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

Abstract

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.