$\phi$-$p$ bound state and completeness of quantum states

The existence of a bound state of a $\phi$ meson and proton has been recently indicated on the basis of a combined analysis of the measured $\phi$-$p$ correlation function and the QCD lattice calculations of $\phi$-$p$ interaction in the spin 1/2 and 3/2 channels. We check whether the correlation functions and bound state formation rate satisfy the sum rule which follows from the completeness of quantum states. The sum rule is not satisfied but it is close to it, suggesting that the inferred scattering parameters, which determine the correlation functions, are not fully consistent with the potential responsible for the bound state existence.