Time dependent transformations in deformation quantization

We study the action of time dependent canonical and coordinate transformations in phase space quantum mechanics. We extend the covariant formulation of the theory by providing a formalism that is fully invariant under both standard and time dependent coordinate transformations. This result considerably enlarges the set of possible phase space representations of quantum mechanics and makes it possible to construct a causal representation for the distributional sector of Wigner quantum mechanics.Comment: 16 pages, to appear in the J. Math. Phy

A QCD sum rule calculation of the X±(5568)→Bs0π±X^\pm(5568) \to B_{s}^0\pi^\pm decay width

To understand the nature of the $X(5568)$, recently observed in the mass spectrum of the $B_{s}^0\pi^\pm$ system by the D0 Collaboration, we have investigated, in a previous work, a scalar tetraquark (diquak-antidiquark) structure for it, within the two-point QCD sum rules method. The result found for its mass agrees well with the experimental value. Encouraged by this finding we now extend our calculations to obtain the decay width of $X(5568)$ to $B_{s}^0\pi^\pm$ using the three-point QCD sum rule. We obtain a value of (20.4\pm8.7)\MeV, which, on comparing with the experimental value of 21.9\pm6.4 (\mbox{sta})^{+5.0}_{-2.5}(\mbox{syst}) \MeV/c^2, reinforces the scalar four quark nature of $X(5568)$.Comment: Minor modifications made. Some new discussions and references adde