Regge analysis of pion - pion ( and pion - kaon ) scattering for energy

We perform a detailed Regge analysis of NN , πN , KN , ππ and πK 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 > 1.4GeV and for momentum transfers |t| < ∼ 0.4GeV. These Regge formulas are perfectly compatible with the low energy (s ∼ 1.4GeV) scattering amplitudes deduced from ππ phase shift analyses as well as with higher energy (s > ∼ 1.4GeV) experimental ππ cross sections. They are also compatible with NN , KN and πN experimental cross sections using factorization, a property that we check with great 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 < s < 2 GeV, 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 s > 1.7 GeV. As a byproduct of our analysis we present also a fit of NN , πN and KN cross sections valid from c.m. kinetic energy Ekin ≃ 1 GeV to multi TeV energies. Typeset with PHysMaTEX -regge analysis of pion-pion (and pion kaon) scattering -