Eur. Phys. J. C (2012) 72: 1860
https://doi.org/10.1140/epjc/s10052-012-1860-1

Regular Article - Theoretical Physics

Regge analysis of the ππ scattering amplitude

¹ Horia Hulubei National Institute for Physics and Nuclear Engineering, P.O.B. MG-6, 077125, Magurele, Romania
² Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

^* e-mail: gilberto@itp.unibe.ch

Received: 30 November 2011
Revised: 23 December 2011
Published online: 3 February 2012

Abstract

The theoretical predictions for the subtraction constants lead to a very accurate dispersive representation of the ππ 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 ππ amplitude (Pomeron, f and ρ), using factorization, phenomenological parametrizations of the πN and NN total cross sections at high energy, and a set of sum rules which connect the high and low energy properties of ππ 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 the threshold.