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

TL;DR

This paper investigates the consistency of the $\

Contribution

It introduces a sum rule check to assess the consistency of the inferred scattering parameters with the potential causing the bound state.

Findings

Sum rule is not fully satisfied but close to it.

Inferred scattering parameters may be inconsistent with the potential.

Highlights the need for refined models of $\

Abstract

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.