## Abstract

An angular analysis of B0→J/ψK+π- decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 fb-1 collected with the LHCb detector. The m(K+π-) spectrum is divided into fine bins. In each m(K+π-) bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by K∗ resonances is examined, making minimal assumptions about the K+π- system. The data reject the K∗-only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the m(J/ψπ-) vs m(K+π-) plane suggests structures near m(J/ψπ-)=4200 and 4600 MeV.

Original language | English |
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Article number | 152002 |

Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Physical Review Letters |

Volume | 122 |

Issue number | 15 |

DOIs | |

Publication status | Published - 17 Apr 2019 |

### Funding

B 0 → J / ψ K + π - Decays Aaij R. 29 Abellán Beteta C. 46 Adeva B. 43 Adinolfi M. 50 Aidala C. A. 77 Ajaltouni Z. 7 Akar S. 61 Albicocco P. 20 Albrecht J. 12 Alessio F. 44 Alexander M. 55 Alfonso Albero A. 42 Alkhazov G. 41 Alvarez Cartelle P. 57 Alves A. A. Jr. 43 Amato S. 2 Amerio S. 25 Amhis Y. 9 An L. 19 Anderlini L. 19 Andreassi G. 45 Andreotti M. 18 Andrews J. E. 62 Archilli F. 29 Arnau Romeu J. 8 Artamonov A. 40 Artuso M. 63 Arzymatov K. 38 Aslanides E. 8 Atzeni M. 46 Audurier B. 24 Bachmann S. 14 Back J. J. 52 Baker S. 57 Balagura V. 9 ,b Baldini W. 18 Baranov A. 38 Barlow R. J. 58 Barsuk S. 9 Barter W. 58 Bartolini M. 21 Baryshnikov F. 73 Batozskaya V. 33 Batsukh B. 63 Battig A. 12 Battista V. 45 Bay A. 45 Beddow J. 55 Bedeschi F. 26 Bediaga I. 1 Beiter A. 63 Bel L. 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B. 54 Zucchelli S. 17 ,h (LHCb Collaboration) * 1 Centro Brasileiro de Pesquisas Físicas (CBPF) , Rio de Janeiro, Brazil 2 Universidade Federal do Rio de Janeiro (UFRJ) , Rio de Janeiro, Brazil Center for High Energy Physics, 3 Tsinghua University , Beijing, China 4 University of Chinese Academy of Sciences , Beijing, China 5 Institute Of High Energy Physics (ihep) , Beijing, China Univ. Grenoble Alpes, 6 Univ. Savoie Mont Blanc , CNRS, IN2P3-LAPP, Annecy, France 7 Université Clermont Auvergne , CNRS/IN2P3, LPC, Clermont-Ferrand, France 8 Aix Marseille Univ , CNRS/IN2P3, CPPM, Marseille, France 9 LAL , Univ. Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 10 LPNHE , Sorbonne Université, Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France 11 I. Physikalisches Institut , RWTH Aachen University, Aachen, Germany Fakultät Physik, 12 Technische Universität Dortmund , Dortmund, Germany 13 Max-Planck-Institut für Kernphysik (MPIK) , Heidelberg, Germany 14 Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg , Heidelberg, Germany School of Physics, 15 University College Dublin , Dublin, Ireland 16 INFN Sezione di Bari , Bari, Italy 17 INFN Sezione di Bologna , Bologna, Italy 18 INFN Sezione di Ferrara , Ferrara, Italy 19 INFN Sezione di Firenze , Firenze, Italy 20 INFN Laboratori Nazionali di Frascati , Frascati, Italy 21 INFN Sezione di Genova , Genova, Italy 22 INFN Sezione di Milano-Bicocca , Milano, Italy 23 INFN Sezione di Milano , Milano, Italy 24 INFN Sezione di Cagliari , Monserrato, Italy 25 INFN Sezione di Padova , Padova, Italy 26 INFN Sezione di Pisa , Pisa, Italy 27 INFN Sezione di Roma Tor Vergata , Roma, Italy 28 INFN Sezione di Roma La Sapienza , Roma, Italy 29 Nikhef National Institute for Subatomic Physics , Amsterdam, Netherlands 30 Nikhef National Institute for Subatomic Physics and VU University Amsterdam , Amsterdam, Netherlands 31 Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences , Kraków, Poland 32 AGH - University of Science and Technology , Faculty of Physics and Applied Computer Science, Kraków, Poland 33 National Center for Nuclear Research (NCBJ) , Warsaw, Poland 34 Horia Hulubei National Institute of Physics and Nuclear Engineering , Bucharest-Magurele, Romania 35 Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI) , Moscow, Russia Institute of Nuclear Physics, 36 Moscow State University (SINP MSU) , Moscow, Russia 37 Institute for Nuclear Research of the Russian Academy of Sciences (INR RAS) , Moscow, Russia 38 Yandex School of Data Analysis , Moscow, Russia 39 Budker Institute of Nuclear Physics (SB RAS) , Novosibirsk, Russia 40 Institute for High Energy Physics NRC Kurchatov Institute (IHEP NRC KI) , Protvino, Russia 41 Petersburg Nuclear Physics Institute NRC Kurchatov Institute (PNPI NRC KI) , Gatchina, Russia 42 ICCUB, Universitat de Barcelona , Barcelona, Spain Instituto Galego de Física de Altas Enerxías (IGFAE), 43 Universidade de Santiago de Compostela , Santiago de Compostela, Spain 44 European Organization for Nuclear Research (CERN) , Geneva, Switzerland Institute of Physics, 45 Ecole Polytechnique Fédérale de Lausanne (EPFL) , Lausanne, Switzerland Physik-Institut, 46 Universität Zürich , Zürich, Switzerland 47 NSC Kharkiv Institute of Physics and Technology (NSC KIPT) , Kharkiv, Ukraine 48 Institute for Nuclear Research of the National Academy of Sciences (KINR) , Kyiv, Ukraine 49 University of Birmingham , Birmingham, United Kingdom H.H. Wills Physics Laboratory, 50 University of Bristol , Bristol, United Kingdom Cavendish Laboratory, 51 University of Cambridge , Cambridge, United Kingdom Department of Physics, 52 University of Warwick , Coventry, United Kingdom 53 STFC Rutherford Appleton Laboratory , Didcot, United Kingdom School of Physics and Astronomy, 54 University of Edinburgh , Edinburgh, United Kingdom School of Physics and Astronomy, 55 University of Glasgow , Glasgow, United Kingdom Oliver Lodge Laboratory, 56 University of Liverpool , Liverpool, United Kingdom 57 Imperial College London , London, United Kingdom School of Physics and Astronomy, 58 University of Manchester , Manchester, United Kingdom Department of Physics, 59 University of Oxford , Oxford, United Kingdom 60 Massachusetts Institute of Technology , Cambridge, Massachusetts, USA 61 University of Cincinnati , Cincinnati, Ohio, USA 62 University of Maryland , College Park, Maryland, USA 63 Syracuse University , Syracuse, New York, USA 64 Laboratory of Mathematical and Subatomic Physics , Constantine, Algeria [associated with Universidade Federal do Rio de Janeiro (UFRJ) , Rio de Janeiro, Brazil] 65 Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio) , Rio de Janeiro, Brazil [associated with Universidade Federal do Rio de Janeiro (UFRJ) , Rio de Janeiro, Brazil] 66 South China Normal University , Guangzhou, China (associated with Center for High Energy Physics, Tsinghua University , Beijing, China) School of Physics and Technology, 67 Wuhan University , Wuhan, China (associated with Center for High Energy Physics, Tsinghua University , Beijing, China) Institute of Particle Physics, 68 Central China Normal University , Wuhan, Hubei, China (associated with Center for High Energy Physics, Tsinghua University , Beijing, China) Departamento de Fisica, 69 Universidad Nacional de Colombia , Bogota, Colombia (associated with LPNHE, Sorbonne Université , Paris Diderot Sorbonne Paris Cité, CNRS/IN2P3, Paris, France) Institut für Physik, 70 Universität Rostock , Rostock, Germany (associated with Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg , Heidelberg, Germany) Van Swinderen Institute, 71 University of Groningen , Groningen, Netherlands (associated with Nikhef National Institute for Subatomic Physics , Amsterdam, Netherlands) 72 National Research Centre Kurchatov Institute , Moscow, Russia [associated with Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI) , Moscow, Russia, Moscow, Russia] 73 National University of Science and Technology “MISIS” , Moscow, Russia [associated with Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI) , Moscow, Russia, Moscow, Russia] 74 National Research University Higher School of Economics , Moscow, Russia (associated with Yandex School of Data Analysis , Moscow, Russia) 75 National Research Tomsk Polytechnic University , Tomsk, Russia [associated with Institute of Theoretical and Experimental Physics NRC Kurchatov Institute (ITEP NRC KI) , Moscow, Russia, Moscow, Russia] Instituto de Fisica Corpuscular, 76 Centro Mixto Universidad de Valencia - CSIC , Valencia, Spain (associated with ICCUB, Universitat de Barcelona , Barcelona, Spain) 77 University of Michigan , Ann Arbor, Michigan, USA (associated with Syracuse University , Syracuse, New York, USA) 78 Los Alamos National Laboratory (LANL) , Los Alamos, New Mexico, USA (associated with Syracuse University , Syracuse, New York, USA) * Full author list given at the end of the article. a Deceased. b Also at Laboratoire Leprince-Ringuet, Palaiseau, France. c Also at Università di Milano Bicocca, Milano, Italy. d Also at Università di Modena e Reggio Emilia, Modena, Italy. e Also at Novosibirsk State University, Novosibirsk, Russia. f Also at Università di Ferrara, Ferrara, Italy. g Also at LIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain. h Also at Università di Bologna, Bologna, Italy. i Also at Università di Pisa, Pisa, Italy. j Also at H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom. k Also at Università di Bari, Bari, Italy. l Also at Sezione INFN di Trieste, Trieste, Italy. m Also at Università di Genova, Genova, Italy. n Also at Università degli Studi di Milano, Milano, Italy. o Also at Universidade Federal do Triângulo Mineiro (UFTM), Uberaba-MG, Brazil. p Also at AGH - University of Science and Technology, Faculty of Computer Science, Electronics and Telecommunications, Kraków, Poland. q Also at Lanzhou University, Lanzhou, China. r Also at Università di Padova, Padova, Italy. s Also at Università di Cagliari, Cagliari, Italy. t Also at MSU - Iligan Institute of Technology (MSU-IIT), Iligan, Philippines. u Also at Scuola Normale Superiore, Pisa, Italy. v Also at Hanoi University of Science, Hanoi, Vietnam. w Also at P.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia. x Also at Università di Roma Tor Vergata, Roma, Italy. y Also at Università di Roma La Sapienza, Roma, Italy. z Also at Università della Basilicata, Potenza, Italy. aa Also at Università di Urbino, Urbino, Italy. bb Also at Physics and Micro Electronic College, Hunan University, Changsha City, China. cc Also at School of Physics and Information Technology, Shaanxi Normal University (SNNU), Xi’an, China. 17 April 2019 19 April 2019 122 15 152002 17 January 2019 © 2019 CERN, for the LHCb Collaboration 2019 CERN Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP 3 . An angular analysis of B 0 → J / ψ K + π - decays is performed, using proton-proton collision data corresponding to an integrated luminosity of 3 fb - 1 collected with the LHCb detector. The m ( K + π - ) spectrum is divided into fine bins. In each m ( K + π - ) bin, the hypothesis that the three-dimensional angular distribution can be described by structures induced only by K * resonances is examined, making minimal assumptions about the K + π - system. The data reject the K * -only hypothesis with a large significance, implying the observation of exotic contributions in a model-independent fashion. Inspection of the m ( J / ψ π - ) vs m ( K + π - ) plane suggests structures near m ( J / ψ π - ) = 4200 and 4600 MeV. CERN, The European Organization for Nuclear Research (Switzerland) 10.13039/100012470 Coordenação de Aperfeiçoamento de Pessoal de Nível Superior 10.13039/501100002322 Conselho Nacional de Desenvolvimento Científico e Tecnológico 10.13039/501100003593 Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro 10.13039/501100004586 Financiadora de Estudos e Projetos 10.13039/501100004809 Ministry of Science and Technology of the People’s Republic of China 10.13039/501100002855 National Natural Science Foundation of China 10.13039/501100001809 Centre National de la Recherche Scientifique 10.13039/501100004794 Institut National de Physique Nucleaire et de Physique des Particules Bundesministerium für Bildung und Forschung 10.13039/501100002347 Deutsche Forschungsgemeinschaft 10.13039/501100001659 Max-Planck-Gesellschaft 10.13039/501100004189 Instituto Nazionale di Fisica Nucleare 10.13039/501100004007 Nederlandse Organisatie voor Wetenschappelijk Onderzoek 10.13039/501100003246 Ministerstwo Nauki i Szkolnictwa Wyższego 10.13039/501100004569 Narodowe Centrum Nauki 10.13039/501100004281 Ministerul Educatiei si Cercetarii Stiintifice 10.13039/501100006730 Institul de Fizica Atomica (MEN/IFA) Ministry of Education and Science of the Russian Federation 10.13039/501100003443 Ministerio de Economía y Competitividad 10.13039/501100003329 Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung 10.13039/501100001711 Staatssekretariat für Bildung, Forschung und Innovation 10.13039/501100007352 National Academy of Sciences of Ukraine 10.13039/501100004742 Science and Technology Facilities Council 10.13039/501100000271 National Science Foundation 10.13039/100000001 Karlsruher Institut für Technologie 10.13039/100009133 Deutsches Elektronen-Synchrotron 10.13039/501100001647 Collaborative organisation for ICT in Dutch higher education and research (SURF) Port d’Informacio Cientifica (PIC) GridPP, UK Computing for Particle Physics National Research Center “Kurchatov” Institute Yandex LLC CSCS IFIN-HH CBPF PL-GRID Ohio Supercomputer Center (OSC) Alexander von Humboldt-Stiftung 10.13039/100005156 EPLANET, The European Particle physics Latin America NETwork European Research council H2020 Marie Skłodowska-Curie Actions 10.13039/100010665 H2020 European Research Council 10.13039/100010663 Agence Nationale de la Recherche 10.13039/501100001665 Labex Physique des 2 Infinis et des Origines (P2IO) Origine Constituants et Evolution de l’Univers (OCEVU) Région Auvergne-Rhône-Alpes 10.13039/501100010115 Russian Foundation for Basic Research 10.13039/501100002261 Russian Science Foundation 10.13039/501100006769 Chinese Academy of Sciences 10.13039/501100002367 CAS President’s International Fellowship Initiative Thousand Talents Program Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia 10.13039/501100008425 Generalitat de Catalunya 10.13039/501100002809 Generalitat Valenciana 10.13039/501100003359 Royal Society 10.13039/501100000288 Leverhulme Trust 10.13039/501100000275 Laboratory Directed Research and Development 10.13039/100007000 Los Alamos National Laboratory 10.13039/100008902 GVA XuntaGal GENCAT Herchel Smith Fund Royal Commission for the Exhibition of 1851 10.13039/501100000700 English-Speaking Union 10.13039/501100000611 Conseil Général de Haute-Savoie In the standard model, the quark model allows for hadrons comprising any number of valence quarks, as long as they are color-singlet states. Yet, after decades of searches, the reason why the vast majority of hadrons are built out of only quark-antiquark (meson) or three-quark (baryon) combinations remains a mystery. The best known exception is the Z ( 4430 ) - resonance with spin-parity 1 - and width Γ = 172 ± 13 MeV [1–3] which has minimal quark content c c ¯ u ¯ d ¯ , and is therefore manifestly exotic, i.e., has components that are neither quark-antiquark or three-quark combinations. The only confirmed decay of the Z ( 4430 ) - state is via Z ( 4430 ) - → ψ ( 2 S ) π - , as seen in B 0 → ψ ( 2 S ) K + π - decays [1,4] . The corresponding Z ( 4430 ) - → J / ψ π - decay rate is suppressed by at least a factor of 10 [5] . The authors of Ref. [6] surmise that in a dynamical diquark picture, this is because of a larger overlap of the Z ( 4430 ) - radial wave function with the excited state ψ ( 2 S ) than with the ground state J / ψ . For the B 0 → J / ψ K + π - channel, the Belle collaboration [5] has reported the observation of a new exotic Z ( 4200 ) - resonance decaying to J / ψ π - that might correspond to the structure in m ( ψ ( 2 S ) π - ) seen in Ref. [1] at around the same mass. A generic concern in searches for broad exotic states like the Z ( 4430 ) - resonance is disentangling contributions from nonexotic components. For B 0 → ψ ( ′ ) K + π - decays [7] , the latter comprise different K J * resonances with spin J , that decay to K + π - . Figure 1 shows the K J * spectrum, which has multiple, overlapping, and poorly measured states. The bulk of the measurements come from the LASS K + π - scattering experiment [8] . In particular, the decay B 0 → J / ψ K + π - is known to be dominated by K J * resonances, with an exotic fit fraction of only 2.4% [5] , compared to a 10.3% contribution from the Z ( 4430 ) - for B 0 → ψ ( 2 S ) K + π - [9] . This smaller exotic fit fraction for the J / ψ case makes it pertinent to study the evidence of exotic contributions in a manner independent of the dominant but poorly understood K J * spectrum. 1 10.1103/PhysRevLett.122.152002.f1 FIG. 1. Spectrum of K J * resonances from Ref. [10] , with the vertical span of the boxes indicating ± Γ 0 , where Γ 0 is the width of each resonance. The horizontal dashed lines mark the m ( K + π - ) physical region for B 0 → J / ψ K + π - decays, whereas the dot-dashed lines mark the specific region, m ( K + π - ) ∈ [ 1085 , 1445 ] MeV , employed for determining the significance of exotic contributions. The BABAR collaboration [11] has performed a model-independent analysis of B 0 → ψ ( ′ ) K + π - decays making minimal assumptions about the K J * spectrum, using two-dimensional (2D) moments in the variables m ( K + π - ) and the K + helicity angle, θ V . The key feature of this approach is that no information on the exact content of the K J * states, including their masses, widths, and m ( K + π - ) -dependent line shapes, is required. An amplitude analysis would require the accurate description of the K J * line shapes which depend on the underlying production dynamics. The model-independent procedure bypasses these problems, requiring only knowledge of the highest spin, J max , among all the contributing K J * states, for a given m ( K + π - ) bin. Within uncertainties, the m ( J / ψ π - ) spectrum in the BABAR data was found to be adequately described using just K J * states, without the need for exotic contributions. In this Letter, a four-dimensional (4D) angular analysis of B 0 → J / ψ K + π - decays with J / ψ → μ + μ - is reported, employing the Run 1 LHCb dataset. The data sample corresponds to a signal yield approximately 40 and 20 times larger than those of the corresponding BABAR [11] and Belle [9] analyses, respectively. The larger sample size allows analysis of the differential rate as a function of the four variables, m ( K + π - ) , θ V , θ l , and χ , that fully describe the decay topology. The lepton helicity angle, θ l , and the azimuthal angle, χ , between the ( μ + μ - ) and ( K + π - ) decay planes, were integrated over in the BABAR 2D analysis [11] . The present 4D analysis therefore benefits from a significantly better sensitivity to exotic components than the previous 2D analysis. The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5 and is described in detail in Ref. [12] . Samples of simulated events are used to obtain the detector efficiency and optimise the selection. The p p collisions are generated using pythia [13] with a specific LHCb configuration [14] . Decays of hadronic particles are described by evtgen [15] , in which final-state radiation is generated using photos [16] . Dedicated control samples are employed to calibrate the simulation for agreement with the data. The selection procedure is the same as in Refs. [17,18] for the rare decay B 0 → μ + μ - K + π - , with the additional requirement that the m ( μ + μ - ) mass is constrained to the known J / ψ mass via a kinematic fit [19] . The data sample is divided into 35 fine bins in m ( K + π - ) such that the m ( K + π - ) dependence can be neglected inside a given bin, and each subsample is processed independently. The bin widths vary depending on the data sample size in a given m ( K + π - ) region. Backgrounds from B + → J / ψ K + , B s 0 → J / ψ K + K - , and Λ b 0 → J / ψ p K - decays are reduced to a level below 1% of the signal yield at the selection stage using the excellent tracking and particle-identification capabilities of the LHCb detector, and are subsequently removed by a background subtraction procedure. The B ( s ) 0 → J / ψ K + π - signal line shape in the m ( J / ψ K + π - ) spectrum is described by a bifurcated Gaussian core and exponential tails on both sides. A sum of two such line shapes is used for the signal template for the mass fit, while the background line shape is a falling exponential. The exponential tails in the signal line shape are fixed from the simulation and all other parameters are allowed to vary in the fit, performed as a binned χ 2 minimization. An example mass fit result is given in the Supplemental Material [20] . The cumulative signal yield in the m ( K + π - ) ∈ [ 745 , 1545 ] MeV region is 554 , 500 ± 800 . The strategy in this analysis is to examine the hypothesis that nonexotic K J * contributions alone can explain all features of the data. Under the approximation that the muon mass can be neglected and within a narrow m ( K + π - ) bin, the C P -averaged transition matrix element squared is [21,22] | M | 2 = ∑ η | ∑ λ , J 2 J + 1 H λ η , J d λ , 0 J ( θ V ) d λ , η 1 ( θ l ) e i λ χ | 2 , (1) where H λ η , J are the K J * helicity amplitudes and d m ′ , m j are Wigner rotation matrix elements. The helicities of the outgoing lepton and K J * are η = ± 1 and λ ∈ { 0 , ± 1 } , respectively. Parity conservation in the electromagnetic J / ψ → μ - μ + decay leads to the relation H λ + , J = H λ - , J ≡ H λ J . The differential decay rate of B 0 → J / ψ ( → μ + μ - ) K + π - with the K + π - system including spin - J partial waves with J ≤ J max k can be written as ( d Γ k d Ω ) J max k ∝ ∑ i = 1 n max k f i ( Ω ) Γ i k , (2) where the angular part in Eq. (1) has been expanded in an orthonormal basis of angular functions, f i ( Ω ) . Here, k enumerates the m ( K + π - ) bin under consideration, and d Ω = d cos θ ℓ d cos θ V d χ is the angular phase space differential element. The angular basis functions, f i ( Ω ) , are constructed from spherical harmonics, Y l m ≡ Y l m ( θ l , χ ) , and reduced spherical harmonics, P l m ≡ 2 π Y l m ( θ V , 0 ) , and are given in the Supplemental Material [20] . The Γ i k moments are observables that have an overall m ( K + π - ) dependence, but within a narrow m ( K + π - ) bin, this dependence can be neglected. The number of moments for the k th bin, n max k , depends on the allowed spin of the highest partial wave, J max k , and is given by Ref. [22] n max k = 28 + 12 × ( J max k - 2 ) , for J max k > 2 . (3) Thus, for spin 3 onward, each additional higher spin component leads to 12 additional moments. In contrast to previous analyses, d cos θ ℓ d χ is not integrated over, which would have resulted in integrating over 10 out of these 12 moments, for each additional spin. Because of the orthonormality of the f i ( Ω ) basis functions, the angular observables, Γ i k , can be determined from the data in an unbiased fashion using a simple counting measurement [21] . For the k th m ( K + π - ) bin, the background-subtracted raw moments are estimated as Γ i , raw k = ∑ p = 1 n sig k f i ( Ω p ) - x k ∑ p = 1 n bkg k f i ( Ω p ) , (4) where Ω p refers to the set of angles for a given event in this m ( K + π - ) bin. The corresponding covariance matrix is C i j , raw k = ∑ p = 1 n sig k f i ( Ω p ) f j ( Ω p ) + ( x k ) 2 ∑ p = 1 n bkg k f i ( Ω p ) f j ( Ω p ) . (5) Here, n sig k and n bkg k correspond to the number of candidates in the signal and background regions, respectively. The signal region is defined within ± 15 MeV of the known B 0 mass, and the background region spans the range m ( J / ψ K + π - ) ∈ [ 5450 , 5560 ] MeV . The scale factor, x k , is the ratio of the estimated number of background candidates in the signal region divided by the number of candidates in the background region and is used to normalize the background subtraction. To unfold effects from the detector efficiency including event reconstruction and selection, an efficiency matrix, E i j k , is used. It is obtained from simulated signal events generated according to a phase space distribution, uniform in Ω , as E i j k = ∑ p = 1 n sim k w p k f i ( Ω p ) f j ( Ω p ) . (6) The w p k weight factors correct for differences between data and simulation, and the summation is over simulated and reconstructed events. They are derived using the B 0 → J / ψ K * ( 892 ) 0 control mode, as described in Refs. [17,18] . The efficiency-corrected moments and covariance matrices are estimated as Γ i k = [ ( E k ) - 1 ] i l Γ l , raw k , (7) C i j k = [ ( E k ) - 1 ] i l C l m , raw k [ ( E k ) - 1 ] j m . (8) The first moment, Γ 1 k , corresponds to the overall rate. The remaining moments and the covariance matrix are normalized to this overall rate as Γ ¯ i k ≡ Γ i k / Γ 1 k and C ¯ i j , stat k = ( C i j k ( Γ 1 k ) 2 + Γ i k Γ j k ( Γ 1 k ) 4 C 11 k - Γ i k C 1 j k + Γ j k C 1 i k Γ 1 k ( Γ 1 k ) 2 ) , (9) for i , j ∈ { 2 , … , n max k } . The normalization with respect to the total rate renders the analysis insensitive to any overall systematic effect not correlated with d Ω in a given m ( K + π - ) bin. The uncertainty from limited knowledge of the background is included in the second term in Eq. (5) . The effect on the normalized moments, Γ ¯ i k , due to the uncertainty in the x k scale factors from the mass fit, is found to be negligible. The effect due to the limited simulation sample size compared to the data is small and accounted for using pseudoexperiments. The last source of systematic uncertainty is the effect of finite resolution in the reconstructed angles. The estimated biases in the measured Γ ¯ i k moments are added as additional uncertainties. The dominant contributions to B 0 → J / ψ K + π - are from the K * ( 892 ) 0 and K 2 * ( 1430 ) 0 states. To maximize the sensitivity to any exotic component, the dominant K * ( 892 ) 0 region that serves as a background for any non - K J * component, the analysis is performed on the m ( K + π - ) ∈ [ 1085 , 1445 ] MeV region, as marked by the dot-dashed lines in Fig. 1 . The value of J max k depends on m ( K + π - ) , with higher spin states suppressed at lower m ( K + π - ) values, due to the orbital angular momentum barrier factor [23] . As seen from Fig. 1 , only states with spin J = { 0 , 1 } contribute below m ( K + π - ) ∼ 1300 MeV and spin J = { 0 , 1 , 2 } below m ( K + π - ) ∼ 1600 MeV . As a conservative choice, J max k is taken to be one unit larger than these expectations J max k = { 2 for 1085 ≤ m ( K + π - ) < 1265 MeV , 3 for 1265 ≤ m ( K + π - ) < 1445 MeV . (10) Any exotic component in the J / ψ π - or J / ψ K + system will reflect onto the entire basis of K J * partial waves and give rise to nonzero contributions from P l ( cos θ V ) components for l larger than those needed to account for K J * resonances. From the completeness of the f i ( Ω ) basis, a model with large enough J max k also describes any exotic component in the data. For a given value of m ( K + π - ) , there is a one-to-one correspondence between cos θ V and the variables m ( J / ψ π - ) or m ( J / ψ K + ) . Therefore, a complete basis of P l ( cos θ V ) partial waves also describes any arbitrary shape in m ( J / ψ π - ) or m ( J / ψ K + ) , for a given m ( K + π - ) bin. The series is truncated at a value large enough to describe the relevant features of the distribution in data, but not so large that it follows bin-by-bin statistical fluctuations. A value of J max k = 15 is found to be suitable. For the k th m ( K + π - ) bin, the probability density function (pdf) for the J max k model is P J max k ( Ω ) = 1 8 π ( 1 8 π + ∑ i = 2 n J max k Γ ¯ i k f i ( Ω ) ) . (11) Simulated events generated uniformly in Ω , after incorporating detector efficiency effects and weighting by the pdf in Eq. (11) , are expected to match the background-subtracted data. The background subtraction is performed using the sPlot technique [24] , where the weights are determined from fits to the invariant m ( J / ψ K + π - ) distributions described previously. Figure 2 shows this comparison between the background-subtracted data and weighted simulated events in the m ( K + π - ) ∈ [ 1085 , 1265 ] MeV region. The J max k = 2 model clearly misses the peaking structures in the data around m ( J / ψ π - ) = 4200 and 4600 MeV. This inability of the J max k = 2 model to describe the data, even though the first spin 2 state, K 2 * ( 1430 ) 0 , lies beyond this mass region, strongly points toward the presence of exotic components. These could be four-quark bound states, meson molecules, or possibly dynamically generated features such as cusps. 2 10.1103/PhysRevLett.122.152002.f2 FIG. 2. Comparison of m ( J ψ π - ) in the m ( K + π - ) ∈ [ 1085 , 1265 ] MeV region between the background-subtracted data and simulated events weighted by moments models with J max k = 2 and J max k = 15 . To obtain a numerical estimate of the significance of exotic states, the likelihood ratio test is employed between the null hypothesis [ K J * -only, from Eq. (10) ] and the exotic hypothesis ( J max k = 15 ) pdfs , denoted as P K J * k and P exotic k , respectively. The test statistic used in the likelihood ratio test is defined as Δ ( - 2 log L ) | k ≡ - ∑ p = 1 n sig k 2 log P K J * k ( Ω p ) P exotic k ( Ω p ) + x k ∑ p = 1 n bkg k 2 log P K J * k ( Ω p ) P exotic k ( Ω p ) + 2 ( n sig k - x k n bkg k ) log ∫ P K J * k ( Ω ) ε ( Ω ) d Ω ∫ P exotic k ( Ω ) ε ( Ω ) d Ω , (12) for the k th m ( K + π - ) bin, where ε ( Ω ) denotes the three-dimensional angular detector efficiency in this bin, derived from the simulation weighted to match the data in the B 0 production kinematics. The last term in Eq. (12) ensures normalization of the relevant pdf and is calculated from simulated events that pass the reconstruction and selection criteria E i k ≡ ∑ p = 1 n sim k w p k f i ( Ω p ) , (13) ∫ P J max k ( Ω ) ε ( Ω ) d Ω ∝ ∑ i = 1 n max k Γ i k E i k . (14) Results from individual m ( K + π - ) bins are combined to give the final test statistic Δ ( - 2 log L ) = ∑ k Δ ( - 2 log L ) | k . From Eq. (3) the number of degrees-of-freedom (ndf) increases by 12 for each additional spin - J wave in each m ( K + π - ) bin. From Eq. (10) , for the J max k = 2 and 3 choices, Δ ndf = 12 × ( 15 - 2 ) = 156 and 12 × ( 15 - 3 ) = 144 , respectively, between the exotic and K J * -only pdfs for each m ( K + π - ) bin. Each additional degree-of-freedom between the exotic and K J * -only pdf adds approximately one unit to the computed Δ ( - 2 log L ) in the data due to increased sensitivity to the statistical fluctuations, and Δ ( - 2 log L ) is therefore not expected to be zero even if there is no exotic contribution in the data. The expected Δ ( - 2 log L ) distribution in the absence of exotic activity is evaluated using a large number of pseudoexperiments. For each m ( K + π - ) bin, 11 000 pseudoexperiments are generated according to the K J * -only model with the moments varied according to the covariance matrix. The number of signal and background events for each pseudoexperiment are taken to be those measured in the data. The detector efficiency obtained from simulation is parametrized in 4D. Each pseudoexperiment is analyzed in exactly the same way as the data, where an independent efficiency matrix is generated for each pseudoexperiment. This accounts for the limited sample size of the simulation for the efficiency unfolding. The pseudoexperiments therefore represent the data faithfully at every step of the processing. Figure 3 shows the distribution of Δ ( - 2 log L ) from the pseudoexperiments in the m ( K + π - ) ∈ [ 1085 , 1445 ] MeV region comprising six m ( K + π - ) bins each with the J max k = 2 or 3 choice. A fit to a Gaussian profile gives Δ ( - 2 log L ) ≈ 2051 between the null and exotic hypothesis, even in the absence of any exotic contributions. This value is consistent with the naïve expectation Δ ( ndf ) = 1800 from the counting discussed earlier. The value of Δ ( - 2 log L ) for the data, as marked by the vertical line in Fig. 3 , shows a deviation of more than 10 σ from the null hypothesis, corresponding to the distribution of the pseudoexperiments. The uncertainty due to the quality of the Gaussian profile fit in Fig. 3 is found to be negligible. The choice of large J max k for P exotic k , as well as the detector efficiency and calibration of the simulation, is systematically varied in pseudoexperiments, with significance for exotic components in excess of 6 σ observed in each case. 3 10.1103/PhysRevLett.122.152002.f3 FIG. 3. Likelihood-ratio test for exotic significance. The data shows a 10 σ deviation from the pseudoexperiments generated according to the null hypothesis ( K J * -only contributions). In summary, employing the Run 1 LHCb dataset, non - K J * contributions in B 0 → J / ψ K + π - are observed with overwhelming significance. Compared to the previous BABAR analysis [11] of the same channel, the current study benefits from a 40-fold increase in signal yield and a full angular analysis of the decay topology. The method relies on a novel orthonormal angular moments expansion and, aside from a conservative limit on the highest allowed K J * spin for a given m ( K + π - ) invariant mass, makes no other assumption about the K + π - system. Figure 4 shows a scatter plot of m ( J / ψ π - ) against m ( K + π - ) in the background-subtracted data. Although the model-independent analysis performed here does not identify the origin of the non - K J * contributions, structures are visible at m ( J / ψ π - ) ≈ 4200 MeV , close to the exotic state reported previously by Belle [5] , and at m ( J / ψ π - ) ≈ 4600 MeV . To interpret these structures as exotic tetraquark resonances and measure their properties will require a future model-dependent amplitude analysis of the data. 4 10.1103/PhysRevLett.122.152002.f4 FIG. 4. Background-subtracted 2D distribution of m ( J / ψ π - ) vs m ( K + π - ) in the region m ( K + π - ) ∈ [ 745 , 1545 ] MeV . The intensity ( z -axis) scale has been highly truncated to limit the strong K * ( 892 ) 0 contribution. 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 the LHCb institutes. We acknowledge support from CERN and from the national agencies CAPES, CNPq, FAPERJ, and FINEP (Brazil); MOST and NSFC (China); CNRS/IN2P3 (France); BMBF, DFG, and MPG (Germany); INFN (Italy); NWO (Netherlands); MNiSW and NCN (Poland); MEN/IFA (Romania); MSHE (Russia); MinECo (Spain); SNSF and SER (Switzerland); NASU (Ukraine); STFC (United Kingdom); NSF (U.S.). We acknowledge the computing resources that are provided by CERN, IN2P3 (France), KIT and DESY (Germany), INFN (Italy), SURF (Netherlands), PIC (Spain), GridPP (United Kingdom), RRCKI and Yandex LLC (Russia), CSCS (Switzerland), IFIN-HH (Romania), CBPF (Brazil), PL-GRID (Poland), and OSC (U.S.). We are indebted to the communities behind the multiple open-source software packages on which we depend. Individual groups or members have received support from AvH Foundation (Germany); EPLANET, Marie Skłodowska-Curie Actions and ERC (European Union); ANR, Labex P2IO and OCEVU, and Région Auvergne-Rhône-Alpes (France); Key Research Program of Frontier Sciences of CAS, CAS PIFI, and the Thousand Talents Program (China); RFBR, RSF, and Yandex LLC (Russia); GVA, XuntaGal, and GENCAT (Spain); the Royal Society and the Leverhulme Trust (United Kingdom); Laboratory Directed Research and Development program of LANL (U.S.). [1] 1 R. Aaij ( LHCb Collaboration ) , Phys. Rev. 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NIMAER 0168-9002 10.1016/j.nima.2005.08.106

Funders | Funder number |
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Not added | ST/J004332/1, ST/N000250/1, ST/K003410/1, 1796908, ST/N000331/1, ST/L003163/1, ST/N000242/1 |

EPLANET | |

Key Research Program of Frontier Sciences of CAS | |

MSHE | |

OCEVU | |

XuntaGal | |

Yandex LLC | |

National Science Foundation | |

Alexander von Humboldt-Stiftung | |

Laboratory Directed Research and Development | |

Los Alamos National Laboratory | |

H2020 Marie Skłodowska-Curie Actions | |

CERN | |

Science and Technology Facilities Council | ST/N000234/1, GRIDPP |

Leverhulme Trust | |

Royal Society | |

European Research Council | |

Deutsche Forschungsgemeinschaft | |

Agence Nationale de la Recherche | |

Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | 166208 |

National Natural Science Foundation of China | |

Russian Foundation for Basic Research | |

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior | |

Bundesministerium für Bildung und Forschung | |

Chinese Academy of Sciences | |

Nederlandse Organisatie voor Wetenschappelijk Onderzoek | |

Generalitat Valenciana | |

Conselho Nacional de Desenvolvimento Científico e Tecnológico | |

Instituto Nazionale di Fisica Nucleare | |

Narodowe Centrum Nauki | |

Ministerstwo Nauki i Szkolnictwa Wyższego | |

Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro | |

Ministry of Science and Technology, Taiwan | |

National Academy of Sciences of Ukraine | |

Centre National de la Recherche Scientifique | |

Financiadora de Estudos e Projetos | |

Russian Science Foundation | |

Région Auvergne-Rhône-Alpes | |

Recruitment Program of Global Experts | |

Institut national de physique nucléaire et de physique des particules | |

Sociedad Española de Reumatología |