstruct φ mesonsvia the K + K − decay channel, requiring the K + K − in-variant mass to be between 1.01 and 1.03 GeV/ c . Thisis the same technique as the one developed in Ref. [17].In order to obtain A CP , we subtract the measuredasymmetry for D + s → φπ + from that for D + → π + η ( ′ ) inthree-dimensional (3D) bins, where the 3D bins are thetransverse momentum, p lab T π , and the polar angle of the π + in the laboratory system, cos θ lab π , and the charmedmeson polar angle in the center-of-mass system, cos θ ∗ D +( s ) .Simultaneous fits to the D +( s ) and D − ( s ) invariant mass dis-tributions for each bin are carried out. A double Gaus-sian for the signal and a linear function for the back-ground are used as PDFs for D + s → φπ + . The averagevalue over all bins is found to be A D + s → φπ + rec = (0.17 ± A D + s → φπ + rec component,weighted averages of the A CP values summed over the3D bins are (+1.74 ± − ± D + → π + η and D + → π + η ′ , respectively, where the un-certainties originate from the finite size of the D + → π + η (1.13%), D + → π + η ′ (1.12%), and D + s → φπ + (0.13%)samples. The χ / d.o.f values summed over the 3D binsare 28.7/11=2.6 for D + → π + η and 15.7/11=1.4 for D + → π + η ′ .The dominant source of systematic uncertainty in the A CP measurement is the uncertainty in the A D + s → φπ + rec de-termination, which originates from the following sources:the statistics of the D + s → φπ + sample (0.13%), pos-sible detection asymmetry of kaons from φ → K + K − (0.05%) [18] and the choice of binning for the 3D map(0.12%, 0.01%), for D + → π + η and D + → π + η ′ , respec-tively. Another source is the fitting of the invariant massdistribution (fit interval, choice of the fitting function),which contributes uncertainties of 0.05% to A D + → π + ηCP ,and 0.07% to A D + → π + η ′ CP . Possible systematic uncertain-ties due to the fixed signal PDF parameters are estimatedto be 0.01% for A D + → π + ηCP and 0.07% for A D + → π + η ′ CP . Bycombining all sources in quadrature, we obtain A D + → π + ηCP = (+1.74 ± ± A D + → π + η ′ CP = ( − ± ± A D + → π + η ( ′ ) CP to date.In conclusion, we report the first observation of DCS D + → K + η ( ′ ) decays using a 791 fb − data sample col-lected with the Belle detector at the KEKB asymmetric-energy e + e − collider. The ratios of branching frac-tions of DCS modes with respect to the SCS modes are B ( D + → K + η )/ B ( D + → π + η ) = (3.06 ± ± B ( D + → K + η ′ )/ B ( D + → π + η ′ ) = (3.77 ± ± D → K + π from Ref. [15], the first measurement of therelative phase difference between the tree and annihila-tion amplitudes in D + decays is reported with δ T A =(72 ± ◦ or (288 ± ◦ using the technique suggested inRef. [4]; this is important information relevant to final-state interactions. We also search for CP asymmetriesin SCS modes down to the O (%) level.We thank the KEKB group for excellent operationof the accelerator, the KEK cryogenics group for effi-cient solenoid operations, and the KEK computer groupand the NII for valuable computing and SINET4 net-work support. We acknowledge support from MEXT,JSPS and Nagoya’s TLPRC (Japan); ARC and DIISR(Australia); NSFC (China); MSMT (Czechia); DST (In-dia); MEST, NRF, NSDC of KISTI, and WCU (Korea);MNiSW (Poland); MES and RFAAE (Russia); ARRS(Slovenia); SNSF (Switzerland); NSC and MOE (Tai-wan); and DOE (USA). E. Won acknowledges supportby NRF Grant No. 2011-0027652 and B. R. Ko acknowl-edges support by NRF Grant No. 2011-0025750. [1] B. 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