EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2013-186 LHCb-PAPER-2013-055 8 October 2013
Observation of decays and measurement of the mixing angle
The LHCb collaboration†††Authors are listed on the following pages.
Decays of and mesons into final states, produced in collisions at the LHC, are investigated using data corresponding to an integrated luminosity of 3 fb collected with the LHCb detector. decays are seen for the first time, and the branching fractions are measured. Using these rates, the mixing angle between strange and non-strange components of its wave function in the structure model is determined to be . Implications on the possible tetraquark nature of the are discussed.
Submitted to Phys. Rev. Lett.
© CERN on behalf of the LHCb collaboration, license CC-BY-3.0.
R. Aaij, B. Adeva, M. Adinolfi, C. Adrover, A. Affolder, Z. Ajaltouni, J. Albrecht, F. Alessio, M. Alexander, S. Ali, G. Alkhazov, P. Alvarez Cartelle, A.A. Alves Jr, S. Amato, S. Amerio, Y. Amhis, L. Anderlini, J. Anderson, R. Andreassen, M. Andreotti, J.E. Andrews, R.B. Appleby, O. Aquines Gutierrez, F. Archilli, A. Artamonov, M. Artuso, E. Aslanides, G. Auriemma, M. Baalouch, S. Bachmann, J.J. Back, A. Badalov, C. Baesso, V. Balagura, W. Baldini, R.J. Barlow, C. Barschel, S. Barsuk, W. Barter, V. Batozskaya, Th. Bauer, A. Bay, J. Beddow, F. Bedeschi, I. Bediaga, S. Belogurov, K. Belous, I. Belyaev, E. Ben-Haim, G. Bencivenni, S. Benson, J. Benton, A. Berezhnoy, R. Bernet, M.-O. Bettler, M. van Beuzekom, A. Bien, S. Bifani, T. Bird, A. Bizzeti, P.M. Bjørnstad, T. Blake, F. Blanc, J. Blouw, S. Blusk, V. Bocci, A. Bondar, N. Bondar, W. Bonivento, S. Borghi, A. Borgia, T.J.V. Bowcock, E. Bowen, C. Bozzi, T. Brambach, J. van den Brand, J. Bressieux, D. Brett, M. Britsch, T. Britton, N.H. Brook, H. Brown, A. Bursche, G. Busetto, J. Buytaert, S. Cadeddu, R. Calabrese, O. Callot, M. Calvi, M. Calvo Gomez, A. Camboni, P. Campana, D. Campora Perez, A. Carbone, G. Carboni, R. Cardinale, A. Cardini, H. Carranza-Mejia, L. Carson, K. Carvalho Akiba, G. Casse, L. Castillo Garcia, M. Cattaneo, Ch. Cauet, R. Cenci, M. Charles, Ph. Charpentier, S.-F. Cheung, N. Chiapolini, M. Chrzaszcz, K. Ciba, X. Cid Vidal, G. Ciezarek, P.E.L. Clarke, M. Clemencic, H.V. Cliff, J. Closier, C. Coca, V. Coco, J. Cogan, E. Cogneras, P. Collins, A. Comerma-Montells, A. Contu, A. Cook, M. Coombes, S. Coquereau, G. Corti, B. Couturier, G.A. Cowan, D.C. Craik, M. Cruz Torres, S. Cunliffe, R. Currie, C. D’Ambrosio, P. David, P.N.Y. David, A. Davis, I. De Bonis, K. De Bruyn, S. De Capua, M. De Cian, J.M. De Miranda, L. De Paula, W. De Silva, P. De Simone, D. Decamp, M. Deckenhoff, L. Del Buono, N. Déléage, D. Derkach, O. Deschamps, F. Dettori, A. Di Canto, H. Dijkstra, M. Dogaru, S. Donleavy, F. Dordei, A. Dosil Suárez, D. Dossett, A. Dovbnya, F. Dupertuis, P. Durante, R. Dzhelyadin, A. Dziurda, A. Dzyuba, S. Easo, U. Egede, V. Egorychev, S. Eidelman, D. van Eijk, S. Eisenhardt, U. Eitschberger, R. Ekelhof, L. Eklund, I. El Rifai, Ch. Elsasser, A. Falabella, C. Färber, C. Farinelli, S. Farry, D. Ferguson, V. Fernandez Albor, F. Ferreira Rodrigues, M. Ferro-Luzzi, S. Filippov, M. Fiore, M. Fiorini, C. Fitzpatrick, M. Fontana, F. Fontanelli, R. Forty, O. Francisco, M. Frank, C. Frei, M. Frosini, E. Furfaro, A. Gallas Torreira, D. Galli, M. Gandelman, P. Gandini, Y. Gao, J. Garofoli, P. Garosi, J. Garra Tico, L. Garrido, C. Gaspar, R. Gauld, E. Gersabeck, M. Gersabeck, T. Gershon, Ph. Ghez, V. Gibson, L. Giubega, V.V. Gligorov, C. Göbel, D. Golubkov, A. Golutvin, A. Gomes, P. Gorbounov, H. Gordon, M. Grabalosa Gándara, R. Graciani Diaz, L.A. Granado Cardoso, E. Graugés, G. Graziani, A. Grecu, E. Greening, S. Gregson, P. Griffith, L. Grillo, O. Grünberg, B. Gui, E. Gushchin, Yu. Guz, T. Gys, C. Hadjivasiliou, G. Haefeli, C. Haen, T.W. Hafkenscheid, S.C. Haines, S. Hall, B. Hamilton, T. Hampson, S. Hansmann-Menzemer, N. Harnew, S.T. Harnew, J. Harrison, T. Hartmann, J. He, T. Head, V. Heijne, K. Hennessy, P. Henrard, J.A. Hernando Morata, E. van Herwijnen, M. Heß, A. Hicheur, E. Hicks, D. Hill, M. Hoballah, C. Hombach, W. Hulsbergen, P. Hunt, T. Huse, N. Hussain, D. Hutchcroft, D. Hynds, V. Iakovenko, M. Idzik, P. Ilten, R. Jacobsson, A. Jaeger, E. Jans, P. Jaton, A. Jawahery, F. Jing, M. John, D. Johnson, C.R. Jones, C. Joram, B. Jost, M. Kaballo, S. Kandybei, W. Kanso, M. Karacson, T.M. Karbach, I.R. Kenyon, T. Ketel, B. Khanji, O. Kochebina, I. Komarov, R.F. Koopman, P. Koppenburg, M. Korolev, A. Kozlinskiy, L. Kravchuk, K. Kreplin, M. Kreps, G. Krocker, P. Krokovny, F. Kruse, M. Kucharczyk, V. Kudryavtsev, K. Kurek, T. Kvaratskheliya, V.N. La Thi, D. Lacarrere, G. Lafferty, A. Lai, D. Lambert, R.W. Lambert, E. Lanciotti, G. Lanfranchi, C. Langenbruch, T. Latham, C. Lazzeroni, R. Le Gac, J. van Leerdam, J.-P. Lees, R. Lefèvre, A. Leflat, J. Lefrançois, S. Leo, O. Leroy, T. Lesiak, B. Leverington, Y. Li, L. Li Gioi, M. Liles, R. Lindner, C. Linn, B. Liu, G. Liu, S. Lohn, I. Longstaff, J.H. Lopes, N. Lopez-March, H. Lu, D. Lucchesi, J. Luisier, H. Luo, E. Luppi, O. Lupton, F. Machefert, I.V. Machikhiliyan, F. Maciuc, O. Maev, S. Malde, G. Manca, G. Mancinelli, J. Maratas, U. Marconi, P. Marino, R. Märki, J. Marks, G. Martellotti, A. Martens, A. Martín Sánchez, M. Martinelli, D. Martinez Santos, D. Martins Tostes, A. Martynov, A. Massafferri, R. Matev, Z. Mathe, C. Matteuzzi, E. Maurice, A. Mazurov, M. McCann, J. McCarthy, A. McNab, R. McNulty, B. McSkelly, B. Meadows, F. Meier, M. Meissner, M. Merk, D.A. Milanes, M.-N. Minard, J. Molina Rodriguez, S. Monteil, D. Moran, P. Morawski, A. Mordà, M.J. Morello, R. Mountain, I. Mous, F. Muheim, K. Müller, R. Muresan, B. Muryn, B. Muster, P. Naik, T. Nakada, R. Nandakumar, I. Nasteva, M. Needham, S. Neubert, N. Neufeld, A.D. Nguyen, T.D. Nguyen, C. Nguyen-Mau, M. Nicol, V. Niess, R. Niet, N. Nikitin, T. Nikodem, A. Nomerotski, A. Novoselov, A. Oblakowska-Mucha, V. Obraztsov, S. Oggero, S. Ogilvy, O. Okhrimenko, R. Oldeman, G. Onderwater, M. Orlandea, J.M. Otalora Goicochea, P. Owen, A. Oyanguren, B.K. Pal, A. Palano, M. Palutan, J. Panman, A. Papanestis, M. Pappagallo, C. Parkes, C.J. Parkinson, G. Passaleva, G.D. Patel, M. Patel, G.N. Patrick, C. Patrignani, C. Pavel-Nicorescu, A. Pazos Alvarez, A. Pearce, A. Pellegrino, G. Penso, M. Pepe Altarelli, S. Perazzini, E. Perez Trigo, A. Pérez-Calero Yzquierdo, P. Perret, M. Perrin-Terrin, L. Pescatore, E. Pesen, G. Pessina, K. Petridis, A. Petrolini, A. Phan, E. Picatoste Olloqui, B. Pietrzyk, T. Pilař, D. Pinci, S. Playfer, M. Plo Casasus, F. Polci, G. Polok, A. Poluektov, E. Polycarpo, A. Popov, D. Popov, B. Popovici, C. Potterat, A. Powell, J. Prisciandaro, A. Pritchard, C. Prouve, V. Pugatch, A. Puig Navarro, G. Punzi, W. Qian, B. Rachwal, J.H. Rademacker, B. Rakotomiaramanana, M.S. Rangel, I. Raniuk, N. Rauschmayr, G. Raven, S. Redford, S. Reichert, M.M. Reid, A.C. dos Reis, S. Ricciardi, A. Richards, K. Rinnert, V. Rives Molina, D.A. Roa Romero, P. Robbe, D.A. Roberts, A.B. Rodrigues, E. Rodrigues, P. Rodriguez Perez, S. Roiser, V. Romanovsky, A. Romero Vidal, M. Rotondo, J. Rouvinet, T. Ruf, F. Ruffini, H. Ruiz, P. Ruiz Valls, G. Sabatino, J.J. Saborido Silva, N. Sagidova, P. Sail, B. Saitta, V. Salustino Guimaraes, B. Sanmartin Sedes, R. Santacesaria, C. Santamarina Rios, E. Santovetti, M. Sapunov, A. Sarti, C. Satriano, A. Satta, M. Savrie, D. Savrina, M. Schiller, H. Schindler, M. Schlupp, M. Schmelling, B. Schmidt, O. Schneider, A. Schopper, M.-H. Schune, R. Schwemmer, B. Sciascia, A. Sciubba, M. Seco, A. Semennikov, K. Senderowska, I. Sepp, N. Serra, J. Serrano, P. Seyfert, M. Shapkin, I. Shapoval, Y. Shcheglov, T. Shears, L. Shekhtman, O. Shevchenko, V. Shevchenko, A. Shires, R. Silva Coutinho, M. Sirendi, N. Skidmore, T. Skwarnicki, N.A. Smith, E. Smith, E. Smith, J. Smith, M. Smith, M.D. Sokoloff, F.J.P. Soler, F. Soomro, D. Souza, B. Souza De Paula, B. Spaan, A. Sparkes, P. Spradlin, F. Stagni, S. Stahl, O. Steinkamp, S. Stevenson, S. Stoica, S. Stone, B. Storaci, M. Straticiuc, U. Straumann, V.K. Subbiah, L. Sun, W. Sutcliffe, S. Swientek, V. Syropoulos, M. Szczekowski, P. Szczypka, D. Szilard, T. Szumlak, S. T’Jampens, M. Teklishyn, G. Tellarini, E. Teodorescu, F. Teubert, C. Thomas, E. Thomas, J. van Tilburg, V. Tisserand, M. Tobin, S. Tolk, L. Tomassetti, D. Tonelli, S. Topp-Joergensen, N. Torr, E. Tournefier, S. Tourneur, M.T. Tran, M. Tresch, A. Tsaregorodtsev, P. Tsopelas, N. Tuning, M. Ubeda Garcia, A. Ukleja, A. Ustyuzhanin, U. Uwer, V. Vagnoni, G. Valenti, A. Vallier, R. Vazquez Gomez, P. Vazquez Regueiro, C. Vázquez Sierra, S. Vecchi, J.J. Velthuis, M. Veltri, G. Veneziano, M. Vesterinen, B. Viaud, D. Vieira, X. Vilasis-Cardona, A. Vollhardt, D. Volyanskyy, D. Voong, A. Vorobyev, V. Vorobyev, C. Voß, H. Voss, R. Waldi, C. Wallace, R. Wallace, S. Wandernoth, J. Wang, D.R. Ward, N.K. Watson, A.D. Webber, D. Websdale, M. Whitehead, J. Wicht, J. Wiechczynski, D. Wiedner, L. Wiggers, G. Wilkinson, M.P. Williams, M. Williams, F.F. Wilson, J. Wimberley, J. Wishahi, W. Wislicki, M. Witek, G. Wormser, S.A. Wotton, S. Wright, S. Wu, K. Wyllie, Y. Xie, Z. Xing, Z. Yang, X. Yuan, O. Yushchenko, M. Zangoli, M. Zavertyaev, F. Zhang, L. Zhang, W.C. Zhang, Y. Zhang, A. Zhelezov, A. Zhokhov, L. Zhong, A. Zvyagin.
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 Padova, Padova, Italy
Sezione INFN di Pisa, Pisa, Italy
Sezione INFN di Roma Tor Vergata, Roma, Italy
Sezione INFN di Roma La Sapienza, Roma, Italy
Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Kraków, Poland
AGH - University of Science and Technology, Faculty of Physics and Applied Computer Science, Kraków, Poland
National Center for Nuclear Research (NCBJ), 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 (SB RAS) and Novosibirsk State University, 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
Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The Netherlands
NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine
University of Birmingham, Birmingham, United Kingdom
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
Massachusetts Institute of Technology, Cambridge, MA, United States
University of Cincinnati, Cincinnati, OH, United States
University of Maryland, College Park, MD, United States
Syracuse University, Syracuse, NY, United States
Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to
Institut für Physik, Universität Rostock, Rostock, Germany, associated to
KVI-University of Groningen, Groningen, The Netherlands, associated to
Celal Bayar University, Manisa, Turkey, associated to
P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, 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
Hanoi University of Science, Hanoi, Viet Nam
Institute of Physics and Technology, Moscow, Russia
Università di Padova, Padova, Italy
Università di Pisa, Pisa, Italy
Scuola Normale Superiore, Pisa, Italy
Light flavorless hadrons, , are not entirely understood as states. Some states with the same quantum numbers such as the and exhibit mixing . Others, such as the and the , could be mixed states, or they could be comprised of tetraquarks . In addition some states, such as the , are discussed as being made solely of gluons . Understanding if the states are indeed explained by the quark model is crucial to identifying other exotic structures. Previous investigations of and decays (called generically ) into a meson and a [8, 9] or [10, 11] pair have revealed the presence of several light flavorless meson resonances including the and the . Use of decays has been suggested as an excellent way of both measuring mixing angles and discerning if some of the states are tetraquarks [12, 13]. In this Letter the final state is investigated with the aim of seeking additional states. (Mention of a particular process also implies the use of its charge conjugated decay.)
Data are obtained from 3 fb of integrated luminosity collected with the LHCb detector  using collisions. One third of the data was acquired at a center-of-mass energy of 7 TeV, and the remainder at 8 TeV. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range , designed for the study of particles containing or quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about , and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system provides a momentum measurement with relative uncertainty that varies from 0.4% at 5 GeV to 0.6% at 100 GeV. (We work in units where =1.) The impact parameter (IP) is defined as the minimum track distance with respect to the primary vertex. For tracks with large transverse momentum, , with respect to the proton beam direction, the IP resolution is approximately 20. Charged hadrons are identified using two ring-imaging Cherenkov (RICH) detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The LHCb trigger  consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage that applies event reconstruction. Events selected for this analysis are triggered by a candidate decay, required to be consistent with coming from the decay of a -hadron by using either IP requirements or detachment from the associated primary vertex. Simulations are performed using Pythia  with the specific tuning given in Ref. , and the LHCb detector description based on Geant4  described in Ref. . Decays of -hadrons are based on EvtGen .
Events are preselected and then are further filtered using a multivariate analyzer based on the boosted decision tree (BDT) technique . In the preselection, all charged track candidates are required to have 250 MeV, while for muon candidates the requirement is 550 MeV. Events must have a combination that forms a common vertex with , an invariant mass between and +43 MeV of the meson mass, and are constrained to the mass. The four pions must have a vector summed GeV, form a vertex with for five degrees of freedom, and a common vertex with the candidate with for nine degrees of freedom. The angle between the momentum and the vector from the primary vertex to the decay vertex is required to be smaller than 2.56. Particle identification  requirements are based on the difference in the logarithm of the likelihood, DLL, to distinguish between the hypotheses and . We require DLL and DLL. We also explicitly eliminate candidate or events by rejecting any candidate where one combination is within 23 MeV of the or 9 MeV of the meson masses. Other resonant contributions such as are searched for, but not found.
The BDT uses 12 variables that are chosen to separate signal and background: the minimum DLL of the and , the scalar sum of the four pions, and the vector sum of the four pions; relating to the candidate: the flight distance, the vertex , the , and the , which is defined as the difference in of a given primary vertex reconstructed with and without the considered particle. In addition, considering the and as pairs of particles, the minimum , and the minimum of each pair are used. The signal sample used for BDT training is based on simulation, while the background sample uses the sideband MeV above the mass peak from 1/3 of the available data. The BDT is then tested on independent samples from the same sources. The BDT selection is optimized by taking the signal, , and background, , events within 20 MeV of the peak from the preselection and maximizing by using the signal and background efficiencies provided as a function of BDT.
The invariant mass distribution is shown in Fig. 1. Multiple combinations are at the 6% level and a single candidate is chosen based on vertex and mass. We fit the mass distribution using the same signal function shape for both and peaks. This shape is a double Crystal Ball function  with common means and radiative tail parameters obtained from simulation. The combinatorial background is parametrized with an exponential function. There are 119346 and 83939 decays. Possible backgrounds caused by particle misidentification, for example decays, would appear as signal if the particle identification incorrectly assigns the as a . In this case the invariant mass is always below the signal region. Evaluating all such backgrounds shows negligible contributions in the signal regions. These and other low-mass backgrounds are described by a Gaussian distribution.
In order to improve the four-pion mass resolution we kinematically fit each candidate with the constraints that the be at the mass and that the be at the mass. The four-pion invariant mass distributions for and decays within 20 MeV of the mass peaks are shown in Fig. 2. The backgrounds, determined from fits to the number of events in the region MeV above the mass, are subtracted.
There are clear signals around 1285 MeV in both and decays with structures at higher masses. The decay angular distribution is used to probe the spin of the recoiling four-pion system. We examine the distribution of the helicity angle of the with respect to the direction in the rest frame, after correcting for the angular acceptance using simulation. The resulting distribution is then fit by the sum of shapes and , where is the fraction of the helicity 1 component. For scalar four-pion states the helicity is 0, while for higher spin states it is a mixture of helicity 0 and helicity 1 components. We also show in Fig. 2 the helicity 1 yields. In the region near 1285 MeV there is a significant helicity 1 component, as expected if the state we are observing is the .
There is also a large and wider peak near 1450 MeV in the channel. Previously we observed a structure at a mass near 1475 MeV using decays that we attributed to decay. However it could equally well be the meson, an interpretation favored by Ochs . While the is known to decay into four pions, the structure observed in our data cannot be pure spin-0 because of the significant helicity 1 component in this mass region. We do not pursue further the composition of the higher mass regions in either or decays in this Letter.
We use the measured branching fractions of  and  for normalizations. The data selection is updated from that used in previous publications to more closely follow the procedure in this analysis. We find signal yields of 22 476177 events and 16 016187 events within 20 MeV of the signal peaks. The overall efficiencies determined by simulation are (1.4110.015)% and (1.3170.015)%, respectively, for and decays, where the uncertainty is statistical only. The relative efficiencies for the final states with respect to are 14.3% and 14.5% for and decays, with small statistical uncertainties. We compute the overall branching fraction ratios \linenomath
The systematic uncertainties arise from the decay model (5.0%), background shape (0.8%), signal shape (0.8%), simulation statistics (1.9%), and tracking efficiencies (2.0%), resulting in a total of 5.8%.
We proceed to determine the yields by fitting the individual four-pion mass spectra in both and final states. The state is modeled by a relativistic Breit-Wigner function multiplied by phase space and convoluted with our mass resolution of 3 MeV. We take the mass and width of the as 1282.10.6 MeV and 24.21.1 MeV, respectively . The combinatorial background is constrained from sideband data and is allowed to vary by its statistical uncertainty. Backgrounds from higher mass resonances are parameterized by Gaussian shapes whose masses and widths are allowed to vary. We restrict the fits to the interval 1.11.5 GeV, which contains 94.3% of the signal. The fits to the data are shown in Fig. 3. The results of the fits are listed in Table 1 along with twice the negative change in the logarithm of the likelihood () if fit without the signal, and the resulting signal significance. The systematic uncertainties from the signal shape and higher mass resonances have been included. Both final states are seen with significance above five standard deviations. This constitutes the first observation of the in -hadron decays. As a consistency check, we also perform a simultaneous fit to both and samples letting the mass and width vary in the fit. We find the mass and width of the to be 1284.22.2 MeV and 32.45.8 MeV, respectively, where the uncertainties are statistical only, consistent with the known values. To determine the systematic uncertainty in the yields we redo the fits allowing variations of the mass and width values independently. We assign 2.7% and 2.0% for the systematic uncertainties on the and yields, respectively, from this source.
We obtain the branching fraction ratios, using an efficiency of 0.18200.0036%, determined by simulation, for the final state as \linenomath
For the latter ratio we use a production ratio of 0.2590.015 ; this uncertainty is taken as systematic. The other systematic uncertainties are listed in Table 2. The shape of the high-mass tail is changed in the case of decays from a single Gaussian to two relativistic Breit-Wigner shapes corresponding to the mass and width values of the and the mesons. For the high mass shape we change from a Gaussian shape to a second order polynomial. The decay model reflects the allowed variation in the fraction of and decays. The total uncertainties are ascertained by adding the individual components in quadrature separately for the positive and negative values.
|Mass & width of||2.0||2.0||2.7||2.7||1.5||1.5|
|Shape of high mass||0.6||0||0||3.7||0||3.8|
Considering the as a mixed state, we characterize the mixing with a 22 rotation matrix containing a single parameter, the angle , so that the wave functions of the and its partner, indicated by , are given by
The decay widths can be written as 
where is the tree level amplitude, and are quark mixing matrix elements, and are phase space factors. The amplitude ratio is taken as unity . The width ratio is given by
where is the lifetime and is the lifetime. The angle is then given by
The ratio of the phase space factors equals 0.855. The other input values are ps , ps, , and . We use the lifetime measured in decays as the helicity components are in approximately the same ratio as in . No uncertainties are assigned on these quantities as they are much smaller than the other errors. The resulting mixing angle is
The systematic uncertainty is computed from the systematic errors assigned to the branching fractions.
The mixing angle has been estimated assuming that it is mixed with the state. Yang finds using radiative decays , consistent with an earlier determination of . A lattice QCD analysis gives , while an another phenomenological calculation gives a range between ; see also Ref.  for other theoretical predictions. In this analysis we do not specify the other mixed partner.
If the is a tetraquark state its wave function would be in order for it to be produced significantly in both and decays into decays. Using this wave function, the tetraquark model described in Ref.  predicts
with small uncertainties. Our measurement of this ratio of % differs by 3.3 standard deviations from the tetraquark interpretation including the systematic uncertainty.