A Stieltjes extrapolation to the unphysical cut of the Ksup(+-)p forward elastic amplitude

Positivity and unimodality of an unknown function chi1(x), related to the imaginary part of the forward elastic K-p amplitude on the unphysical cut, allow one, through a dispersion relation, to obtain upper and lower moment sequences of that function. The inversion of the moment sequences using a Stieltjes-Chebyshev technique allows the calculation of the scattering amplitude on the unphysical cut, so completing the map obtained in a previous work. A range of values is obtained for the K-p elastic threshold real part between -1.075 and -0.865 fm, in agreement with recent determinations by low-energy parametrisation. A corridor for the real parts of the amplitude has been determined in the unphysical region using (two) upper and lower error sequences. (author)