$Z_c$-like spectra from QCD Laplace sum rules at NLO

International audienceWe present a global analysis of the observed Zc, Zcs, and future Zcss-like spectra using (inverse) Laplace sum rule within stability criteria. Integrated compact QCD expressions of the leading order spectral functions up to dimension-six condensates are given. Next-to-leading order factorized perturbative contributions are included. We reemphasize the importance to include pertubative radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at leading order in the literature. We also demonstrate that, contrary to a qualitative large Nc counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the Laplace sum rule predictions. Our results are summarized in Tables III to VI. The Zc(3900) and Zcs(3983) spectra are well reproduced by the Tc(3900) and Tcs(3973) tetramoles (superposition of quasidegenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Zc(4025) or Zc(4040) state can be fitted with the D0*D1 molecule having a mass 4023(130) MeV while the Zcs bump around 4.1 GeV can be likely due to the Ds0*D1⊕D0*Ds1 molecules. The Zc(4430) could be a radial excitation of the Zc(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634∼6527) MeV. The double strange tetramole state Tcss, which one may identify with the future Zcss, is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass splittings of the tetramoles due to SU(3) breakings: MTcs-MTc≈MTcss-MTcs≃(73∼91) MeV