EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2011-011 1 February 2011
First observation of decays
The LHCb Collaboration
Using data collected with the LHCb detector in proton-proton collisions at a centre-of-mass energy of 7 TeV, the hadronic decay is observed. This CP eigenstate mode could be used to measure mixing-induced CP violation in the system. Using a fit to the mass spectrum with interfering resonances gives . In the interval 90 MeV around 980 MeV, corresponding to approximately two full widths we also find , where in both cases the uncertainties are statistical and systematic, respectively.
Keywords: LHC, Hadronic decays, meson
PACS: 14.40.Nd, 13.25.Hw, 14.40.Be
To be published in Physics Letters B
LHCb author listauthors
The LHCb Collaboration
R. Aaij, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, Y. Amhis, J. Amoraal, J. Anderson, R.B. Appleby, O. Aquines Gutierrez, L. Arrabito, M. Artuso, E. Aslanides, G. Auriemma, S. Bachmann, D.S. Bailey, V. Balagura, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, A. Bates, C. Bauer, Th. Bauer, A. Bay, I. Bediaga, K. Belous, I. Belyaev, E. Ben-Haim, M. Benayoun, G. Bencivenni, R. Bernet, M.-O. Bettler, M. van Beuzekom, S. Bifani, A. Bizzeti, P.M. Bjørnstad, T. Blake, F. Blanc, C. Blanks, J. Blouw, S. Blusk, A. Bobrov, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, E. Bos, T.J.V. Bowcock, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, S. Brisbane, M. Britsch, T. Britton, N.H. Brook, H. Brown, A. Büchler-Germann, A. Bursche, J. Buytaert, S. Cadeddu, J.M. Caicedo Carvajal, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, L. Camilleri, P. Campana, G. Capon, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, L. Carson, K. Carvalho Akiba, G. Casse, M. Cattaneo, M. Charles, Ph. Charpentier, N. Chiapolini, X. Cid Vidal, P.J. Clark, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, C. Coca, V. Coco, J. Cogan, P. Collins, F. Constantin, G. Conti, A. Contu, M. Coombes, G. Corti, G.A. Cowan, R. Currie, B. D’Almagne, C. D’Ambrosio, W. Da Silva, P. David, I. De Bonis, S. De Capua, M. De Cian, F. De Lorenzi, J.M. De Miranda, L. De Paula, P. De Simone, D. Decamp, H. Degaudenzi, M. Deissenroth, L. Del Buono, C. Deplano, O. Deschamps, F. Dettori, J. Dickens, H. Dijkstra, M. Dima, P. Diniz Batista, S. Donleavy, D. Dossett, A. Dovbnya, F. Dupertuis, R. Dzhelyadin, C. Eames, S. Easo, U. Egede, V. Egorychev, S. Eidelman, D. van Eijk, F. Eisele, S. Eisenhardt, L. Eklund, D.G. d’Enterria, D. Esperante Pereira, L. Estève, E. Fanchini, C. Färber, G. Fardell, C. Farinelli, S. Farry, V. Fave, V. Fernandez Albor, M. Ferro-Luzzi, S. Filippov, C. Fitzpatrick, F. Fontanelli, R. Forty, M. Frank, C. Frei, M. Frosini, J.L. Fungueirino Pazos, S. Furcas, A. Gallas Torreira, D. Galli, M. Gandelman, P. Gandini, Y. Gao, J-C. Garnier, J. Garofoli, L. Garrido, C. Gaspar, N. Gauvin, M. Gersabeck, T. Gershon, Ph. Ghez, V. Gibson, V.V. Gligorov, C. Göbel, D. Golubkov, A. Golutvin, A. Gomes, H. Gordon, M. Grabalosa Gándara, R. Graciani Diaz, L.A. Granado Cardoso, E. Graugés, G. Graziani, A. Grecu, S. Gregson, B. Gui, E. Gushchin, Yu. Guz, T. Gys, G. Haefeli, S.C. Haines, T. Hampson, S. Hansmann-Menzemer, R. Harji, N. Harnew, P.F. Harrison, J. He, K. Hennessy, P. Henrard, J.A. Hernando Morata, E. van Herwijnen, A. Hicheur, E. Hicks, W. Hofmann, K. Holubyev, P. Hopchev, W. Hulsbergen, P. Hunt, T. Huse, R.S. Huston, D. Hutchcroft, V. Iakovenko, C. Iglesias Escudero, P. Ilten, J. Imong, R. Jacobsson, M. Jahjah Hussein, E. Jans, F. Jansen, P. Jaton, B. Jean-Marie, F. Jing, M. John, D. Johnson, C.R. Jones, B. Jost, F. Kapusta, T.M. Karbach, J. Keaveney, U. Kerzel, T. Ketel, A. Keune, B. Khanji, Y.M. Kim, M. Knecht, S. Koblitz, A. Konoplyannikov, P. Koppenburg, A. Kozlinskiy, L. Kravchuk, G. Krocker, P. Krokovny, F. Kruse, K. Kruzelecki, M. Kucharczyk, S. Kukulak, R. Kumar, T. Kvaratskheliya, V.N. La Thi, D. Lacarrere, G. Lafferty, A. Lai, R.W. Lambert, G. Lanfranchi, C. Langenbruch, T. Latham, R. Le Gac, J. van Leerdam, J.-P. Lees, R. Lefèvre, A. Leflat, J. Lefrançois, O. Leroy, T. Lesiak, L. Li, Y.Y. Li, L. Li Gioi, M. Lieng, M. Liles, R. Lindner, C. Linn, B. Liu, G. Liu, J.H. Lopes, E. Lopez Asamar, N. Lopez-March, J. Luisier, B. M’charek, F. Machefert, I.V. Machikhiliyan, F. Maciuc, O. Maev, J. Magnin, A. Maier, S. Malde, R.M.D. Mamunur, G. Manca, G. Mancinelli, N. Mangiafave, U. Marconi, R. Märki, J. Marks, G. Martellotti, A. Martens, L. Martin, A. Martin Sanchez, D. Martinez Santos, A. Massafferri, Z. Mathe, C. Matteuzzi, M. Matveev, V. Matveev, E. Maurice, B. Maynard, A. Mazurov, G. McGregor, R. McNulty, C. Mclean, M. Meissner, M. Merk, J. Merkel, M. Merkin, R. Messi, S. Miglioranzi, D.A. Milanes, M.-N. Minard, S. Monteil, D. Moran, P. Morawski, J.V. Morris, R. Mountain, I. Mous, F. Muheim, K. Müller, R. Muresan, F. Murtas, B. Muryn, M. Musy, J. Mylroie-Smith, P. Naik, T. Nakada, R. Nandakumar, J. Nardulli, M. Nedos, M. Needham, N. Neufeld, M. Nicol, S. Nies, V. Niess, N. Nikitin, A. Oblakowska-Mucha, V. Obraztsov, S. Oggero, O. Okhrimenko, R. Oldeman, M. Orlandea, A. Ostankov, B. Pal, J. Palacios, M. Palutan, J. Panman, A. Papanestis, M. Pappagallo, C. Parkes, C.J. Parkinson, G. Passaleva, G.D. Patel, M. Patel, S.K. Paterson, G.N. Patrick, C. Patrignani, C. Pavel -Nicorescu, A. Pazos Alvarez, A. Pellegrino, G. Penso, M. Pepe Altarelli, S. Perazzini, D.L. Perego, E. Perez Trigo, A. Pérez-Calero Yzquierdo, P. Perret, A. Petrella, A. Petrolini, B. Pie Valls, B. Pietrzyk, D. Pinci, R. Plackett, S. Playfer, M. Plo Casasus, G. Polok, A. Poluektov, E. Polycarpo, D. Popov, B. Popovici, C. Potterat, A. Powell, T. du Pree, V. Pugatch, A. Puig Navarro, W. Qian, J.H. Rademacker, B. Rakotomiaramanana, I. Raniuk, G. Raven, S. Redford, W. Reece, A.C. dos Reis, S. Ricciardi, K. Rinnert, D.A. Roa Romero, P. Robbe, E. Rodrigues, F. Rodrigues, C. Rodriguez Cobo, P. Rodriguez Perez, G.J. Rogers, V. Romanovsky, J. Rouvinet, T. Ruf, H. Ruiz, G. Sabatino, J.J. Saborido Silva, N. Sagidova, P. Sail, B. Saitta, C. Salzmann, A. Sambade Varela, M. Sannino, R. Santacesaria, R. Santinelli, E. Santovetti, M. Sapunov, A. Sarti, C. Satriano, A. Satta, M. Savrie, D. Savrina, P. Schaack, M. Schiller, S. Schleich, M. Schmelling, B. Schmidt, O. Schneider, A. Schopper, M.-H. Schune, R. Schwemmer, A. Sciubba, M. Seco, A. Semennikov, K. Senderowska, N. Serra, J. Serrano, B. Shao, M. Shapkin, I. Shapoval, P. Shatalov, Y. Shcheglov, T. Shears, L. Shekhtman, O. Shevchenko, V. Shevchenko, A. Shires, E. Simioni, H.P. Skottowe, T. Skwarnicki, A.C. Smith, K. Sobczak, F.J.P. Soler, A. Solomin, P. Somogy, F. Soomro, B. Souza De Paula, B. Spaan, A. Sparkes, E. Spiridenkov, P. Spradlin, F. Stagni, O. Steinkamp, O. Stenyakin, S. Stoica, S. Stone, B. Storaci, U. Straumann, N. Styles, M. Szczekowski, P. Szczypka, T Szumlak, S. T’Jampens, V. Talanov, E. Teodorescu, H. Terrier, F. Teubert, C. Thomas, E. Thomas, J. van Tilburg, V. Tisserand, M. Tobin, S. Topp-Joergensen, M.T. Tran, A. Tsaregorodtsev, N. Tuning, A. Ukleja, P. Urquijo, U. Uwer, V. Vagnoni, G. Valenti, R. Vazquez Gomez, P. Vazquez Regueiro, S. Vecchi, J.J. Velthuis, M. Veltri, K. Vervink, B. Viaud, I. Videau, X. Vilasis-Cardona, J. Visniakov, A. Vollhardt, D. Voong, A. Vorobyev, An. Vorobyev, H. Voss, K. Wacker, S. Wandernoth, J. Wang, D.R. Ward, A.D. Webber, D. Websdale, M. Whitehead, D. Wiedner, L. Wiggers, G. Wilkinson, M.P. Williams, M. Williams, F.F. Wilson, J. Wishahi, M. Witek, W. Witzeling, S.A. Wotton, K. Wyllie, Y. Xie, F. Xing, Z. Yang, G. Ybeles Smit, R. Young, O. Yushchenko, M. Zavertyaev, L. Zhang, W.C. Zhang, Y. Zhang, A. Zhelezov, L. Zhong, E. Zverev.
Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, Brazil
Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil
Center for High Energy Physics, Tsinghua University, Beijing, China
LAPP, Université de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
Clermont Université, Université Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France
CPPM, Aix-Marseille Université, CNRS/IN2P3, Marseille, France
LAL, Université Paris-Sud, CNRS/IN2P3, Orsay, France
LPNHE, Université Pierre et Marie Curie, Université Paris Diderot, CNRS/IN2P3, Paris, France
Fakultät Physik, Technische Universität Dortmund, Dortmund, Germany
Max-Planck-Institut für Kernphysik (MPIK), Heidelberg, Germany
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
School of Physics, University College Dublin, Dublin, Ireland
Sezione INFN di Bari, Bari, Italy
Sezione INFN di Bologna, Bologna, Italy
Sezione INFN di Cagliari, Cagliari, Italy
Sezione INFN di Ferrara, Ferrara, Italy
Sezione INFN di Firenze, Firenze, Italy
Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy
Sezione INFN di Genova, Genova, Italy
Sezione INFN di Milano Bicocca, Milano, Italy
Sezione INFN di Roma Tor Vergata, Roma, Italy
Sezione INFN di Roma Sapienza, Roma, Italy
Nikhef National Institute for Subatomic Physics, Amsterdam, Netherlands
Nikhef National Institute for Subatomic Physics and Vrije Universiteit, Amsterdam, Netherlands
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland
Faculty of Physics & Applied Computer Science, Cracow, Poland
Soltan Institute for Nuclear Studies, Warsaw, Poland
Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania
Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia
Budker Institute of Nuclear Physics (BINP), Novosibirsk, Russia
Institute for High Energy Physics(IHEP), Protvino, Russia
Universitat de Barcelona, Barcelona, Spain
Universidad de Santiago de Compostela, Santiago de Compostela, Spain
European Organization for Nuclear Research (CERN), Geneva, Switzerland
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Physik-Institut, Universität Zürich, Zürich, Switzerland
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom
Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
Department of Physics, University of Warwick, Coventry, United Kingdom
STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom
School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom
Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom
Imperial College London, London, United Kingdom
School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom
Department of Physics, University of Oxford, Oxford, United Kingdom
Syracuse University, Syracuse, NY, United States of America
CC-IN2P3, CNRS/IN2P3, Lyon-Villeurbanne, France, associated member
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moskow, Russia
Università di Bari, Bari, Italy
Università di Bologna, Bologna, Italy
Università di Cagliari, Cagliari, Italy
Università di Ferrara, Ferrara, Italy
Università di Firenze, Firenze, Italy
Università di Urbino, Urbino, Italy
Università di Modena e Reggio Emilia, Modena, Italy
Università di Genova, Genova, Italy
Università di Milano Bicocca, Milano, Italy
Università di Roma Tor Vergata, Roma, Italy
Università di Roma La Sapienza, Roma, Italy
Università della Basilicata, Potenza, Italy
LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain
Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain
In decays some final states can be reached either by a direct decay amplitude or via a mixing amplitude. For the case of decays, the interference between these two amplitudes allows observation of a CP violating phase. In the Standard Model (SM) this phase is radians, where , and the are CKM matrix elements . This is about 20 times smaller in magnitude than the measured value of the corresponding phase in mixing. Being small, this phase can be drastically increased by the presence of new particles beyond the SM. Thus, measuring is an important probe of new physics.
Attempts to determine have been made by the CDF and D0 experiments at the Tevatron using the decay mode . While initial results hinted at possible large deviations from the SM, recent measurements are more consistent [3, 4]. However, the Tevatron limits are still not very constraining. Since the final state consists of two spin-1 particles, it is not a CP eigenstate. While it is well known that CP violation can be measured using angular analyses , this requires more events to gain similar sensitivities to those obtained if the decay proceeds via only CP-even or CP-odd channels. In Ref.  it is argued that in the case of the analysis is complicated by the presence of an S-wave system interfering with the that must be taken into account, and that this S-wave would also manifest itself by the appearance of decays. This decay is to a single CP-odd eigenstate and does not require an angular analysis. Its CP violating phase in the Standard Model is (up to corrections due to higher order diagrams). In what follows, we use the notation to refer to the state.
By comparing decays where the was detected in both and modes it was predicted that 
A decay rate at this level would make these events very useful for measuring if backgrounds are not too large.
The dominant decay diagram for these processes is shown in Fig. 1.
It is important to realize that the system accompanying the is an isospin singlet (isoscalar), and thus cannot produce a single meson that is anything but isospin zero. Thus, for example, in this spectator model production of a meson is forbidden. The dominant low mass isoscalar resonance decaying into is the but other higher mass objects are possible.
Although the mass is relatively well estimated at 98010 MeV (we use units with ) by the PDG, the width is poorly known. Its measurement appears to depend on the final state, and is complicated by the opening of the channel close to the pole; the PDG estimates 40100 MeV . Recently CLEO measured these properties in the semileptonic decay , where hadronic effects are greatly reduced, determining a width of MeV .
2 Data sample and analysis requirements
We use a data sample of approximately 33 pb collected with the LHCb detector in 2010 . The detector elements are placed along the beam line of the LHC starting with the Vertex Locator (VELO), a silicon strip device that surrounds the proton-proton interaction region and is positioned 8 mm from the beam during collisions. It provides precise locations for primary interaction vertices, the locations of decays of long-lived particles, and contributes to the measurement of track momenta. Other devices used to measure track momenta comprise a large area silicon strip detector (TT) located in front of a 3.7 Tm dipole magnet, and a combination of silicon strip detectors (IT) and straw drift chambers (OT) placed behind. Two Ring Imaging Cherenkov (RICH) detectors are used to identify charged hadrons. Further downstream an Electromagnetic Calorimeter (ECAL) is used for photon detection and electron identification, followed by a Hadron Calorimeter (HCAL), and a system consisting of alternating layers of iron and chambers (MWPC and triple-GEM) that distinguishes muons from hadrons (MUON). The ECAL, MUON, and HCAL provide the capability of first-level hardware triggering.
This analysis is restricted to events accepted by a trigger. Subsequent analysis selection criteria are applied that serve to reject background, yet preserve high efficiencies on both the and final states, as determined by Monte Carlo events generated using PYTHIA , and LHCb detector simulation based on GEANT4 . Tracks are reconstructed as described in Ref. . To be considered as a candidate opposite sign tracks are required to have transverse momentum, , greater than 500 MeV, be identified as muons, and form a common vertex with fit per number of degrees of freedom (ndof) less than 11. The invariant mass distribution is shown in Fig. 2 with an additional requirement, used only for this plot, that the pseudo proper-time, , be greater than 0.5 ps, where is the distance that the candidate travels downstream parallel to the beam, along , times the known mass divided by the component of the candidate’s momentum. The data are fit with a Crystal Ball signal function  to account for the radiative tail towards low mass, and a linear background function. There are 549,0001100 signal events in the entire mass range. For subsequent use only candidates within 48 MeV of the known mass are selected.
Pion and kaon candidates are selected if they are inconsistent with having been produced at the closest primary vertex. The impact parameter (IP) is the minimum distance of approach of the track with respect to the primary vertex. We require that the formed by using the hypothesis that the IP is equal to zero be for each track. For further consideration these tracks must be positively identified in the RICH system. Particles forming opposite-sign di-pion candidates must have their scalar sum MeV, while those forming opposite-sign di-kaon candidates must have their vector sum MeV, and have an invariant mass within 20 MeV of the mass.
To select candidates we further require that the two pions or kaons form a vertex with a , that they form a candidate vertex with the where the vertex fit /ndof , and that this candidate points to the primary vertex at an angle not different from its momentum direction by more than 0.68.
Simulations are used to evaluate our detection efficiencies. For the final state we use the measured decay parameters from CDF . The final state is simulated using full longitudinal polarization of the meson. The efficiencies of having all four decay tracks in the geometric acceptance and satisfying the trigger, track reconstruction and data selection requirements are (1.4710.024)% for , requiring the invariant mass be within 500 MeV of 980 MeV, and (1.4540.021)% for , having the invariant mass be within 20 MeV of the mass. The uncertainties on the efficiency estimates are statistical only.
The invariant mass distribution is shown in Fig. 3. The di-muon invariant mass has been constrained to have the known value of the mass; this is done for all subsequent invariant mass distributions. The data are fit with a Gaussian signal function and a linear background function. The fit gives a mass of 5366.70.4 MeV, a width of 7.4 MeV r.m.s., and a yield of 63526 events.
Initially, to search for a signal we restrict ourselves to an interval of 90 MeV around the mass, approximately two full widths . The candidate invariant mass distribution for selected combinations is shown in Fig. 4. The signal is fit with a Gaussian whose mean and width are allowed to float. We also include a background component due to that is taken to be Gaussian, with mass allowed to float in the fit, but whose width is constrained to be the same as the signal. Other components in the fit are , combinatorial background taken to have an exponential shape, , and other specific decay backgrounds including , , , . The shape of the sum of the combinatorial and components is taken from the like-sign events. The shapes of the other components are taken from Monte Carlo simulation with their normalizations allowed to float.
We perform a simultaneous unbinned likelihood fit to the opposite-sign and sum of and like-sign event distributions.
The fit gives a mass of 5366.11.1 MeV in good agreement with the known mass of 5366.30.6 MeV, a Gaussian width of 8.21.1 MeV, consistent with the expected mass resolution and 11114 signal events within 30 MeV of the mass. The change in twice the natural logarithm of the fit likelihood when removing the signal component, shows that the signal has an equivalent of 12.8 standard deviations of significance. The like-sign di-pion yield correctly describes the shape and level of the background below the signal peak, both in data and Monte Carlo simulations. There are also 239 events.
Having established a clear signal, we perform certain checks to ascertain if the structure peaking near 980 MeV is a spin-0 object. Since the is spinless, when it decays into a spin-1 and a spin-0 , the decay angle of the should be distributed as , where is the angle of the in the rest frame with respect to the direction. The polarization angle, , the angle of the in the rest frame with respect to the direction, should be uniformly distributed. A simulation of the detection efficiency in these decays shows that it is approximately independent of . The acceptance for as a function of the decay angle shows an inefficiency of about 50% at with respect to its value at . It is fit to a parabola and the inefficiency corrected in what follows.
The like-sign background subtracted helicity distribution is fit to a function as shown in Fig. 5(a). The fit gives consistent with a longitudinally polarized (spin perpendicular to its momentum) and a spin-0 meson. The of the fit is 10.3 for 8 degrees of freedom.
Similarly, we subtract the like-sign background and fit the efficiency corrected helicity distribution to a constant function as shown in Fig. 5(b). The fit has a /ndof equal to 15.9/9, still consistent with a uniform distribution as expected for a spinless particle.
To view the spectrum of masses, between 580 and 1480 MeV, in the final state we select events within 30 MeV of the and plot the invariant mass spectrum in Fig. 6.
The data show a strong peak near 980 MeV and an excess of events above the like-sign background extending up to 1500 MeV. Our mass spectrum is similar in shape to those seen previously in studies of the S-wave system with quarks in the initial state [13, 14, 15]. To establish a value for requires fitting the shape of the resonance. Simulation shows that our acceptance is independent of the mass, and we choose an interval between 580 and 1480 MeV. Guidance is given by the BES collaboration who fit the spectrum in decays . We include here the and resonances, though other final states may be present, for example the a state [13, 14]; it will take much larger statistics to sort out the higher mass states. We use a coupled-channel Breit-Wigner amplitude (Flatté) for the resonance  and a Breit-Wigner shape (BW) for the higher mass . Defining as the invariant mass, the mass distribution is fit with a function involving the square of the interfering amplitudes
where is a normalization constant, is the momentum of the , the momentum of the in the rest-frame, and is the relative phase between the two components. The Flatté amplitude is defined as
where refers to the mass of the and and are Lorentz invariant phase space factors equal to for . The term accounts for the opening of the kaon threshold. Here where is the momentum a kaon would have in the rest-frame. It is taken as an imaginary number when is less than twice the kaon mass. We use GeV, and as determined by BES .
The mass and width values used here are 143420 MeV, and 17233 MeV from an analysis by E791 . We fix the central values of these masses and widths in the fit, as well as and the ratio for the amplitude. The mass resolution is incorporated as a Gaussian convolution in the fit as a function of mass. It has an r.m.s. of 5.4 MeV at 980 MeV. We fit both the opposite-sign and like-sign distributions simultaneously. The results of the fit are shown in Fig. 6. The /ndof is 44/56. We find an mass value of 97225 MeV. There are 26526 events above background in the extended mass region, of which % are associated with the , % are ascribed to the and % are from interference. The fit determines . The fit fraction is defined as the integral of a single component divided by the coherent sum of all components. The yield is 169 events. The lower mass cutoff of the fit region loses 1% of the events. The change in twice the log likelihood of the fit when removing the component shows that it has an equivalent of 12.5 standard deviations of significance.
Using the 169 events from , and the 635 events from , correcting by the relative efficiency, and ignoring a possible small S-wave contribution under the peak , yields
Here and throughout this Letter whenever two uncertainties are quoted the first is statistical and the second is systematic. This value of depends on the decay amplitudes used to fit the mass distribution and could change with different assumptions. To check the robustness of this result, an incoherent phase space background is added to the above fit function. The number of signal events is decreased by 7.3%. If we leave the out of this fit, the original yield is decreased by 6.5%. The larger number of these two numbers is included in the systematic uncertainty. The BES collaboration also included a resonance in their fit to the mass spectrum in decays . We do not find it necessary to add this component to the fit.
The systematic uncertainty has several contributions listed in Table 1. There is an uncertainty due to our kaon and pion identification. The identification efficiency is measured with respect to the Monte Carlo simulation using samples of , events for kaons, and samples of decays for pions. The correction to is 0.9470.009. This correction is already included in the efficiencies quoted above, and the 1% systematic uncertainty is assigned for the relative particle identification efficiencies.
The efficiency for detecting versus a pair is measured using meson decays into and in a sample of semileptonic decays where . The simulation underestimates the efficiency relative to the efficiency by (69)%, so we take 9% as the systematic error.
Besides the sources of uncertainty discussed above, there is a variation due to varying the parameters of the two resonant contributions. We also include an uncertainty for a mass dependent efficiency as a function of mass by changing the acceptance function from flat to linear and found that the yield changed by 2.3%. The difference between even and odd eigenstates is taken as 0.088. Ignoring this difference results in less than a 1% change in the relative efficiency.
|Parameter||Negative change||Positive change|
|mass dependent efficiency||2.3||2.3|
|Addition of non-resonant||0|
|MC statistics (efficiency ratio)||2.3|
In order to give a model independent result we also quote the fraction, , in the interval 90 MeV around 980 MeV, corresponding to approximately two full-widths, where there are 11114 events. Then
This ratio is based on the fit to the mass distribution and does not have any uncertainties related to the fit of the mass distribution. Based on our fits to the mass distribution, there are negligible contributions from any other signal components than the in this interval.
Based on the polarization and rate estimates described above, the first observation of a new CP-odd eigenstate decay mode of the meson into has been made. Using a fit including two interfering resonances, the and , the ratio to production is measured as
By selecting events within 90 MeV of the mass the ratio becomes
The events around the mass are large enough in rate and have small enough backgrounds that they could be used to measure without angular analysis. It may also be possible to use other data in the mass region above the for this purpose if they turn out to be dominated by S-wave.
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at CERN and at the LHCb institutes, and acknowledge support from the National Agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); CERN; NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (Netherlands); SCSR (Poland); ANCS (Romania); MinES of Russia and Rosatom (Russia); MICINN, XUNGAL and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowledge the support received from the ERC under FP7 and the Région Auvergne.
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