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

New section added, extending the pion-nucleon and nucleon nucleon Regge description to Multi TeV energies. Conclusions on pion-pion scattering unchanged

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• A new analysis of $\pi K$ scattering from Roy and Steiner type equations
• On the precision of chiral-dispersive calculations of $\pi \pi$ scattering
• The quadratic scalar radius of the pion and the mixed $\pi -K$ radius

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