Coupled-channel influence on the $a_0(1700/1800)$ line shape

The current situation with the recently discovered $a_0(1700/1800)$ resonance is very paradoxical: it is believed that $a_0(1700/1800)$ must be strongly coupled with two vector mesons, but there is no direct experimental confirmation of this yet. Based on the assumption that the $a_0(1700/1800)$ is a state similar to the four-quark state from the MIT bag, belonging to either the $\underline{9}^*$ or the $\underline{36}^*$ $q^2\bar q^2$ multiplet, we analyze the influence of the strong $a_0(1700/1800)$ coupling to the vector channels $K^* \bar K^*$, $\rho\phi$, and $\rho \omega$ on its line shape in the decay channels into pseudoscalar mesons $K\bar K$, $\pi\eta$, and $\pi\eta'$. This effect depends on the location of the resonance mass $m_{a_0}$ relative to the nominal thresholds of vector channels. For example, if $m_{a_0}\approx 1700$ MeV, then the influence turns out to be hidden in a fairly wide range of coupling constants. On the whole, our analysis shows that, to confirm the presence of the strong $a_0(1700/1800)$ coupling to the vector channels, utterly required is the direct detection of the decays $a_0(1700/1800)\to K^*\bar K^*$, $\rho\phi$, $\rho\omega$. The appearance of even certain hints at the existence of these decays would make it possible to fundamentally advance in understanding the nature of the new $a_0$ state.