We perform a detailed Regge analysis of NN, $\pi N,$ KN, ππ, and $\pi K$ scattering. From it, we find expressions that represent the ππ scattering amplitudes with an accuracy of a few percent for exchange of isospin zero and ∼15% for exchange of isospin 1, and this for energies $s^{1/2}>1.4\mathrm{}\mathrm{GeV}$ and for momentum transfers $|t{|}^{1/2}\lesssim 0.4\mathrm{GeV}.$ These Regge formulas are perfectly compatible with the low energy ${(s}^{1/2}\sim 1.4\mathrm{GeV})$ scattering amplitudes deduced from ππ phase shift analyses as well as with higher energy ${(s}^{1/2}\gtrsim 1.4\mathrm{GeV})$ experimental ππ cross sections. They are also compatible with NN, KN, and $\pi N$ experimental cross sections using factorization, a property that we check with precision. This contrasts with results from current phase shift analyses of the ππ scattering amplitude, which bear little resemblance to reality in the region $1.4<\mathrm{}{s}^{1/2}<2\mathrm{}\mathrm{GeV},$ as they are not well defined and increasingly violate a number of physical requirements when the energy grows. $\pi K$ scattering is also considered, and we present a Regge analysis for these processes valid for energies $s^{1/2}>1.7\mathrm{}\mathrm{GeV}.$ As a by-product of our analysis, we obtain also a fit of NN, $\pi N,$ and KN cross sections valid from c.m. kinetic energy $E_{\mathrm{kin}}\simeq 1\mathrm{GeV}$ to multi-TeV energies.

• Received 22 December 2003

DOI:https://doi.org/10.1103/PhysRevD.69.114001