Low-energy π-π scattering in a crossing-symmetric model

Abstract

Several topics in low-energy π-π scattering are investigated using a model which is crossing-symmetric, approximately unitary, and constrained to satisfy certain finite-energy sum rules. The sensitivity of some recently derived inequalities amongS-, P- andD-wave amplitudes is studied, and it is found that although these inequalities are highly sensitive to small violations of crossing symmetry, they are satisfied by several different choices of parameters in our model. The properties of the ρ-meson and of the asymptotic cross-section consistent with our low-energy behaviour are discussed; the ρ width tends to be too small, but σ∞ is quite consistent with factorization. A solution with a broad, low-mass ɛ0-resonance is examined, but our model cannot cope with such a resonance, should it exist. Finally the contours of zeros of the real and imaginary parts of the amplitude are traced in the (t, s, u)-plane.