Calculation of the Coupling ConstantsgΛKN2andgΣKN2Using Kaon-Nucleon Dispersion Relations

We apply forward kaon-nucleon dispersion relations to determine whether the known energy dependence of the low-energy $\mathrm{Kp}$ elastic scattering amplitude uniquely and consistently prescribes the coupling constants $g_{\Lambda K^{-}p}^{}{}_{}{}^2$ and $g_{{\Sigma }^0{K}^{-}p}^{}{}_{}{}^2$. In one application, we check the consistency of the multichannel effective-range continuation below the physical threshold by calculating the coupling constants over a range of energies. In the second application, we use a theorem which places bounds on the energy dependence of certain types of unknown dispersion integrals, to find bounds on the coupling constants.