Analysis of the Quantum Numbers <em><strong>J</strong>^PC</em> of the X(3872) Particle

Article

Reference

Analysis of the Quantum Numbers J

of the X(3872) Particle

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We present an analysis of angular distributions and correlations of the X(3872) particle in the exclusive decay mode X(3872)→J/ψπ+π− with J/ψ→μ+μ−. We use 780  pb−1 of data from pp collisions at s√=1.96  TeV collected with the CDF II detector at the Fermilab Tevatron. We derive constraints on spin, parity, and charge conjugation parity of the X(3872) particle by comparing measured angular distributions of the decay products with predictions for different JPC hypotheses. The assignments JPC=1++ and 2−+ are the only ones consistent with the data.

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Analysis of the Quantum Numbers J

of the X(3872) Particle. Physical Review Letters , 2007, vol. 98, no. 13, p. 132002

DOI : 10.1103/PhysRevLett.98.132002

Available at:

http://archive-ouverte.unige.ch/unige:38375

Disclaimer: layout of this document may differ from the published version.

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Analysis of the Quantum Numbers J

of the X(3872) Particle

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J. Zhou,⁵³and S. Zucchelli⁵ (CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Baylor University, Waco, Texas 76798, USA

5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

6Brandeis University, Waltham, Massachusetts 02254, USA

7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA

9University of California, San Diego, La Jolla, California 92093, USA

10University of California, Santa Barbara, Santa Barbara, California 93106, USA

11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

16Duke University, Durham, North Carolina 27708, USA

17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

18University of Florida, Gainesville, Florida 32611, USA

19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

20University of Geneva, CH-1211 Geneva 4, Switzerland

21Glasgow University, Glasgow G12 8QQ, United Kingdom

22Harvard University, Cambridge, Massachusetts 02138, USA

23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

132002-2

24University of Illinois, Urbana, Illinois 61801, USA

25The Johns Hopkins University, Baltimore, Maryland 21218, USA

26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

27High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

28Center for High Energy Physics: Kyungpook National University, Taegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea and SungKyunKwan University, Suwon 440-746, Korea

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

30University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom

32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

34Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8 and University of Toronto, Toronto, Canada M5S 1A7

35University of Michigan, Ann Arbor, Michigan 48109, USA

36Michigan State University, East Lansing, Michigan 48824, USA

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 87131, USA

39Northwestern University, Evanston, Illinois 60208, USA

40The Ohio State University, Columbus, Ohio 43210, USA

41Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom

44University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

47Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

49Purdue University, West Lafayette, Indiana 47907, USA

50University of Rochester, Rochester, New York 14627, USA

51The Rockefeller University, New York, New York 10021, USA

52Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855, USA

54Texas A&M University, College Station, Texas 77843, USA

55Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 02155, USA

58Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 48201, USA

60University of Wisconsin, Madison, Wisconsin 53706, USA

61Yale University, New Haven, Connecticut 06520, USA (Received 21 December 2006; published 28 March 2007)

We present an analysis of angular distributions and correlations of theX3872particle in the exclusive decay mode X3872 !J= withJ= !. We use780 pb¹of data fromppcollisions at ps

1:96 TeVcollected with the CDF II detector at the Fermilab Tevatron. We derive constraints on spin, parity, and charge conjugation parity of the X3872 particle by comparing measured angular distributions of the decay products with predictions for differentJ^PChypotheses. The assignmentsJ^PC 1and2are the only ones consistent with the data.

DOI:10.1103/PhysRevLett.98.132002 PACS numbers: 14.40.Gx, 12.39.Mk, 13.25.Gv

The recent discovery of the X3872 particle [1,2] has revived general interest in charmonium spectroscopy. The exact nature of this particle is still unknown. Attempts to explain the X3872 particle as a conventional bound quark-antiquark state have shortcomings, such as devia- tions from mass predictions or violation of isospin conser- vation [3]. The close proximity of the X3872 particle

mass to theD⁰D⁰ mass threshold has raised the question whether the X3872 particle is an exotic form of matter [3]. The determination of the quantum numbers spin J, parity P, and charge conjugation parity C is of vital im- portance for establishing the nature of theX3872particle.

The evidence for the decay modeX3872 !J= [4] and the measurement of the dipion mass distribution [5], which

is in agreement with the decay mode X3872 !J= ⁰, are consistent with a C-even assignment. Reference [6]

observes an enhancement in the D⁰D⁰⁰ mass spec- trum and concludes that, if assigned to theX3872parti- cle, low values for the spin quantum number are favored.

Neglecting effects from model uncertainties in the dipion mass spectrum (see [5]), preliminary results from [7] favor J^PC1. In this Letter we report the angular distribu- tions in the decayX3872 !J= ,J= !, and compare them with predictions for differentJ^PCstates.

The analysis is independent of any specific model of the internal structure of theX3872particle. We consider all allowed states up to spin two andC-odd spin three states.

We use a sample of pp collisions at a center-of-mass energy of

ps

1:96 TeVwith an integrated luminosity of 780 pb¹ collected with the CDF II detector at the Fermilab Tevatron. The CDF II detector [8] consists of a magnetic spectrometer surrounded by electromagnetic and hadronic calorimeters and muon detectors. The tracking system is composed of a silicon microstrip detector [9]

surrounded by an open-cell drift chamber called the central outer tracker (COT) [10]. We detect muons in planes of multiwire drift chambers [11] in the pseudorapidity range jj 1:0. TheJ= !decays used in this analysis are recorded using a dimuon trigger, which requires two oppositely charged COT tracks matched to muon cham- ber track segments with an invariant mass from 2.7 to 4:0 GeV=c².

The basic event selection is described in [2,5], although we do not cut on the dipion mass. Additional criteria are imposed on the number of candidates per event, the trans- verse momentum p_T of the X3872 particle candidate (>6 GeV=c), the p_T of the J= (>4 GeV=c), and the kinetic energy released in theX3872particle decay,Q mJ= mJ= m (<100 MeV=c²), where mJ= is from [12]. The cuts are chosen to optimize the significanceS=

SB

p of the observed signal, whereSand

Bare the fitted number of signal and combinatorial back- ground events in a1:5window centered on theX3872 particle mass. The resulting distribution of the invariant J= mass is shown in Fig.1.

To simulate the decays ofX3872 particle states with specific J^PC assumptions, we first generate phase-space decays ofX3872 !J= , J= !. Detec- tor effects are included using parameterized efficiencies and acceptances. This sample is weighted according to each specificJ^PChypothesis using the corresponding ma- trix elementMtotdescribed below.

The decay of the narrowX3872 particle is modeled as the sequential two-body decay chain X3872 ! J= , J= ! and the decay of the inter- mediate () state to . Assuming low relative angular momentum between the pions and conservation of C parity, the intermediate pion state can be in either a relative S-wave (_S) or a P-wave (⁰) state. Mtot is

formed by the product of a matrix element Mi for each decay and a term Tm, which describes the mass dependence of the intermediate () system. Because of the very narrow width of the intermediateJ= , we can neglect theJ= mass dependence.

With fixed helicities the angular dependence of a two- body decay amplitude is given by the Wigner function D^Ji

i;i;1_i;2 [13,14], where J_i and _i are the spin and helicity of the decaying particle, and _i;1 and_i;2 are the helicities of the child particles in the parent rest frame. The function is multiplied by two Clebsch-Gordan coefficients, coupling the spins of the child particles to their summed spinS_i, andS_iwith their relative angular momentumL_ito J_i.

In general, in theX3872 !J= decay there is more than one combination to form J fromLandSin a parity-conserving way. Of the independent amplitudes cor- responding to these combinations, only the ones with low- est L, assumed to be dominant, are taken into account. If more than one amplitude remains, mixing parameters are introduced to describe the physical state. Since the virtual photon in the J= ! decay can be treated as transverse, helicity combinations with 0 are neglected.

The dependence ofMtoton the dipion mass has model ambiguities. Therefore, we do not use the information from m to distinguish between different J^PC hypotheses.

The influence of the mmodel on the angular distri- butions via acceptance effects is very small. Nevertheless we choose for allJ^PChypotheses the same model for the m-dependent terms, which agrees with the m spectrum measurement. In this way, no hypothesis is re- jected due to a wrong m model. In detail, we fix Tm to a relativistic Breit-Wigner formula with mass and width of a ⁰ [12]. Following [5], we also fix the momentum dependence of the matrix element of the

2 ] ) [ GeV/c π-

π+

ψ m(J/

3.65 3.7 3.75 3.8 3.85 3.9 3.95 4

2 entries / 2.5 MeV/c

0 1000 2000 3000 4000 5000

6000 20 285 ± 228 ψ(2s)

113 X(3872)

± 2292

FIG. 1 (color online). The J= mass spectrum after optimizing the selection cuts, fitted by a double Gaussian func- tion for the 2S (left), a Gaussian function for theX3872 particle (right), and a second order polynomial for the combi- natorial background.

132002-4

! decay to k f₁k, where k is the magnitude of the three-momentum of one of the pions in the () rest frame and f₁k is a Blatt-Weisskopf form factor [15] to counter the divergence for rising k. This form factor has the effective sizerof the particle as a free parameter which we set to a common choice ofr 1 fm.

A weight is formed from the square of the total matrix elementMtot by averaging over all initial state helicities assuming unpolarized X3872 particle production, inco- herently summing over all final state helicities, and coher- ently summing over all intermediate state helicities.

The decay is described by the decay angles _X, _J= ,

J= ,, , and, as defined in Fig.2. For unpo- larized X3872 particle production and because of rota- tional symmetry, theJ^PC of theX3872particle and the () system affect the distribution of only four varia- bles:m,cos_J= ,cos, and.

The angular distributions are analyzed with a three- dimensional fit to take into account their correlations.

From simulation studies, the optimal binning is determined to be three bins injjj ₂j, and two bins in each of jcos_J= jandjcosj, where absolute values are used to exploit final state charge symmetry. The invariant J= mass spectrum is fitted in each of the resulting 12 bins in a mass window of 110 MeV=c² around the X3872 particle position using a binned maximum like- lihood fit, where the bin width is2:5 MeV=c². The distri- bution is described by a Gaussian function for theX3872 particle and a second order polynomial for the background.

The position and width of the Gaussian function describing theX3872particle are first determined from a fit to the full invariant mass spectrum and are then fixed in the subsequent fits. We compare the fitted yield as a function of the angular variables with the predictions for different J^PC assignments by forming a ² based on statistical uncertainties of the measurement. We determine the nor- malization of the simulated distributions from the mea- surement so that 11 degrees of freedom remain.

The decay amplitude for the state withJ^PC1 con- sists of threeLS-terms with the sameLvalue; theJ^PC 2 state has an amplitude with two LS-terms (see TableI). None of the1 terms describes the data alone, so we fit for a mixed state by minimizing the². For the 2state, the amplitude forS1is sufficient to describe the data.

TableIshows the² for eachJ^PCassignment. We find that only the assignmentsJ^PC1 and2are able to describe the data. All other states are rejected by more than 3 standard deviations (²prob:2:710³). Figure 3 shows the measurement and the expected distribution for four of the assignments.

An important cross-check of the analysis is to verify whether the correct result is obtained for the 2S, with TABLE I. Result of the X3872 particle angular analysis.

Listed are the state, the decay mode, the L and S quantum numbers of the J= - system, the² with 11 degrees of freedom and the²probability.

J^PC decay LS ²(11 d.o.f.) ²prob.

1 J= ⁰ 01 13.2 0.28

2 J= ⁰ 11,12 13.6 0.26

1 J= _S 01 35.1 2:410⁴

2 J= _S 11 38.9 5:510⁵

1 J= _S 11 39.8 3:810⁵

2 J= _S 21 39.8 3:810⁵

3 J= _S 31 39.8 3:810⁵

3 J= _S 21 41.0 2:410⁵

2 J= ⁰ 02 43.0 1:110⁵

1 J= ⁰ 10,11,12 45.4 4:110⁶

0 J= ⁰ 11 104 3:510¹⁷

0 J= _S 11 129 110²⁰

0 J= ⁰ 00 163 110²⁰

π/2|

π| - Φ -

∆

||

X(3872) yield / bin volume

0 50 100 150 200 250 300 350 400 450

0 0.63 1.15 π/2

0 0.63 1.15 0 0.63 1.15π/2 π/2

0 0.63 1.15 π/2 )| < 0.6

ψ

θJ/

|cos( |cos(θ_J/ψ)| > 0.6

π)|

θπ

|cos(

< 0.5

π)|

θπ

|cos(

> 0.5

π)|

θπ

|cos(

< 0.5

π)|

θπ

|cos(

> 0.5

FIG. 3 (color online). Measured 3D angular distribution with acceptance corrected predictions for J^PC0 (solid line), 1 (dotted line), 2 (dashed line), and 1 (dash-dotted line). The plot is divided into 22regions, corresponding to intervals of jcos_J= jandjcosj. Each region shows the distribution ofjjj ₂jin 3 bins. The bin contents have been scaled to the same bin volume.

µ+ µ−

J/ψ π− π+

φJ/ψ

− π 2 φ_ππ µ−

J/ψ π+

π− µ+

θJ/ψ

θππ

θX _{X ππ}

∆Φ

X ππ

FIG. 2 (color online). Definition of the decay angles. The polar angles () are calculated from the parent momenta and the child momenta in the corresponding parent rest frame.

known quantum numbers J^PC1, which decays into the same exclusive final state as theX3872particle. For the1assignment, the fit probability is 1.5%. Using the 2Smodel of Novikov and Shifman [16], which includes a small D-wave admixture in the description of the () system, the fit probability is 17.9%. The sensitiv- ity to such a small admixture is only present in the high statistics 2S sample. The next best modelJ^PC2 has a fit probability of 0.58%, and all other hypotheses that were tested yielded fit probabilities smaller than210⁶. We vary several inputs to the fitting procedure and the model of theX3872particle to investigate the stability of the ². Figure 4 shows the resulting ² values for the different J^PC hypotheses for the variations investigated.

The default analysis is shown as variation (1). The follow- ing effects are considered: (2)/(3) decrease/increase the fit window by 20 MeV=c², (4)/(5) decrease/increase the bin width to 2:0=2:86 MeV=c², (6)/(7) vary fixed X3872 particle mass by1, (8)/(9) vary fixedX3872particle width by1.

To evaluate the contribution to the systematic uncer- tainty from our choice of themspectrum, the follow- ing variations are considered: (10) fix form-factor r to 0.001 fm, (11) fix form-factor r to 100.0 fm, (12) use simple phase space form.

Finally, systematic uncertainty due to details concerning the simulation has been considered by varying distributions for (13)p_Tand (14)of theX3872particle, switching off (15) a p_T dependent efficiency correction for the pions, (16) a dependent correction of the COT, and (17) an

effective correction used to model the position of the generated primary vertex. All variations are consistent with 1 and2 being the only likely assignments.

A conventional explanation for theX3872resonance is a charmonium (cc) state. In this picture, the state with J^PC1could be identified with the⁰_c1and the assign- ment J^PC2 with the_c2. An exotic interpretation is that the X3872 particle is a molecular state or that a significant four-quark interaction contributes to the wave- function [17]. The result of this analysis is compatible with the models of a molecular state developed by Tornqvist [18] and Swanson [19], who predict the quantum numbers J^PC1for a boundDDstate.

In summary, a spin-parity analysis of theX3872 par- ticle in the final state has been performed.

The method of helicity amplitudes has been used to ana- lyzeX3872 !J= _SandX3872 !J= ⁰ transi- tions. Using a ² approach to compare expected angular distributions with measured distributions, it is found that only the C-even assignments J^PC1 and 2, both decaying viaJ= ⁰, describe the data. All other states are excluded at 99.7% confidence level.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.

This work was supported by the U. S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Founda- tion; the A.P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK; the Institut National de Physique Nucleaire et Physique des Particules/

CNRS; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain;

the European Community’s Human Potential Programme under Contract No. HPRN-CT-2002-00292; and the Academy of Finland.

aVisiting scientist from University of Athens.

bVisiting scientists from University of Bristol.

cVisiting scientist from University Libre de Bruxelles.

dVisiting scientists from Cornell University.

eVisiting scientist from University of Cyprus.

fVisiting scientist from University of Dublin.

gVisiting scientist from University of Edinburgh.

hVisiting scientist from University of Heidelberg.

iVisiting scientists from Universidad Iberoamericana.

jVisiting scientist from University of Manchester.

χ2

10 20 30 40 50

no. analysis variation for X(3872)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1++

2-+

1--

2+-

1+-

3--

2++

1-+

11 d.o.f. > 3σ

FIG. 4. Total²for different analysis variations on the y-axis, explained in the text. Vertical bars are added for visual guidance.

The²values of the spin 0 states are all above 100. The2and 3states have the same angular distribution as the1state.

132002-6

kVisiting scientist from Nagasaki Institute of Applied Science.

lVisiting scientist from University de Oviedo.

mVisiting scientist from University of London, Queen Mary and Westfield College.

nVisiting scientists from Texas Tech University.

oVisiting scientist from IFIC (CSIC-Universitat de Valencia).

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