We present recent studies of charmonium multiquark states. We use different
interacting models and numerical methods to study deeply bound four-quark
states and meson-meson molecules. No deeply bound four-quark states are found
in our analysis. A nice description of the X(3872) is obtained as a
$D\bar{D}^*-J/\Psi\omega$ coupled channel state.Comment: 3 pages. Talk presented at the Conference MESON 2010, 10-15 june
  2010, Krakow, Poland. To be published in International Journal of Modern
  Physics 

ALFREDO VALCARCE

Isgur N.

JAVIER VIJANDE

English

arXiv

 We present recent studies of charmonium multiquark states. We use different interacting models and numerical methods to study deeply bound four-quark states and meson-meson molecules. No deeply bound four-quark states are found in our analysis. A nice description of the X (3872) is obtained as a [Formula: see text] coupled channel state. </jats:p

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International Journal of Modern Physics A

ON THE NATURE OF THE <font>X</font>(3872)

We present recent studies of charmonium multiquark states. We use different interacting models and numerical methods to study deeply bound four-quark states and meson-meson molecules. No deeply bound four-quark states are found in our analysis. A nice description of the X(3872) is obtained as a D (D) over bar* - J/Psi w coupled channel state

Valcarce Mejía, Alfredo

Vijande Asenjo, Javier

Repositori d'Objectes Digitals per a l'Ensenyament la Recerca i la Cultura

arXiv:1012.4630v1  [hep-ph]  21 Dec 2010December 22, 2010 1:13 WSPC/INSTRUCTION FILE valcarce-11B1-krakowInternational Journal of Modern Physics Ac© World Scientific Publishing CompanyON THE NATURE OF THE X(3872)A. VALCARCEDepartamento de F´ısica FundamentalUniversidad de Salamanca, Salamanca, Spainvalcarce@usal.esJ. VIJANDEDepartamento de F´ısica Ato´mica, Molecular y NuclearUniversidad de Valencia (UV) and IFIC (UV-CSIC), Valencia, Spainjavier.vijande@uv.esReceived Day Month YearRevised Day Month YearWe present recent studies of charmonium multiquark states. We use different interactingmodels and numerical methods to study deeply bound four-quark states and meson-meson molecules. No deeply bound four-quark states are found in our analysis. A nicedescription of the X(3872) is obtained as a DD∗− J/Ψω coupled channel state.Keywords: Mesons; multiquarks; charmonium.PACS numbers: 14.40.Gx, 21.30.Fe, 12.39.MkSince 2003 several states have been discovered in the charmonium mass region.While in the conventional description of charmonium in terms of quark-antiquarkpairs some states are still missing, the number of experimental states reported up tonow is larger than empty spaces in the cc¯ spectrum. This overpopulation, togetherwith other difficulties to explain observed states as simple quark-antiquark pairs,triggered discussions 1 on a possible exotic interpretation, four-quark states eitheras compact tetraquarks or slightly bound meson-meson molecules.Understanding of charmonium spectroscopy is challenging for experimentalistsand theorists alike. Charmonium has been used as the test bed to demonstrate thecolor Fermi-Breit structure of quark atoms obeying the same principles as ordinaryatoms 2. Its nonrelativistic character gave rise to an amazing agreement between ex-periment and simple quark potential model predictions as cc¯ states 3. The openingof charmed meson thresholds was expected to modify the trend in the constructionof quark-antiquark models. In the adiabatic approximation meson loops were ab-sorbed into the static interquark potential. Thus, close to the threshold productionof charmed mesons models required of an improved interaction 4.The discussion above suggests that charmonium spectroscopy could be rathersimple below the threshold production of charmed mesons but much more complex1December 22, 2010 1:13 WSPC/INSTRUCTION FILE valcarce-11B1-krakow2 A. Valcarce, J. Vijandeabove it. In particular, the coupling to the closest (cc¯)(nn¯) system, referred to asunquenching the naive quark model 5, could be an important spectroscopic ingre-dient. Therefore, hidden-charm four-quark states could explain the overpopulationof quark-antiquark theoretical states. Thus, the new experimental discoveries areoffering exciting new insights into the subtleties of the strong interaction.In an attempt to disentangle the role played by multiquark configurations in thecharmonium spectroscopy we obtained an exact solution of the four-body problembased on an infinite expansion of the four-quark wave function in terms of hyper-spherical harmonics 6. From our analysis, we concluded that those four-quark stateswith two different asymptotic physical thresholds (as it is the case of the cc¯nn¯ sys-tem that may split either into a (cc¯)(nn¯) or (cn¯)(nc¯) two-meson states) can hardlypresent a bound state since the interaction between any pair of quarks contributesto the energy of one of the two physical thresholds. Close to a threshold we haveused a different technique that we developed when studying baryon spectra withscreened potentials. We solved the Lippmann-Schwinger equation looking for attrac-tive channels that may contain a meson-meson molecule 7. In order to account forall basis states we allow for the coupling to charmonium-light two-meson systems.Thus, we consider the system of two mesonsM1 andM2 (Mi = D,D∗) in a relativeS−state interacting through a potential V that contains a tensor force, and there-fore there is a coupling to the M1M2 D−wave. Moreover, the two D-meson systemcan couple to a charmonium-light two-meson state, for example DD∗is coupled toJ/Ψω. We have consistently used the same interacting Hamiltonian to study thetwo- and four-quark systems to guarantee that thresholds and possible bound statesare eigenstates of the same Hamiltonian.Table 1. Attractive channels for the two D−meson systems.System DD DD∗D∗D∗JPC(I) 0++(0) 1++(0) 0++(0) 2++(0) 2++(1)Our results are shown in Table 1. This study has been the first systematic analy-sis of four-quark hidden-charm states as compact states or meson-meson molecules.For the first time we have performed a consistent study of all quantum numberswithin the same model. Our predictions robustly show that no deeply bound statescan be expected for this system. Only a few channels can be expected to presentobservable resonances or slightly bound states. Among them, we have found thatthe DD∗system must show a bound state slightly below the threshold for charmedmesons production with quantum numbers JPC(I) = 1++(0), that could corre-spond to the widely discussed X(3872). Of the systems made of a particle and itscorresponding antiparticle, DD and D∗D∗, the JPC(I) = 0++(0) is attractive. Itwould be the only candidate to accommodate a wide resonance for the DD sys-tem. For the D∗D∗the attraction is stronger and structures may be observed closeDecember 22, 2010 1:13 WSPC/INSTRUCTION FILE valcarce-11B1-krakowOn the nature of the X(3872) 3and above the charmed meson production threshold. Also, we have shown that theJPC(I) = 2++(0, 1) D∗D∗channels are attractive due to the coupling to the J/Ψωand J/Ψρ channels, respectively.Among these exotic theoretical states, charged states have an unique feature:by construction they cannot be accommodated into the conventional cc¯ spectrum.Two different experimental findings show positive results on charge charmoniummesons. The first one was a Ψ(2S)pi+ peak at about 4430 MeV/c2 observed by Bellein the B¯0 → Ψ(2S)pi+K− decays 8. A second positive observation was reported byBelle from the B0 → Ξc1pi+K− decay, with two resonances in Ξc1pi+ at massesof about 4050 and 4250 MeV/c2 9. In the first case, BaBar has presented its ownanalysis 10 performing a detailed study of the acceptance and possible reflectionsconcluding that no significant signal exists on the data. While the two experimentsmade different conclusion, the data itself seem to be in a reasonable agreementexcept for the lower available statistics of the BaBar experiment. The states foundin Ref. 9 could correspond to the D∗D∗JPC(I) = 2++(1) we have predicted 7.Its confirmation would represent a unique tool in discriminating among differenttheoretical models.Due to heavy quark symmetry, replacing the charm quarks by bottom quarksdecreases the kinetic energy without significantly changing the potential energy.In consequence, four-quark bottomonium mesons must also exist and have largerbinding energies. An experimental effort in this direction will confirm or rule outthe theoretical expectations. If the scenario presented here turns out to be correct,it will open a new interesting spectroscopic area.AcknowledgmentsThis work has been partially funded by the Spanish Ministerio de Educacio´n yCiencia and EU FEDER under Contract No. FPA2007-65748, by Junta de Castillay Leo´n under Contract No. GR12, and by the Spanish Consolider-Ingenio 2010Program CPAN (CSD2007-00042).References1. D. V. Bugg, J. Phys. G 37, 055002 (2010).2. N. Isgur and G. Karl, Phys. Tod. Nov. 1983, 36 (1983).3. E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane and T.-M. Yan, Phys. Rev. D 21,203 (1980).4. N. Isgur, Phys. Rev. D 60, 054013 (1999); E. J. Eichten, K. Lane and C. Quigg, Phys.Rev. D 69, 094019 (2004).5. F. E. Close, arXiv:0706.2709.6. J. Vijande, E. Weissman, N. Barnea and A. Valcarce, Phys. Rev. D 76, 094022 (2007).7. T. Ferna´ndez-Carame´s, A. Valcarce and J. Vijande, Phys. Rev. Lett. 103, 222001(2009).8. S. K. Choi et al. (Belle Collaboration), Phys. Rev. Lett. 100, 142001 (2008).9. R. Mizuk et al. (Belle Collaboration), Phys. Rev. D 78, 072004 (2008).10. B. Aubert et al. (BaBar Collaboration), Phys. Rev. D 79, 112001 (2009).

On the nature of the X(3872)

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