Complex Regge poles and high energy scattering data

For the high energy data on σ_tot^pp the proton-proton total cross section, and on ?, the ratio of real to imaginary part of the forward elastic amplitude, including the recent ISR results, an excellent fit is obtained with P, P', ω Regge poles plus a pair of complex conjugate Regge poles. The complex poles describe the possible oscillatory behavior of the quantities σ_tot^pp and ?. The physical meaning of these complex poles and extrapolation to future measurements of the above quantities are discussed.