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 BK molecule and (su)((bd) over bar) four-quark states. We improve these results by adding NLO and N2LO corrections to the PT contributions giving a more precise meaning on the b-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 (tau-sum rule variable, t(c) continuum threshold and subtraction constant mu). The smallness of the higher order PT corrections justifies (a posteriori) the LO order results circle plus the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173 similar to 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavors (buds), do not support some previous interpretations of the D0 candidate,(1) X(5568), as a pure molecule or a four-quark state. If experimentally confirmed, it could result from their mixing with an angle: sin 2 theta approximate to 0.15. One can also scan the region (2327 similar to 2444) MeV (where the D-s0* (2317) might be a good candidate) and the one (5173 similar to 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or pi + hadrons decays.