Do the QCD sum rules support four-quark states?

Abstract

We test the validity of the QCD sum rules applied to the light scalar mesons, the charmed mesons $D_{s0}(2317)$ and $D_{s1} (2460)$, and the X(3872) axial meson, considered as tetraquark states. We find that, with the studied currents, it is possible to find an acceptable Borel window only for the X(3872) meson. In such a Borel window we have simultaneouly a good OPE convergence and a pole contribution which is bigger than the continuum contribution. We interpret these results as a strong argument against the assignment of a tetraquark structure for the light scalars and the $D_{s0}(2317)$ and $D_{s1} (2460)$ mesons.