A Review of pi-pi Phase Shifts

In the past several years several bits of evidence have been collected for the presence of a 0⁺ isoscalar S-wave π-π resonance. In this paper we review the previous evidence in the light of recent work. For low π-π masses the decay of the K⁺ meson, K⁺→π⁺+π^-+e⁺+ν gives useful information on the $I=0$ phase shift. To gain information at higher mass values, a large collection of data from many experiments on the reactions involving pion production in π-p collision has been made. Both the data on K decay and π-π collisions indicate a positive $I=0$ phase shift at low energies followed by a gradual rise in the phase shift. Although one cannot rule out a resonant behavior near the ρ mass, it seems unlikely. The $I=2$ phase shift seems to be negative, small ({~}20^∘{}) and slowly varying. Our results seem to differ from predictions based on current algebra.