wave function, in the case of small binding, strongly limits the cc probability, which roughly lies in the range 7-11%, for the average experimental binding energy of 0.16 MeV and a between 2 and 3 GeV −1 . Furthermore, a reasonable value of 7.8 fm is obtained for the X(3872) r.m.s. radius at the latter binding energy, as well as an S-wave D 0 D * 0 scattering length of 11.6 fm. Finally, the S-matrix pole trajectories as a function of coupling constant show that X(3872) can be generated either as a dynamical pole or as one connected to the bare cc confinement spectrum, depending on details of the model. From these results we conclude that X (3872) is not a genuine meson-meson molecule, nor actually any other mesonic system with non-exotic quantum numbers, due to inevitable mixing with the corresponding quark-antiquark states. IntroductionThe Belle Collaboration discovered [1] the charmoniumlike state X(3872) almost a decade ago, observing it in the decay On the theory side, the discussion about the nature of X(3872) continues most vivid. Although the PDG [6] lists 1 ++ and 2 −+ as the meson's possible quantum numbers, and a recent BABAR analysis [9] of the 3π invariant mass distribution in the decay X(3872) → ωJ/ψ even seems to slightly favor the 2 −+ assignment, most model builders describe the state as an axial vector. For instance, model calculations of semi-inclusive B → η c2 + X processes [10] as well as electromagnetic η c2 decays [11] have been shown to disfavor the 2 −+ scenario. The same conclusion was reached in a tetraquark description of X(3872) [12], while pion exchange in a molecular picture would be repulsive in this case [13] and so inhibitive of a bound state. Finally, unquenching a 1 1 D 2 cc state by including meson-meson loops can only further lower the bare mass, which lies in the range 3.79-3.84 GeV for all quenched quark models we know of, thus making a 2 −+ charmonium resonance at 3.872 GeV very unlikely [14]. For further information and more references concerning X(3872), see e.g. a recent review [15], as well as our prior coupled-channel analysis [14].The first suggestion of possible meson-meson molecules bound by pion exchange, in particular a DD * 1 state with quantum numbers 1 ++ or 0 −+ , was due to Törnqvist [13]. With the discovery of X(3872) just below the D 0 D * 0 threshold, this idea was revived, of course. In the present paper, we intend to study the issue, not from Törnqvist's pion-exchange point of view, but rather as regards its possible implications for models based on quark degrees of freedom. In this context, it is worthwhile to quote from Ref. [16], in which a molecular interpretation is advocated (also see Ref.[17]):"Independent of the original mechanism for the resonance, the strong coupling transforms the resonance into a bound state just below the two-particle threshold if a > 0 or into a virtual state just above the two-particle threshold if a < 0. If a > 0, the 1 Henceforth, we omit the bar in DD * , for notational simplicity.

The last few years have been witness to a proliferation of new results concerning heavy exotic hadrons. Experimentally, many new signals have been discovered that could be pointing towards the existence of tetraquarks, pentaquarks, and other exotic configurations of quarks and gluons. Theoretically, advances in lattice field theory techniques place us at the cusp of understanding complex coupled-channel phenomena, modelling grows more sophisticated, and effective field theories are being applied to an ever greater range of situations. It is thus an opportune time to evaluate the status of the field. In the following, a series of high priority experimental and theoretical issues concerning heavy exotic hadrons is presented.

A multichannel calculation of excited J P C = 1 −− φ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the φ(2170) resonance, discovered by BABAR and originally denoted X(2175). In this framework, a complete spectrum of bare ss states is coupled to those OZI-allowed decay channels that should be most relevant for the considered energy range. The included S-and P -wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the qq sector both the 3 S1 and 3 D1 states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the φ(1020), but come out reasonably close to previously used values. Among the model's Tmatrix poles, there are good candidates for observed resonances, as well other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at (2186 − i246) MeV. The huge width makes its interpretation as the φ(2170) somewhat dubious, but further improvements of the model may change this conclusion.

We study the non-Breit-Wigner line-shape of the ψ(3770) resonance, predominantly a 1 3 D 1c c state, using an unitarized effective Lagrangian approach, including the one-loop effects of the nearby thresholds D + D − and D 0D0 . A fit of the theoretical result to the total cross-section e + e − → DD is performed, leading to a good description of data (χ 2 /d.o.f. ∼ 1.03). The partial cross sections e + e − → D 0D0 and e + e − → D + D − turn out to be separately in good agreement with the experiment. We find a pole at 3777−i12 MeV, that is within the Particle Data Group (PDG) mass and width estimation for this state. Quite remarkably, we find an additional, dynamically generated, companion pole at 3741 − i19 MeV, which is responsible for the deformation on the lower energy side of the line-shape. The width for the leptonic decay ψ(3770) → e + e − is 112 eV, hence smaller than the PDG fit of 262 ± 18 eV, yet in agreement with a recent experimental study. 45 monium seed state, which gets dressed by "clouds" of D + D − and D 0D0 mesons.Our aim is to study the deformation seen on the left side of the resonance in Ref.[9] with mesonic loops combined with the nearby thresholds. To this end, we use an effective relativistic Lagrangian approach in which a single vector state ψ ≡ ψ(3770) is coupled to channels D + D − and D 0D0 , as well as to lepton 50 pairs. The propagator of ψ is calculated at the resummed one-loop level and fulfills unitarization requirements. Then, we perform a fit of the four parameters of our approach, i.e. the effective couplings of ψ to DD and of ψ to leptons, the mass of ψ, and a cutoff responsible for the finite dimension of the ψ meson, to the experimental cross-section of the reaction e + e − → DD in Refs. [7] and 55[5], in the energy region up to 100 MeV above the D 0D0 threshold. We assume that the ψ(3770) resonance dominates in this energy range. We obtain a very good description of the data, which in turn allows us to determine in a novel and independent way the mass, width, and branching ratios of the ψ(3770).Moreover, we study in detail, to our knowledge for the first time, the poles of 60 this state. In fact, a pole was found in Ref. [16], using Fano resonances, at about 3778 − i14 MeV, though in lesser detail. Quite remarkably, we find two poles for this resonance, one which roughly corresponds to the peak of the resonance, the seed pole, and one additional dynamically generated pole, responsible for the enhancement left from the peak, which emerges due to the strong coupling function, turns out to be rather small, possibly due to the fact that the ψ(3770)

Masses and widths of the axial-vector charmed mesons D1(2420), D1(2430), Ds1(2536), and Ds1(2460) are calculated nonperturbatively in the Resonance-Spectrum-Expansion model, by coupling various open and closed meson-meson channels to the bare J P = 1 + cq (q = u, d) and cs states. The coupling to two-meson channels dynamically mixes and lifts the mass degeneracy of the spectroscopic 3 P1 and 1 P1 states, as an alternative to the usual spin-orbit splitting. Of the two resulting S-matrix poles in either case, one stays very close to the energy of the bare state, as a quasi-bound state in the continuum, whereas the other shifts considerably. This is in agreement with the experimental observation that the D1(2420) and Ds1(2536) have much smaller widths than one would naively expect. The whole pattern of masses and widths of the axial-vector charmed mesons can thus be quite well reproduced with only two free parameters, one of which being already strongly constrained by previous model calculations. Finally, predictions for pole positions of radially excited axial-vector charmed mesons are presented.