XYZ-like spectra from Laplace sum rule at N2LO in the chiral limit

Abstract

We present new compact integrated expressions of QCD spectral functions of heavy-light molecules and four-quark [Formula: see text]-like states at lowest order (LO) of perturbative (PT) QCD and up to [Formula: see text] condensates of the Operator Product Expansion (OPE). Then, by including up to next-to-next leading order (N2LO) PT QCD corrections, which we have estimated by assuming the factorization of the four-quark spectral functions, we improve previous LO results from QCD spectral sum rules (QSSR), on the [Formula: see text]-like masses and decay constants which suffer from the ill-defined heavy quark mass. PT N3LO corrections are estimated using a geometric growth of the PT series and are included in the systematic errors. Our optimal results based on stability criteria are summarized in Tables 11–14 and compared, in Sec. 10, with experimental candidates and some LO QSSR results. We conclude that the masses of the [Formula: see text] observed states are compatible with (almost) pure [Formula: see text], [Formula: see text] molecule or/and four-quark states. The ones of the [Formula: see text], [Formula: see text] molecule/four-quark states are about 1.5 GeV above the [Formula: see text] mesons experimental candidates and hadronic thresholds. We also find that the couplings of these exotics to the associated interpolating currents are weaker than that of ordinary [Formula: see text] mesons [Formula: see text] and may behave numerically as [Formula: see text] (respectively [Formula: see text]) for the [Formula: see text], [Formula: see text] (respectively [Formula: see text], [Formula: see text]) states which can stimulate further theoretical studies of these decay constants.