Bounds on thegKNΣ2coupling constant from positivity and charge-exchange data

Positivity of the imaginary part of the forward $K^{\mathrm{-}}$n elastic amplitude on the unphysical cut allows the calculation of bounds on the $g_{\mathrm{KN}\Sigma }$ ${\mathrm{}}^2$ coupling constant using the forward differential cross sections of the charge-exchange reaction $K^{\mathrm{-}}$p→K¯ ${}_{}{}^0{}_{}{}^{}n$, the scarce $K^{\mathrm{-}}$n real-part data, and a Stieltjes parametrization of the $K^{\mathrm{-}}$p real-part data. The bounds on the coupling constant are 2.11<$g_{\mathrm{KN}\Sigma }$ ${\mathrm{}}^2$<3.70 and real parts of the $K^{\pm }$n amplitudes are also obtained, as well as the position of the complex-conjugate zeros of the $K^{\mathrm{-}}$n amplitude: (0.35±0.05)±(0.16±0.04)i GeV/c.