Regge analysis of pion-pion (and pion-kaon) scattering for energy s1/2>1.4 GeV

We perform a detailed Regge analysis of NN, πN, KN, {π}{π}, and πK scattering. From it, we find expressions that represent the {π}{π} 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 s1/2>1.4GeV and for momentum transfers |t|1/20.4GeV. These Regge formulas are perfectly compatible with the low energy (s1/2~1.4GeV) scattering amplitudes deduced from {π}{π} phase shift analyses as well as with higher energy (s1/21.4GeV) experimental {π}{π} cross sections. They are also compatible with NN, KN, and πN experimental cross sections using factorization, a property that we check with precision. This contrasts with results from current phase shift analyses of the {π}{π} scattering amplitude, which bear little resemblance to reality in the region 1.4<s1/2<2GeV, as they are not well defined and increasingly violate a number of physical requirements when the energy grows. πK scattering is also considered, and we present a Regge analysis for these processes valid for energies s1/2>1.7GeV. As a by-product of our analysis, we obtain also a fit of NN, πN, and KN cross sections valid from c.m. kinetic energy Eₖᵢₙ1GeV to multi-TeV energies.