In 2003 the X(3872) particle was discovered by the Belle collaboration.
Despite results collected since then, the nature of the state still remains
unclear. In this contribution we report on new results on properties of the
X(3872) state using data collected with CDF II detector at the Fermilab
Tevatron. The dipion mass spectrum and angular distributions are used to
determine the $J^{PC}$ quantum numbers of the state.Comment: ICHEP Moscow 2006 proceedings, added missed referenc

Kreps, M.

English

arXiv

In 2003 the X(3872) particle was discovered by the Belle collaboration. Despite results collected since then, the nature of the state still remains unclear. In this contribution we report on new results on properties of the X(3872) state using data collected with CDF II detector at the Fermilab Tevatron. The dipion mass spectrum and angular distributions are used to determine the J{sup PC} quantum numbers of the state

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arXiv:hep-ex/0611004 v2   6 Nov 2006November 6, 2006 14:51 WSPC/Trim Size: 10in x 7in for Proceedings ichep2006˙krepsNEW RESULTS ON X(3872) FROM CDFM. KREPS∗ ON BEHALF OF THE CDF COLLABORATIONInstitut fu¨r Experimentelle Kernphysik, University of Karlsruhe, Germany∗E-mail: kreps@ekp.uni-karlsruhe.deIn 2003 the X(3872) particle was discovered by the Belle collaboration. Despite results collectedsince then, the nature of the state still remains unclear. In this contribution we report on newresults on properties of the X(3872) state using data collected with CDF II detector at the FermilabTevatron. The dipion mass spectrum and angular distributions are used to determine the JPCquantum numbers of the state.Keywords: X(3872); charmonium; exotic mesons.1. IntroductionThe recent discovery of the X(3872) state1,2led to new interest in charmonium spec-troscopy. It was found in a search for miss-ing charmonium resonances. Despite enor-mous experimental and theoretical effort itsexact nature is still unknown. Shortcomingsof conventional explanations and the proxim-ity of the D0D∗0 threshold have raised ques-tions whether theX(3872) could be an exoticform of matter, e.g. a mesonic molecule, ccghybrid, etc.Important for the understanding of theX(3872) state are the quantum numbers spinJ , parity P and charge conjugation parityC. Here we present a determination of thesequantum numbers using X(3872) → J/ψpipidecays collected by the CDF II detector3.As quantities sensitive to the JPC quantumnumbers, the dipion invariant mass and theangular distributions are used. In both cases,the measured distributions are compared tothe predictions for different JPC hypothesisto infer the JPC quantum numbers.Details of the presented analysis can befound in Ref.4,5.2. Theoretical predictionsTo obtain predictions for different JPC com-binations, we consider the X(3872) decay asa sequence of two-body decays. First, theX(3872) decays to the J/ψ and (pipi)s,p sys-tem, which is followed by decays J/ψ →µ+µ− and (pipi)s,p → pi+pi−. In this view,the full decay amplitude is given by threeamplitudes, one for each of the two-body de-cays and two ”propagators”, which connectvertices of the two-body decays. The am-plitudes for the decay vertices are obtainedusing the helicity formalism.The final amplitude for a given JPC hy-pothesis is obtained from the squared totalmatrix element by averaging over all initialstate helicities, incoherently summing overall final state helicities and coherently sum-ming over intermediate state helicities.The angular distributions are deter-mined fully by the matrix elements for thevertices, which for the fixed helicities aregiven by the Wigner functions. In generalmore than one possibility to form spin J fromthe relative angular momentum L and spinS of the daughter particles exist. Of theseindependent amplitudes, only the ones withlowest L are used, as the higher L amplitudesare usually suppressed.The ”propagator” for the J/ψ is mod-elled by a δ function due to the very smallwidth of the J/ψ. For the (pipi) system”propagator”, the situation is more compli-cated as any description has some unknowns1FERMILAB-CONF-06-392-ENovember 6, 2006 14:51 WSPC/Trim Size: 10in x 7in for Proceedings ichep2006˙kreps2inside, which doesn’t allow one to make aprecise prediction. For the (pipi) systemin the S-wave we use multipole expansion6.The (pipi) system in P-wave is described bythe intermediate ρ resonance for which weuse a relativistic Breit-Wigner formuladΓXdmpipi= 2mpipiΓX(mpipi) · 2mρΓρ(mpipi)(m2pipi −m2ρ)2 +m2ρΓ2ρ(mpipi)In a case of broad resonances such as ρ thewidth in the Breit-Wigner formula has to bymodified toΓρ = Γ0,ρ(k∗k∗0)2L+1(f(k∗)f(k∗0))2(mm0)due to the variation of the kinematic factoracross the width. Here, k∗ is the momentumof the decay product in the centre-of-masssystem of the decaying particle and f(k∗) isa form-factor. The model suggested by Blattand Weisskopf is used in our analysis7. Thismodel has one free parameter, which is theeffective radius of the resonance for whichtypical values are in the range from 0.3 fm to1 fm8. Another complication arises from pos-sible ρ-ω interference, which is also includedin our description.3. ResultsThe first distribution, to which we look isdipion invariant mass distribution4. It isshown in Figure 1. The 3S1,1P1 and3DJmultipole expansion for charmonia and L =0 and L = 1 decay to the J/ψ ρ were tested.Out of the tested models the 3S1 multipoleexpansion and both L = 0 and L = 1 decayto the J/ψ ρ are able to fit the data. While3S1 multipole expansion is able to describedata, it is disfavoured as this would be in ten-sion with non-observation of the X(3872) bythe BES experiment9. Therefore only decaysto J/ψ ρ remain as a viable options for theX(3872) decay. Unfortunately, at the cur-rent level of understanding, it is not possi-ble to distinguish between L = 0 or L = 1decays. The main reason is the uncertaintyin the modelling of the dipion mass shape.With reasonable parameters for the form-factors both can describe data. If we allowin addition ρ-ω mixing, for certain mixingphases, the L = 1 describes data even betterthan L = 0. This conclusion is in contra-diction to the conclusion by Belle10. Theorigin of this disagreement stems from dif-ferent modelling of the dipion mass distri-bution. The model used by the Belle col-laboration doesn’t include the form-factor inthe Breit-Wigner formula. If we drop theform-factor from the description, the CDFdipion mass distribution is also inconsistentwith the L = 1 decay to the J/ψ ρ. As it isnot clear which model is the correct one andtherefore, one should remain cautious at thisstage.In order to gain more information on theproperties of the X(3872) we now considerangular distributions5. The angles describ-ing the decay are defined in Figure 2. Outof all angles, for unpolarised production, onlythree are sensitive to the JPC quantum num-bers. Those are θJ/ψ, θpipi and ∆Φ. Thelast sensitive variable is the dipion invariantmass, but as we saw, there is considerableambiguity in modelling. Therefore to avoidwrong conclusions, we fix the dipion massdistribution to an L = 0 ρ Breit-Wigner,which was found to describe data.To extract angular distributions from0.4 0.6 0.82X(3872) yield per 20 MeV/c-50050100150200250]2 Mass [GeV/cpipi-pi+piψ J/→X(3872)  (L=0)ρ ψJ/ (L=1)ρ ψJ/1S3 x 51P1JD3:cMultipole Expansions for c-1            CDF II   360 pbFig. 1. Dipion invariant mass distribution with thepredictions from multipole expansions and L = 0 andL = 1 decay to J/ψ ρ.November 6, 2006 14:51 WSPC/Trim Size: 10in x 7in for Proceedings ichep2006˙kreps3data, a slicing technique with a binned max-imum likelihood fit is used, where the back-ground is described by a second order poly-nomial and the signal by a Gaussian. Theposition and width of the Gaussian are fixedto the result of the fit to the full sample. Inorder to increase the discriminating powerof the analysis, we exploit also correlationsamong the angles by usage of a 3-dimensionalfit. We use 3×2×2 binning, where three binsare used for ∆Φ angle. The measured distri-butions are shown in Figure 3 together withthe expectations for several JPC hypotheses.To quantify the agreement between data andexpectations, a χ2 comparison is done. Theresulting χ2 values for different assignmentsare shown in Table 1. From the results we−pi+pi−µ+µψJ/J/ψθpipiθθ XXpipiµ +-µJ/ ψ +pi-pi−pi2pipiφJ/ψφX pipi∆ΦFig. 2. Definition of the angles used in the angularanalysis./2|pi| - pi - Φ ∆||X(3872) yield / unit volume01002003004005000 0.63 1.15 /2pi0 0.63 1.15 /2pi0 0.63 1.15 /2pi0 0.63 1.15 /2pi)| < 0.6 ψJ/θ|cos( )| > 0.6 ψJ/θ|cos()| < 0.5 pi piθ|cos( )| > 0.5 pi piθ|cos( )| < 0.5 pi piθ|cos( )| > 0.5 pi piθ|cos(CDF Run II Preliminary -1 780pb≈L X(3872)data pointsacc. correctedprediction for++p0--s1++p1-+p2Fig. 3. Measured angular distributions (points)with expectations for several JPC (lines).conclude, that only the 1++ and 2−+ assign-ments are able to describe data, while all theothers are excluded by more than 3 σ.Table 1. Result of the angular analysis forall tested assignments.hypothesis 3D χ2 / 11 d.o.f. χ2 prob.1++ 13.2 27.8%2−+ 13.6 25.8%1−− 35.1 0.02%2+− 38.9 5.5·10−51+− 39.8 3.8·10−52−− 39.8 3.8·10−53+− 39.8 3.8·10−53−− 41.0 2.4·10−52++ 43.0 1.1·10−51−+ 45.4 4.1·10−60−+ 103.6 3.5·10−170+− 129.2 ≤1·10−200++ 163.1 ≤1·10−202χ0 10 20 30 40 50no. systematic check for X(3872)1234567891011121314151617CDF Run II Preliminary ++1-+2--1+-2+-1--3++2-+111 d.o.f. σ> 3Fig. 4. Variation of the total χ2 for different analy-sis variation. Vertical error bars are for visual guid-ance.To evaluate the stability of the result, weinvestigate several effects. The result of theinvestigation is shown in Figure 4, where thex-axis shows the resulting χ2, while the y-axis denotes the studied effect. The defaultanalysis is shown as variation 1. We inves-tigate the following variations: 2,3 variationin the fit window, 4,5 variation of the binwidth, 6,7 variation of the Gaussian posi-tion, 8,9 variation of the Gaussian width, 10-12 variations in the dipion mass distribution,November 6, 2006 14:51 WSPC/Trim Size: 10in x 7in for Proceedings ichep2006˙kreps413,14 variation of the pT and η distributionof theX(3872) and 15-17 variation of the de-tails of acceptance correction. From Figure 4we conclude, that none of the studied effectscan alter the conclusion of the analysis.4. Interpretation andConclusionsAfter constraining the quantum numbers ofthe X(3872) we come back to the questionof the nature of X(3872). The natural ex-planation is that the X(3872) is a conven-tional charmonium state. In this picture thestate with JPC = 1++ could be identifiedwith χ′c1 and the JPC = 2−+ with the 11D2state. However in both cases there is somedifficulty with the conventional explanationas the predicted masses11 are different thanthe observed value. In addition the decayto J/ψ ρ would violate isospin. But thesearguments alone are not enough to rule outconventional charmonium.The curious fact that the mass is closeto the D0D∗0threshold gives raise to thespeculations about exotic interpretation ofthe X(3872). The most popular exotic inter-pretation is that it is D0D∗0molecule. Theidea of the molecular interpretation datesback to mid seventies 12. Recently the mod-els of a molecular state were developed byTornqvist13 and Swanson14. For a molecu-lar state they predict the quantum numbersJPC = 1++, which is compatible with theresult of the analysis.It should be added, that the recent obser-vation of the X(3872)→ D0D0pi0 by Belle15prefers the 1++ assignment compared to the2−+.To conclude we presented a determina-tion of the JPC quantum numbers of theX(3872) state using dipion invariant massdistribution and angular analysis. We find,that only the assignments 1++ and 2−+ areable to describe data. All other tested assign-ments are excluded by more than 3 sigma.While this result significantly constrains JPCboth the conventional charmonium explana-tion and the exotic one are still viable op-tions. To distinguish them further studiesboth from experiment and theory side areneeded.AcknowledgementsThis work was partially supported by theEuropean Community’s Human PotentialProgramme under contract HPRN-CT-2002-00292.References1. S. K. Choi et al., Phys. Rev. Lett. 91, 262001(2001)2. D. Acosta et al., Phys. Rev. Lett. 93, 072001(2004)3. D. Acosta et al., Phys. Rev. D71, 032001(2005)4. A. Abulencia et al., Phys. Rev. Lett. 96,102002 (2006)5. CDF Collaboration, Analysis of the quantumnumbers of the X(3872), CDF Public Note82016. Y.-P. Kuang, S. F. Tuan and T.-M. Yan,Phys. Rev. D37, 1210 (1988)7. J. M. Blatt and V. F. Weisskopf, TheoreticalNuclear Physics, John Wiley & Sons, NewYourk 19528. S. Kopp et al., Phys. Rev. D63, 092001(2001); H. Albrecht et al., Phys. Lett. B308,435 (1993); D. Aston et al., Nucl. Phys.B296, 493 (1988)9. C. Z. Yuana, X. H. Mo and P. Wanga, Phys.Lett. B579, 74 (2004)10. K. Abe et al., Lepton-Photon 2005,hep-ex/050503811. T. Barnes and S. Godfrey, Phys. Rev. D69,054008 (2004)12. M.B. Voloshin and L.B. Okun, JTEP Lett.23, 333 (1976); A. De Rujula, H. Georgiand S. L. Glashow, Phys. Rev. Lett. 38, 317(1977)13. N. A. Tornqvist, Phys. Lett. B590, 209(2004)14. E. S. Swanson, Phys. Lett. B588, 189 (2004)15. K. Abe et al., hep-ex/0608031, Submittedto Phys. Rev. Lett.

New results on X(3872) from CDF

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New Results on X(3872) from CDF

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