The large-Nc limit of borelized spectral sum rules and the slope of radial Regge trajectories

We put forward a new phenomenological method for calculating the slope of radial trajectories from values of ground states and vacuum condensates. The method is based on a large-[Formula: see text] extension of borelized spectral sum rules. The approach is applied to the light nonstrange vector, axial and scalar mesons. The extracted values of slopes proved to be approximately universal and are in the interval [Formula: see text] GeV2. As a by-product, the given method leads to prediction of the second radial trajectory with ground state mass lying near 0.6 GeV.

XYZ-SU3 breakings from Laplace sum rules at higher orders

We present new compact integrated expressions of SU3 breaking corrections to 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). Including next-to-next-to-leading order (N2LO) PT corrections 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 [Formula: see text]-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 [Formula: see text] nonperturbative contributions. Our optimal results, based on stability criteria, are summarized in Tables 18–21 while the [Formula: see text] and [Formula: see text] 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: [Formula: see text] (respectively [Formula: see text]) for the [Formula: see text] (respectively [Formula: see text])-quark channel but can be large for the couplings ([Formula: see text]). Within the lowest dimension currents, most of the [Formula: see text] and [Formula: see text] 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 [Formula: see text] [Formula: see text] might have a large [Formula: see text] molecule component while an interpretation of the [Formula: see text] candidates as four-quark ground states is not supported by our findings. The [Formula: see text] [Formula: see text] and [Formula: see text] are compatible with the [Formula: see text], [Formula: see text] molecules and/or with the axial-vector [Formula: see text] four-quark ground state. Our results for the [Formula: see text], [Formula: see text] and for different beauty states can be tested in the future data. Finally, we revisit our previous estimates1 for the [Formula: see text] and [Formula: see text] and present new results for the [Formula: see text].

Large-Nc masses of light mesons from QCD sum rules for nonlinear radial Regge trajectories

The large-[Formula: see text] masses of light vector, axial, scalar and pseudoscalar mesons are calculated from QCD spectral sum rules for a particular ansatz interpolating the radial Regge trajectories. The ansatz includes a linear part plus exponentially degreasing corrections to the meson masses and residues. The form of corrections was proposed some time ago for consistency with analytical structure of Operator Product Expansion of the two-point correlation functions. We revised that original analysis and found the second solution for the proposed sum rules. The given solution describes better the spectrum of vector and axial mesons.

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

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.

Nature of the X(5568) — A critical Laplace sum rule analysis at N2LO

We scrutinize recent QCD spectral sum rules (QSSR) results to lowest order (LO) predicting the masses of the [Formula: see text] molecule and [Formula: see text] four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the [Formula: see text]-quark mass definition used in the analysis. We extract our optimal predictions using Laplace sum rule (LSR) within the standard stability criteria versus the changes of the external free parameters ([Formula: see text]-sum rule variable, [Formula: see text] continuum threshold and subtraction constant [Formula: see text]). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results ⊕ the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range [Formula: see text] MeV, summarized in Table 7, for exotic hadrons built with four different flavors [Formula: see text], do not support some previous interpretations of the D0 candidate,1 [Formula: see text], as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: [Formula: see text]. One can also scan the region [Formula: see text] MeV (where the [Formula: see text] might be a good candidate) and the one [Formula: see text] MeV for detecting these [Formula: see text] and [Formula: see text] unmixed exotic hadrons (if any) via, eventually, their radiative or [Formula: see text][Formula: see text]+[Formula: see text]hadrons decays.