Measurement of the Dipion Mass Spectrum in <em>X(3872)</em>-&gt;<em>J/ψπ⁺π⁻</em> Decays

Article

Reference

Measurement of the Dipion Mass Spectrum in X(3872) -> J/ψπ

π

Decays

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al.

Abstract

We measure the dipion mass spectrum in X(3872)→J/ψπ+π− decays using 360  pb−1 of pp collisions at s√=1.96  TeV collected with the CDF II detector. The spectrum is fit with predictions for odd C-parity (S13, P11, and DJ3) charmonia decaying to J/ψπ+π−, as well as even C-parity states in which the pions are from ρ0 decay. The latter case also encompasses exotic interpretations, such as a D0D*0 molecule. Only the S13 and J/ψρ hypotheses are compatible with our data. Since S13 is untenable on other grounds, decay via J/ψρ is favored, which implies C=+1 for the X(3872). Models for different J/ψ−ρ angular momenta L are considered. Flexibility in the models, especially the introduction of ρ−ω interference, enables good descriptions of our data for both L=0 and 1.

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the Dipion Mass Spectrum in X(3872) -> J/ψπ

π

Decays. Physical Review Letters , 2006, vol. 96, no. 10, p.

102002

DOI : 10.1103/PhysRevLett.96.102002

Available at:

http://archive-ouverte.unige.ch/unige:38323

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

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Measurement of the Dipion Mass Spectrum in X3872 ! J=

Decays

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(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

14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

15Duke University, Durham, North Carolina 27708, USA

16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

17University of Florida, Gainesville, Florida 32611, USA

18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

19University of Geneva, CH-1211 Geneva 4, Switzerland

20Glasgow University, Glasgow G12 8QQ, United Kingdom

102002-2

21Harvard University, Cambridge, Massachusetts 02138, USA

22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014 Helsinki, Finland

23University of Illinois, Urbana, Illinois 61801, USA

24The Johns Hopkins University, Baltimore, Maryland 21218, USA

25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

27Center 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

28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

29University of Liverpool, Liverpool L69 7ZE, United Kingdom

30University College London, London WC1E 6BT, United Kingdom

31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

33University of Michigan, Ann Arbor, Michigan 48109, USA

34Michigan State University, East Lansing, Michigan 48824, USA

35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

36University of New Mexico, Albuquerque, New Mexico 87131, USA

37Northwestern University, Evanston, Illinois 60208, USA

38The Ohio State University, Columbus, Ohio 43210, USA

39Okayama University, Okayama 700-8530, Japan

40Osaka City University, Osaka 588, Japan

41University of Oxford, Oxford OX1 3RH, United Kingdom

42Istituto Nazionale di Fisica Nucleare, University of Padova, Sezione di Padova-Trento, I-35131 Padova, Italy

43LPNHE-Universite de Paris, 6/IN2P3-CNRS, France

44University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

45Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

46University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

47Purdue University, West Lafayette, Indiana 47907, USA

48University of Rochester, Rochester, New York 14627, USA

49The Rockefeller University, New York, New York 10021, USA

50Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome, ‘‘La Sapienza,’’ I-00185 Roma, Italy

51Rutgers University, Piscataway, New Jersey 08855, USA

52Texas A&M University, College Station, Texas 77843, USA

53Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy

54University of Tsukuba, Tsukuba, Ibaraki 305, Japan

55Tufts University, Medford, Massachusetts 02155, USA

56Waseda University, Tokyo 169, Japan

57Wayne State University, Detroit, Michigan 48201, USA

58University of Wisconsin, Madison, Wisconsin 53706, USA

59Yale University, New Haven, Connecticut 06520, USA (Received 16 December 2005; published 17 March 2006)

We measure the dipion mass spectrum in X3872 !J= decays using 360 pb¹ of pp collisions atps

1:96 TeV collected with the CDF II detector. The spectrum is fit with predictions for oddC-parity (³S₁,¹P₁, and³D_J) charmonia decaying toJ= , as well as evenC-parity states in which the pions are from⁰ decay. The latter case also encompasses exotic interpretations, such as a D⁰D⁰molecule. Only the³S₁andJ= hypotheses are compatible with our data. Since³S₁is untenable on other grounds, decay viaJ= is favored, which impliesC 1for theX3872. Models for different J= angular momenta L are considered. Flexibility in the models, especially the introduction of !interference, enables good descriptions of our data for bothL0and 1.

DOI:10.1103/PhysRevLett.96.102002 PACS numbers: 14.40.Gx, 12.39.Mk, 13.25.Gv

The charmoniumlikeX3872stands as a major spectro- scopic puzzle. Its mass [1– 4] and what is known of its decays make assignments to the normal spectrum of cc states problematic [5,6]. Its remarkable proximity to the D⁰D⁰ mass —indistinguishable within uncertainties —

has fueled speculations that it is a loosely bound deuteron- like D⁰D⁰ ‘‘molecule,’’ i.e., a uc c u system [1,7].

Although a molecule is prominent among exotic interpre- tations, others have been proffered [8]. Non-qqmesons are allowed within QCD, but an unequivocal example remains

elusive. Even as a conventional meson, the X3872 re- mains interesting, as theccspectrum above the 3770is not well known.

Insight into the X3872 is offered by the dipion mass spectrum inX!J= . Belle observed a preference for highmasses, contrary to expectations for triplet-D cc states [9]— the naive interpretation. Belle noted that X!J= ⁰ decay — isospin violating for charmonium — produces high masses, and thus may be a hint for aD⁰D⁰ molecule. Dipion spectra have been published [1,10], and a preliminary analysis partially based onmasses argues for aJ^PC 1 assignment [6], consistent with that ex- pected for aD⁰D⁰ molecule.

At the Tevatron, large X3872 samples are available, albeit with high backgrounds. Previously, we have mea- sured theXmass and confirmed the propensity for high masses [2]. We also have made a preliminary measurement of the inclusive production fraction arising frombhadrons [11]. Here we measure themass spectrum.

We use a sample of pp collisions at ps

1:96 TeV collected with the Collider Detector at Fermilab (CDF II) between February 2002 and August 2004. The detector is described in detail elsewhere [12], and only the most relevant components for this analysis are summarized here. The central tracking system is immersed in a 1.4 T solenoidal magnetic field for the measurement of charged particle momenta p_T transverse to the beam line. It is composed of six layers of silicon-strip detectors (L00 [13] and SVX [14]) surrounded by an open-cell drift chamber called the central outer tracker (COT) [15]. The active volume of the COT is a 3.1 m long cylinder with 8 superlayers of 12 wires each. The outermost detection system is planes of multilayer drift chambers for detecting muons [16]. The central muon system (CMU) coversjj 0:6, where pseudorapidity ln tan=2andis the angle of the particle with respect to the direction of the proton beam. Additional chambers (CMX) extend the muon coverage tojj 1:0.

A dimuon trigger is used to obtain a J= ! sample. At level 1 of a three-level trigger system, the extremely fast tracker (XFT) [17] uses COT information to select tracks based on p_T. XFT tracks with p_T 1:52:0 GeV=c are extrapolated to the CMU (CMX) chambers and compared with the positions of muon- chamber tracks. The event passes level 1 if two or more XFT tracks are matched to muon tracks. Opposite-charge and opening-angle cuts are imposed at level 2. At level 3, full COT tracking information is used to reconstruct candidates. Events with candidates from 2.7 to 4:0 GeV=c² in mass are recorded for further analysis.

This analysis [18] is based on an integrated luminosity of360 pb¹. Candidate selection follows Ref. [2] with two exceptions (see below). After constraining candi- dates to a common vertex, the dimuon mass must be within 60 MeV=c² (4 standard deviations) of the J= mass

[19]. This 1 degree of freedom (d.o.f.) fit must have²<

15. Pairs of charged tracks, each with p_T 0:4 GeV=c and assumed to be pions, are fit with thetracks to a common vertex. In this fit, the dimuon mass is constrained to theJ= mass, and we demand²<25(6 d.o.f.). We re- duce combinatorial backgrounds by requiringp_TJ=

4 GeV=c and R0:7 for both pions, where R ^{2 2}

p ,is the difference in azimuthal angle between the J= system and the pion, andis the difference in pseudorapidity. The mass range for the sam- ple includes bothX3872and 2Ssignals [2]; the latter is used as a control sample.

We depart from Ref. [2] by dropping a cut on the number of candidates allowed per event [20]. This removes a pos- sible bias and improves the X signal at highmasses.

We also add fiducial criteria:p_TJ= >6 GeV=cand jJ= j<0:6. This eliminates the region of rapidly changing efficiency and sacrifices 25% of the 2S yield, leaving 11 500220 2S mesons. We have 1260130X3872 candidates for m>500 MeV=c² [2].

To extractdN=dmspectra, we divide the sample into

‘‘slices’’ ofmand fit eachJ= mass distribution for the signal per slice. The J= mass fits use a Gaussian for theX3872signal and an exponential times power law for the background. We also fit the 2S control signal in the same way, but use two Gaussians for the better defined shape arising from the larger 2S signal. As slices may have small signals —or none at all — we inhibit the fit from latching onto fluctuations by fixing the position and width of the signal to values from full-sample fits. Sample slices are shown in Fig. 1.

The fitteddN=dm yield is corrected for detector and selection efficiencies determined by Monte Carlo simula- tion. Only the efficiencies relative to other mslices are needed. An important input affecting the efficiency is the production p_T spectrum. For the X3872, there is no a priori model, and we rely upon data. The generated spectra, exponentials raised to a quadratic polynomial in p_T, are adjusted until the simulation, after detector and reconstruction effects, reproduces the respective X3872 or 2Sspectra of the data. We use a parametrization of the well-knownmshape of the 2Sfor both states.

Uncertainties on our mass spectra are dominated by statistics, but we examined two sources of systematic effects: the fits for signal yields and the efficiency corrections.

To check the yield stability, we changed the width of the J= fit range of 200 MeV=c² by 50 MeV=c², altered the signal and background models, and allowed the signal mean and width to float. We saw no bias in the yields, but nevertheless allotted an uncertainty based on the statistical precision to which we could observe one:

3:6 2Sand8:4X3872candidates per slice. The high- est threeXslices —highest two for the 2S— are treated 102002-4

specially for effects near the upper kinematic limit: the background begins to turn on under the signal, and reso- lution effects can distort the signal shape in the mass fit.

Yield systematics are assigned to these slices based on variations in the fit model for these issues.

The other type of uncertainty is from the efficiency corrections. The 2S model for dN=dm is inexact.

We assign an uncertainty based on phase space as an alternate shape — including retuning the p_T spectrum.

The ratio of the alternate correction to the nominal one quantifies the change in shape of the efficiency when switching from the 2S-likedN=dm to phase space.

The ratio of efficiencies for the 2Sgives an uncertainty

&3%over what will be the main region of interest,m>

360 MeV=c², and by &2:5% for the X3872 above 570 MeV=c². For the uncertainty in the mesonp_T spectra, we use alternate spectra 1 standard deviation steeper and shallower in theirp_Tfalloff based on the errors from thep_T spectrum fit to the data. We again take the ratio of the new efficiencies relative to the nominal shape to quantify the uncertainty. For the mass ranges of interest the 2S variation is almost 3%, but less than 1% for the X. The p_Tspectrum of theXis more poorly measured than for the 2S; but with higher dipion masses, theXsuffers smaller variations in efficiency, and thus a smaller uncertainty.

The dN=dm spectrum for our 2S control signal, after corrections and including systematic uncertainties, is shown in Fig. 2 with a scale preserving the raw fitted yield of 11 500 candidates. It agrees well with results from the BES Collaboration using a sample of 20 000 events [21].

This is reflected by the mutual agreement in fits to a QCD multipole expansion model [22]. BES obtained0:336 0:0090:019 for this model’s single shape parameter

‘‘B=A,’’ whereas our fit yields 0:3420:022 (6.9% fit probability). The systematic uncertainties are incorporated in this and laterXfits, including themcorrelations in the efficiency uncertainties.

TheX3872dipion spectrum is shown in Fig. 3. We fit our data with multipole expansion calculations forC-odd

ccoptions [23]. The³D_J states are a natural choice for the X according to potential models [5]. A fit of ³D_J ! J= [22] is unacceptable with a ² of 113 for 14 d.o.f. The¹P₁ !J= [24] fit is worse (²=d:o:f:

146=14). The 2S spectrum is similar to that of theX, and indeed, our³S₁[22] fit to theXhas a 28% probability.

However, no new³S₁ccstate can be near3872 MeV=c²as the 3Slies at4040 MeV=c² [5].

The above C-odd states produce dipions, to lowest L between the pions, with J^PC0. C-even states yield 1 isovector dipions, which we associate with the ⁰. Isospin conservation suppressesccdecays toJ= . Thus, this mode is seen as suggestive of aD⁰D⁰molecule [1,7].

Even as charmonium, however, theXmay break isospin by coupling toD⁰D⁰ due to its close proximity in mass.

We modelX!J= as a zero-width state decaying to two bodies by phase space generalized for angular mo- mentum Lof theJ= system, and theby a relativ- istic Breit-Wigner parametrization. That is, dN=dm/ k^2L1 f_LX² kjBj², wherek is theJ= momentum in the

X rest frame, B/

m

q = m²m²im,

0.3 0.4 0.5 0.6

2 (2S) yield per 10 MeV/cψ

0 200 400 600 800 1000

2] Mass [GeV/c π

π π-

π+

ψ

→ J/

(2S) Ψ

Multipole Expansion S1

3

CDF II 360 pb-1

FIG. 2 (color online). The CDF dipion mass spectrum for the 2Swith a fit of a QCD multipole expansion calculation for

3S₁[22].

2 Candidates per 5 MeV/c 0

100 200 300 400 500

3.8 3.9

CDF II 360 pb-1

± 39

= -15 NX

Fit Prob = 32%

< 570 MeV/c2 π

540 < mπ

3.8 3.9

π Ma π ψ J/

± 38

= 102 NX

Fit Prob = 30%

< 650 MeV/c2 π

625 < mπ

3.8 3.9 4

2] ss [GeV/c

± 35

= 165 NX

Fit Prob = 52%

< 710 MeV/c2 π

690 < mπ

3.9 4

± 30

= 182 NX

Fit Prob = 50%

< 765 MeV/c2 π

750 < mπ

FIG. 1 (color online). Examples of slices in dipion massmof theJ= mass distributions and theirX3872fits. The raw yieldsN_Xprior to efficiency corrections are quoted, and the arrow in the first panel marks theX3872mass.

m ₀ q=q₀³ m=m f₁q=f₁q₀²,q is themomentum in therest frame,q₀ qm,mis 775:8 MeV=c², and ₀ is 146.4 MeV. The f_Lip are f_0ip 1 and f_1ip 1R²_ip²¹⁼² [25], where R_i is a radius of interaction for meson ‘‘i.’’ TheR_iare poorly known. A common value for light mesons is 0.3 fm, but for Dmesons larger values like 1 fm are often taken [26]. We use these respective values forR andR_X.

Fits with thismodel are shown in Fig. 3 forL0and 1. HigherLsoftens the falloff at the high kinematic limit, worsening the agreement: the fit probability goes from 55% for L0 down to 7.7% for L1 [27]. The P-wave fit is somewhat disfavored, but the results are sensitive to R_X and R. The latter probability can be increased by loweringR or raisingR_X.

Another modeling uncertainty is the effect of!in- terference. Belle reports evidence for X!J= ⁰ and interprets it as decay via a virtual !. As such, they measure the ratio ofJ= !toJ= branching ratiosR3=2

to be 1:00:40:3 [28]. The rate of !! is normally negligible, but its interference effects may not be.

We generalize jBj² to jABeⁱA_!B_!2j² in dN₂=dm, where A and A_! are (positive) decay am- plitudes viaand!, and is their relative phase. Using dN₃=dm₃/ jA_!B_!3j² for J= ⁰ [29], R3=2

determines jA_!=Aj given . We take a of 95, the value if the only phase is from!! decaying via ! mixing [30]. Similar phases are seen in ee ! [31]. The!fraction is small (<10%), but inter- ference is constructive and contributes23%for bothL, preferentially at high masses. Fits with this model are shown in Fig. 4, along with the breakdown into interfer- ence and ‘‘pure’’and!parts. The probability is 19% for theSfit, and 53% for thePfit. The results are not critically dependent onR3=2: probabilities remain above 7% over a 1 standard deviation span of Belle’s R3=2 for both L

values. ThePfit is sensitive toandR_X, as is shown in the inset. We conclude that there is ample flexibility in models ofX!J= of either Lto accommodate the data.

In summary, we measured the dipion mass spectrum in X3872 !J= . Our spectrum is inconsistent with calculations for ¹P₁ and ³D_J charmonia. A good fit is obtained for X!J= ⁰, an interpretation supported by recent evidence for theC-even decayX!J= [28]. Our data are compatible with bothS- andP-waveJ= decays, where in the latter case this is partly due to modeling uncertainties. The P fit benefits from constructive! interference at levels implied by the rate of X! J= ⁰. TheJ= interpretation does not by itself distinguish betweenC-even charmonia (e.g.,1 or2) and exotic options like a1 D⁰D⁰molecule.

We thank E. Eichten, S. Olsen, P. Ko, Y.-P. Kuang, and C. Quigg for helpful discussions, and 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 Foundation; the A. P. Sloan Foundation;

the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foun- dation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, U.K.; the Russian Foundation for Basic Research;

the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; in part by the European Community’s Human

0.6 0.7

2 X(3872) yield per 20 MeV/c 0

50 100 150 200 250

2] Mass [GeV/c π

π

Total ρ Intrf

ω

L=1 L=0

Phase [degrees] ω

ρ-

-100 0 100 200 300

[fm]

X

R

0.40.2 0.80.6 1

Probability [%]

0 10 20 30 40 50

ψρ

→ J/

P-Wave X

CDF II 360 pb-1

FIG. 4 (color online). A blowup of theX3872spectrum with J= fits which include !interference (95 phase) with relative amplitudes set by R3=21:0. Fits for both L0 (lines) and 1 (shaded regions) are shown, along with their decomposition into , !, and interference terms. The inset showsL1fit probabilities as a function ofandR_Xin 5%

contours.

0.4 0.6 0.8

2 X(3872) yield per 20 MeV/c

-50 0 50 100 150 200 250

2] Mass [GeV/c π

π π-

π+

ψ

→ J/

X(3872) (L=0) ρ ψ J/

(L=1) ρ ψ J/

S1 3

1 x 5

1P DJ 3

: c Multipole Expansions for c CDF II 360 pb-1

FIG. 3 (color online). The dipion mass spectrum for the X3872 and fits to various hypotheses (see text). The fitted curve for the¹P₁ model is scaled up by a factor of 5 for better visibility.

102002-6

Potential Programme under Contract No. HPRN-CT-2002- 00292; and the Academy of Finland.

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