References

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 collaborationAuthors 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.

 

LHCb collaboration

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, 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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, 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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 [1]. Others, such as the and the , could be mixed states, or they could be comprised of tetraquarks [2]. In addition some states, such as the , are discussed as being made solely of gluons [6]. 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 [15] 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 [16] 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 [17] with the specific tuning given in Ref. [18], and the LHCb detector description based on Geant4 [19] described in Ref. [21]. Decays of -hadrons are based on EvtGen [22].

Events are preselected and then are further filtered using a multivariate analyzer based on the boosted decision tree (BDT) technique [23]. 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 [24] 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 [25] 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.

Figure 1: Invariant mass distribution for combinations. The data are fit with Crystal Ball functions for [(red) dashed curve] and [(purple) dot-dashed curve] signals, an exponential function for combinatoric background (black) dotted, and a Gaussian shape for lower mass background (blue) long-dashed. The total is shown with a (blue) solid curve.

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.

Figure 2: Background subtracted invariant mass distributions of the four pions in (a) and (b) decays are shown in the histogram overlaid with the (black) filled points with the error bars indicating the uncertainties. The open (red) circles show the helicity 1 components of the signals.

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 [6]. 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 [8] and [9] 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

\endlinenomath

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 [1]. 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

\endlinenomath
Figure 3: Fits to the four-pion invariant mass in (a) and (b) decays. The data are shown as points, the signals components as (black) dashed curves, the combinatorial background by (black) dotted curves, and the higher mass resonance tail by (red) dot-dashed curves.
Yield Significance ()
58.1 7.2
  29.5 5.2
Table 1: Fit results for and decays.

For the latter ratio we use a production ratio of 0.2590.015 [26]; 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.

Source Ratio
+ + +
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
Efficiency 2.0 2.0 2.0 2.0 0 0
Tracking 2.0 2.0 2.0 2.0 0 0
Simulation statistics 2.0 2.0 2.0 2.0 0 0
Total 4.0 4.0 4.4 5.7 1.5 4.1
Table 2: Systematic uncertainties of the branching fractions and the rate ratio. The “+” and “–” signs indicate the positive and negative uncertainties, respectively. All numbers are in (%).

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

(1)

The decay widths can be written as [12]

(2)

where is the tree level amplitude, and are quark mixing matrix elements, and are phase space factors. The amplitude ratio is taken as unity [12]. The width ratio is given by

(3)

where is the lifetime and is the lifetime. The angle is then given by

(4)

The ratio of the phase space factors equals 0.855. The other input values are  ps [28],  ps, , and [1]. 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 [29], consistent with an earlier determination of [30]. A lattice QCD analysis gives , while an another phenomenological calculation gives a range between [31]; see also Ref. [33] 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. [12] predicts

(5)

with small uncertainties. Our measurement of this ratio of % differs by 3.3 standard deviations from the tetraquark interpretation including the systematic uncertainty.

Branching fraction ratios are converted into branching fractions using the previously measured rates listed in Table 3. We correct the rates to reflect the updated value of the to production fraction of 0.2590.015 [26]. We determine \linenomath