Abstract
We present a global analysis of the observed Z_c, Z_cs and future Z_css-like spectra using the inverse Laplace transform (LSR) version of QCD spectral sum rules (QSSR) within stability criteria. Integrated compact QCD expressions of the LO spectral functions up to dimension-six condensates are given. Next-to-Leading Order (NLO) factorized perturbative contributions are included. We re-emphasize the importance to include PT 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 LO in the literature. We also demonstrate that, contrary to a na\"ive qualitative 1/N_c counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the LSR predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973) tetramoles (superposition of quasi-degenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1 molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a radial excitation of the Z_c(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634-6527) MeV. The double strange tetramole state T_css which one may identify with the future Z_css is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs= (73- 91) MeV.
Highlights
We have applied the Laplace sum rules (LSR) for interpreting the new states around (6.2–6.9) GeV found by the LHCb group [41] to be a doubly/fully hiddencharm molecules ðQ QÞðQQ Þ and ðQ Q ÞðQQÞ tetraquarks states [42], while the new states found by the same group from the DK invariant mass [43] have been interpreted by a 0þ and 1− tetramoles slightly mixed with their radial excitations [44]
Compared to the previous nonstrange case where the molecule DÃD is quasidegenerated with the tetraquark Acd, which leads us to conclude that the observed state is a tetramole T c, in this channel, we find the tetraquark Acss is almost degenerated with the molecule DÃsDs and has the same couplings implying that it can be a tetramole T css state with a coupling and mass: fT css 1⁄4 114ð10Þ keV; MT css 1⁄4 4064ð46Þ MeV: ð29Þ
Introduced the tetramole states as a superposition of quasidegenerated molecules and tetraquark states having the same quantum numbers JPC with almost the same couplings strengths to the interpolating currents
Summary
Beyond the successful quark model of Gell-Mann [1] and Zweig [2], Rossi and Veneziano have introduced the four-quark states within the string model [3] in order to describe baryon-antibaryon scattering, while Jaffe [4] has. QCD spectral sum rules (QSSR) has been used to estimate the I 1⁄4 0 light scalar mesons (σ, f0,) masses and widths [8] assumed to be four-quark states. We have applied the Laplace sum rules (LSR) for interpreting the new states around (6.2–6.9) GeV found by the LHCb group [41] to be a doubly/fully hiddencharm molecules ðQ QÞðQQ Þ and ðQ Q ÞðQQÞ tetraquarks states [42], while the new states found by the same group from the DK invariant mass [43] have been interpreted by a 0þ and 1− tetramoles (superposition of almost degenerate molecules and tetraquark states having the same quantum numbers and couplings) slightly mixed with their radial excitations [44]. A narrow peak is experimentally found at (in units of MeV):
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