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)\bar(bd) 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 + the uses of the ambiguous heavy quark mass to that order. However, our predicted spectra in the range (5173\sim 5226) MeV, summarized in Table 7, for exotic hadrons built with four different flavours (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\approx 0.15. One can also scan the region (2327~ 2444) MeV (where the D*_{s0}(2317) might be a good candidate) and the one (5173~ 5226) MeV for detecting these (cuds) and (buds) unmixed exotic hadrons (if any) via, eventually, their radiative or \pi+hadrons decays.Comment: Version matching with the publised version : some references added and updated, comments added, misprint corrected (51 pages, 66 figures, 7 tables

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