Abstract
We apply the diabatic framework, a QCD-based formalism for the unified study of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor meson-meson components, to the description of coupled-channel meson-meson scattering. For this purpose, we first introduce a numerical scheme to find the solutions of the diabatic Schr\"odinger equation for energies in the continuum, then we derive a general formula for calculating the meson-meson scattering amplitudes from these solutions. We thus obtain a completely nonperturbative procedure for the calculation of open-flavor meson-meson scattering cross sections from the diabatic potential, which is directly connected to lattice QCD calculations. A comprehensive analysis of various elastic cross sections for open-charm and open-bottom meson-meson pairs is performed in a wide range of the center-of-mass energies. The relevant structures are identified, showing a spectrum of quasiconventional and unconventional quarkoniumlike states. In addition to the customary Breit-Wigner peaks, we obtain nontrivial structures such as threshold cusps and minimums. Finally, our results are compared with existing data and with results from our previous bound-state--based analysis, finding full compatibility with both.
Highlights
Ever since the discovery of the χc1ð3872Þ back in 2003 [1], many quarkoniumlike meson states, whose properties defy the conventional description as heavy quark-antiquark bound states, have been discovered [2]
This scaled JPC cross section is more convenient for our theoretical analysis for a number of reasons: (i) it makes easier the distinction of resonances; (ii) it is a dimensionless quantity; (iii) it is not affected by the purely kinematical ðpðjÞÞ−2 behavior of the cross section, what allows for a more detailed study for energies close above threshold; (iv) it is symmetric under exchanges j ↔ j0, as per the detailed balance principle; (v) iPts j;vj0aσlujJ←ePCsj0 are bounded by the unitarity condition ≤ 1, where the maximum value of 1 is expected at the mass of an isolated resonance without nonresonant background
We have extended the diabatic framework, a QCD-based formalism for the description of quarkoniumlike systems in terms of QQand open flavor meson-meson components, to the study of coupled-channel meson-meson scattering
Summary
Ever since the discovery of the χc1ð3872Þ back in 2003 [1], many quarkoniumlike meson states, whose properties defy the conventional description as heavy quark-antiquark bound states, have been discovered [2]. A more general framework for the interaction of a QQpair (where Q stands for a heavy quark, b, or c) with an arbitrary number of meson-meson channels has been obtained through the implementation of the diabatic approach in QCD [21,22,23] This type of approach, first developed in molecular physics [24], has been applied to calculate the mass spectrum and OZI-allowed strong decay widths of charmoniumlike [21,22] and bottomoniumlike [23] states. The dynamics, including the Q-Qinteraction and the QQ –meson-meson mixing induced by string breaking, is completely described by a potential matrix whose elements are directly related to the static energy levels calculated in lattice QCD This diabatic potential matrix is plugged into a multichannel Schrödinger equation involving all the QQand mesonmeson components for a given set of JPC quantum numbers.
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