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 simultaneously a good operator product expansion convergence and a pole contribution which is bigger than the continuum contribution. These results may indicate that light many-quark states cannot be considered as resonances separated from the continuum.