Further Analysis of ππ Scattering Dispersion Relations

The naive use of higher order perturbation theory leads to the left-hand cut integrals in ππ dispersion relations Phys. Lett. B 536 (2002) 59; B 549 (2002) 362; Nucl. Phys. A 695 (2001) 273 to be divergent. This problem is discussed and solved. We point out that the Adler zero condition imposes three constraints on the dispersion relations. The σ pole position is determined using the improved method, M_σ = 483±13 MeV, Γ_σ = 705±50 MeV. The scattering length parameter is found to be in excellent agreement with the experimental result.