Towards Meson Spectroscopy Instead of Bump Hunting

Mesonic resonances are generally observed in data as narrow, moderately broad, or wide peaks in scattering or production processes. In the eyes of nearly all experimentalists, any suchlike bump is a true resonance as soon as its statistical significance exceeds certain minimal values. However, this simple point of view ignores possible effects from competing hadronic channels and the opening of the corresponding thresholds. On the other hand, most theoretical hadron-model builders consider mesons merely bound states of a quark and an antiquark, or of more exotic combinations sometimes involving valence gluons as well. Also the latter description is much too naive, since considerable mass shifts or even the dynamical generation of extra states due to unquenching are equally ignored. In the present paper, a largely empirical yet very successful approach to meson spectroscopy is revisited, in which all the above phenomena can be accounted for non-perturbatively, with concrete examples of some enigmatic mesonic states described in detail. First, the X(4260) charmonium enhancement is argued to be a non-resonant structure resulting from depletion effects due to competing channels and resonances. Then, the X(3872) charmonium-like meson is described as a unitarised $J^{PC}=1^{++}$ $c\bar{c}$ state. Also, the unusual pattern of masses and widths of the open-charm axial-vector mesons $D_1(2420)$, $D_1(2430)$, $D_{s1}(2536)$, and $D_{s1}(2460)$ is shown to follow from highly non-perturbative coupled-channel and mixing effects. Finally, first indications of a very light scalar boson are presented, on the basis of published BABAR data.Comment: Invited seminar given by G. Rupp at the International School of Nuclear Physics, 33rd course: "From Quarks and Gluons to Hadrons and Nuclei", Erice, Sicily, Italy, 16 - 24 September 2011; 7 pages, 5 figures (9 plots), style of Progress in Particle and Nuclear Physic

Multichannel calculation for Ds* vector states and the Ds(2632) resonance

We study bound states below threshold and resonances above threshold in the D0-K+ and Ds-eta systems, using a many-coupled-channel model for non-exotic meson-meson scattering applied to states with the quantum numbers of c-sbar quark-antiquark vector mesons. We fit the ground state at 2.112 GeV, whence the lowest resonances in D0-K+ come out at 2.61, 2.72, 3.03, and 3.08 GeV. The resonance at 2.61 GeV acquires a width of about 8 MeV, while its partial P-wave cross section is up to six times larger in Ds-eta than in D0-K+, provided a mechanism accounting for Okubo-Zweig-Iizuka--forbidden decays is included. The latter finding is in agreement with the observations of the SELEX collaboration with respect to the recently reported DsJ(2632) resonance. Therefore, we conclude that the DsJ(2632) is most probably the first recurrence excitation of the Ds*(2112) meson.Comment: 11 pages, 6 figures; v2: Significant improvements for threshold behavior, and for the hadronic widths by including additional two-meson channels. Misprints in formulas correcte

Multichannel calculation of the very narrow Ds0∗(2317)D_{s0}^*(2317) and the very broad D0∗(2300−2400)D_0^*(2300-2400)

The narrow $D_{s0}^{\ast}$(2317) and broad $D_0^{\ast}$(2300-2400) charmed scalar mesons and their radial excitations are described in a coupled-channel quark model that also reproduces the properties of the light scalar nonet. All two-meson channels containing ground-state pseudoscalars and vectors are included. The parameters are chosen fixed at published values, except for the overall coupling constant $\lambda$, which is fine-tuned to reproduce the $D_{s0}^{\ast}$(2317) mass, and a damping constant $\alpha$ for subthreshold contributions. Variations of $\lambda$ and $D_0^{\ast}$(2300-2400) pole postions are studied for different $\alpha$ values. Calculated cross sections for $S$-wave $DK$ and $D\pi$ scattering, as well as resonance pole positions, are given for the value of $\alpha$ that fits the light scalars. The thus predicted radially excited state ${D_{s0}^*}'$(2850), with a width of about 50 MeV, seems to have been observed already.Comment: 3 pages, EPJ LaTeX, 2 Postscript figures, 1 table; parallel talk at the IVth International Conference on Quarks and Nuclear Physics (QNP06), Madrid, 5-10 June 200

Coupling constants and transition potentials for hadronic decay modes of a meson

Within the independent-harmonic-oscillator model for quarks inside a hadron, a rigorous method is presented for the calculation of coupling constants and transition potentials for hadronic decay, as needed in a multi-channel description of mesons.Comment: 19 pages, 4 figure

A very broad X(4260) and the resonance parameters of the 3D vector charmonium state

We argue that the X(4260) enhancement contains a wealth of information on vector c-cbar spectroscopy. We discuss the shape of the X(4260) observed in the OZI-forbidden process "electron-positron into J/psi and a pair of charged pions", in particular at and near vector charmonium resonances as well as open-charm threshold enhancements. The resulting very broad X(4260) structure does not seem to classify itself as a vector charmonium resonance, but its detailed shape allows to identify new vector c-cbar states. Here, we estimate the resonance parameters of the psi(3D) state.Comment: 4 pages, 5 figures; version 2: 2 figures replace

D_{sJ}(2860) as the first radial excitation of the D_{s0}^*(2317)

A coupled-channel model previously employed to describe the narrow $D_{s0}^*$(2317) and broad $D_0^*$(2400) charmed scalar mesons is generalized so as to include all ground-state pseudoscalar-pseudoscalar and vector-vector two-meson channels. All parameters are chosen fixed at published values, except for the overall coupling constant, which is fine-tuned to reproduce the $D_{s0}^*$(2317) mass. Thus, the radial excitations $D_{s0}^*$(2850) and $D_0^*$(2740) are predicted, both with a width of about 50 MeV. The former state appears to correspond to the new $D_{sJ}$(2860) resonance decaying to $DK$ announced by BABAR in the course of this work. Also the $D_0^*$(2400) resonance is roughly reproduced, though perhaps with a somewhat too low central resonance peak.Comment: Plain LaTeX, 4 pages, 2 Postscript figures; v2: REVTeX, 4 pages, introduction expanded, "Note added in proof" and references added, figures with more detail and improved quality, version accepted for publication in Physical Review Letter

Continuum bound states K-long, D_{1}(2420), D_{s1}(2536) and their partners K-short, D_{1}(2400), D*_{sJ}(2463)

The very recently observed $D^{\ast}_{sJ}(2463)$ meson is described as a $J^{P}=1^{+}$ $c\bar{s}$ bound state in a unitarised meson model, owing its existence to the strong OZI-allowed $^{3}P_{0}$ coupling to the nearby $S$-wave $D^{\ast}K$ threshold. By the same non-perturbative mechanism, the narrow axial-vector $D_{s1}(2536)$ resonance shows up as a quasi-bound-state partner embedded in the $D^{\ast}K$ continuum. With the same model and parameters, it is also shown that the preliminary broad $1^{+}$ $D_{1}(2400)$ resonance and the established narrow $1^{+}$ $D_{1}(2420)$ may be similar $c\bar{n}$ partners, as a result of the strong OZI-allowed $^{3}P_{0}$ coupling to the nearby $S$-wave $D^{\ast}\pi$ threshold. The continuum bound states $D_{1}$(2420) and $D_{s1}(2536)$ are found to be mixtures of 33% $^{3}P_{1}$ and 67% $^{1}P_{1}$, whereas their partners $D_{1}(2400)$ and $D^{\ast}_{sJ}(2463)$ have more or less the opposite $^{2S+1}P_1$-state content, but additionally with some $D^{\ast}\pi$ or $D^{\ast}K$ admixture, respectively. The employed mechanism also reproduces the ratio of the $K_{L}$-$K_{S}$ mass difference and the $K_{S}$ width, by describing $K_{L}$ as a bound state embedded in the $\pi\pi$ continuum. The model's results for $J^{P}=1^{+}$ states containing one $b$ quark are also discussed.Comment: 11 pages, plain LaTeX, v2:relation to work of Kokoski and Godfrey in conclusions and more references v3:B-states included. More reference

Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. A=T/V and Im(A)=T*A, are fulfilled, while in the small-coupling limit the usual isobar model is recovered.Comment: 16 pages, 3 figures, plain LaTeX

Relativistic Unitarized Quark/Meson Model in Momentum Space

An outline is given how to formulate a relativistic unitarized constituent quark model of mesons in momentum space, employing harmonic quark confinement. As a first step, the momentum-space harmonic-oscillator potential is solved in a relativistically covariant, three-dimensional quasipotential framework for scalar particles, using the spline technique. Then, an illustrative toy model with the same dynamical equations but now one $q\bar{q}$ and one meson-meson channel, coupled to one another through quark exchange describing the $^3P_0$ mechanism, is solved in closed form on a spline basis. Conclusions are presented on how to generalize the latter to a realistic multichannel quark/meson model.Comment: Plain LaTeX, 12 pages, 2 EPS figures. Contribution to the Second International Workshop on Hadron Physics, Effective Theories of Low Energy QCD, 25-29 September, 2002 (Coimbra, Portugal