Bounds for ππ scattering lengths

A well-known feature of π-π scattering is that the values of the s-wave scattering lengths αsub(0,2) are expected to be confined within a small region in the (αsub(0),αsub(2)) plane, surrounding a ''universal'' curve whose equation has been given in the existing literature. Numerically, this implies the following bounds: -0.10(<=)msub(π)αsub(0)(<=)0.60 -0.15(<=)msub(π)αsub(2)(<=)0.05, which are commonly accepted as a semiphenomenological property of the process, independent on both the unknown very low and very high energy details