Regge analysis of the pi pi scattering amplitude
  The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the pi pi scattering amplitude below 0.8 GeV. The extension of this representation up to the maximum energy of validity of the Roy equations (1.15 GeV) requires a more precise input at high energies. In this paper we determine the trajectories and residues of the leading Regge contributions to the pi pi amplitude (Pomeron, f and rho), using factorization, phenomenological parametrizations of the pi N and NN total cross sections at high energy and a set of sum rules which connect the high and low energy properties of pi pi scattering. We find that nonleading Regge terms are necessary in order to achieve a smooth transition from the partial waves to the Regge representation at or below 2 GeV. We obtain thus a Regge representation consistent both with the experimental information at high energies and the Roy equations for the partial waves with l =< 4. The uncertainties in our result for the Regge parameters are sizable but in the solutions of the Roy equations, these only manifest themselves above K-Kbar threshold. 
Irinel Caprini, Gilberto Colangelo and Heinrich Leutwyler
hep-ph