D_s (2317) as a four-quark state in QCD sum rules

We perform a QCD sum rule study of the open-charmed $D_s (2317)$ as a four-quark state. Using the diquark-antidiquark picture for the four-quark state, we consider four possible interpolating fields for $D_s (2317)$, namely, scalar-scalar, pseudoscalar-pseudoscalar, vector-vector, and axial-vector--axial-vector types. We test all four currents by constructing four separate sum rules. The sum rule with the scalar-scalar current gives a stable value for the $D_s$ mass which qualitatively agrees with the experimental value, and the result is not sensitive to the continuum threshold. The vector-vector sum rule also gives a stable result with small sensitivity to the continuum threshold and the extracted mass is somewhat lower than the scalar-scalar current value. On the other hand, the two sum rules in the pseudoscalar and axial-vector channels are found to yield the mass highly sensitive to the continuum threshold, which implies that a four-quark state with the combination of pseudoscalar-pseudoscalar or axial-vector--axial-vector type would be disfavored. These results would indicate that $D_s (2317)$ is a bound state of scalar-diquark and scalar-antidiquark and/or vector-diquark and vector-antidiquark.