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Abstract
We calculate the masses of χc(2P) and χb(3P) states with threshold corrections in a coupled-channel model. Here, the meson quarkonium core is augmented by higher Fock components due to pair-creation effects. According to our results, we interpret the resonances characterized by very small threshold corrections, like χb(3P)'s, as almost pure quarkonia, and those states characterized by non-negligible threshold corrections, like the X(3872), as quarkonium cores plus meson–meson components. We also study the J/ψρ and J/ψω hidden-flavor strong decays of the X(3872). The decays are calculated as the dissociation of one of these components (D0D¯0⁎) into a cc¯ state (J/ψ) plus a light meson (ρ or ω) in a potential model. In particular, our result for the ratio between the X(3872)→J/ψω and J/ψρ widths (0.6) is compatible with the present experimental data (0.8±0.3) within the experimental error.
Highlights
In the latest years, several new quarkonium-like states, the so-called XY Z mesons, have been included in the PDG [1]
We interpret the resonances characterized by very small threshold corrections, like χb(3P )’s, as almost pure quarkonia, and those states characterized by non-negligible threshold corrections, like the X(3872), as quarkonium cores plus meson-meson components
The previous states are labeled as suspected exotics and interpreted as compact tetraquark states [7,8,9,10,11,12,13,14,15,16,17,18], meson-meson molecules [19,20,21,22,23,24,25,26,27,28,29], the result of kinematic or threshold effects caused by virtual particles [30,31,32,33,34,35,36,37,38,39], hadro-quarkonia [40,41,42,43,44,45,46,47,48,49], or the rescattering effects arising by anomalous triangular singularities [50,51,52]; see Ref. [53], where the X(4260), with 1−− quantum numbers, was interpreted as a member of the first hybrid supermultiplet
Summary
Several new quarkonium-like states, the so-called XY Z mesons, have been included in the PDG [1]. We discuss a coupled-channel model to compute the physical masses of quarkonium-like mesons, Ma, with threshold corrections This is done under the following hypotheses: a) Only the closest complete set of accessible SU(N)flavor⊗ SU(2)spin open-flavor meson-meson intermediate states (e.g. 1S1S, 1S1P or 1S2S) can influence the multiplet structure. It is worth noting that: I) Our theoretical predictions agree with the data within the typical error of a QM calculation, of the order of 30 − 50 MeV; II) Among the χc(2P ) multiplet members, the χc1(2P ) receives the largest contribution from the continuum This nonnegligible continuum contribution, resulting in a large self-energy correction, is necessary to lower the relativized QM prediction, 3.95 GeV, towards the observed value of the mass, 3871.69 MeV [1]; III) In the χc(2P ) case, threshold effects break the usual mass pattern of a χ-type multiplet, namely Mχ0 < Mχ1 ≈ Mh < Mχ2.
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