On the $\pi\pi$ contribution to the QCD sum rules for the light tetraquark

Abstract

We perform a QCD sum rule analysis for the $f_0$ light tetraquark taking into account the contribution arising from the two pion intermediate state. With the interpolating currents of the different chiral combinations of scalar and pseudoscalar diquarks, it is demonstrated that the interpolating current with maximum chirality has a large coupling to the two pion state, but the current with zero chirality interacts only weekly with this state. Taking into account the form factor in the $f_0$--two pion vertex, it is shown that the $f_0$--coupling to the two pion state leads to an increase of the lightest tetraquark mass by a value of about 100 MeV. The analysis of the resulting sum rule shows that the $\sigma(f_0(600))$--meson state might be treated as the four--quark bound state in the instanton field which has a rather strong coupling to the two pion state.