Regge analysis of pion-pion (and pion-kaon) scattering for energy s^(1/2)> 1.4 GeV

Abstract

We perform a detailed Regge analysis of NN, πN, KN, π π, and πK scattering. From it, we find expressions that represent the pp 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 GeV and for momentum transfers |t|^( ½) ≤0.4 GeV. These Regge formulas are perfectly compatible with the low energy [s^(1/2)~1.4 GeV] scattering amplitudes deduced from π π phase shift analyses as well as with higher energy [s^(1/2)≥1.4 GeV] 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<s^(1/2)<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^(1/2) ˃1.7 GeV. 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 E_(kin)≈.1 GeV to multi-TeV energies.