Do the QCD sum rules support four-quark states?

TL;DR

This paper evaluates the validity of QCD sum rules for light scalar, charmed, and exotic mesons, finding support only for the X(3872) as a tetraquark, thus challenging tetraquark interpretations of other states.

Contribution

It provides a critical assessment of QCD sum rules' applicability to various mesons, highlighting their limitations for certain states.

Findings

QCD sum rules support the tetraquark interpretation only for X(3872).

Light scalar and D_s mesons are unlikely to be tetraquarks based on sum rule analysis.

Acceptable Borel windows are only found for X(3872).

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.