XYZ -SU3 breakings from Laplace sum rules at higher orders

Abstract

We present new compact integrated expressions of SU3 breaking corrections to QCD spectral functions of heavy{light molecules and four-quark XY Z-like states at lowest order (LO) of perturbative (PT) QCD and up to d = 8 condensates of the Operator Product Expansion (OPE). Including next-to-next-to-leading order (N2LO) PT correc- tions in the chiral limit and next-to-leading order (NLO) SU3 PT corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results for the XY Z-like masses and decay constants from QCD spectral sum rules (QSSR). Systematic errors are estimated from a geometric growth of the higher order PT corrections and from some partially known d = 8 nonperturba- tive contributions. Our optimal results, based on stability criteria, are summarized in Tables 18-21 while the 0++ and 1++ channels are compared with some existing LO results in Table 22. One can note that, in most channels, the SU3 corrections on the meson masses are tiny: ≤ 10% (respectively ≤ 3%) for the c (respectively b)-quark chan- nel but can be large for the couplings (≤ 20%). Within the lowest dimension currents, most of the 0++ and 1++ states are below the physical thresholds while our predictions cannot discriminate a molecule from a four-quark state. A comparison with the masses of some experimental candidates indicates that the 0++ X(4500) might have a large D∗s0 D∗s0 molecule component while an interpretation of the 0++ candidates as four- quark ground states is not supported by our findings. The 1++ X(4147) and X(4273) are compatible with the D∗s0Ds, D∗s00Ds1 molecules and/or with the axial-vector Ac four- quark ground state. Our results for the 0-±, 1-± and for different beauty states can be tested in the future data. Finally, we revisit our previous estimates1 for the D∗0 D∗0 and D∗0 D1 and present new results for the D1 D1.