A new determination of the πN sigma term using hyperbolic dispersion relations in the (ν2,t) plane

Abstract

Dispersion relations in the (ν2,t) plane along hyperbolas are used in order to extrapolate the invariant isospin-even πN amplitude D+(ν2,t) to the Cheng-Dashen point, ν=0, t=2μ. The fluctuation of the results obtained with different hyperbolas gives a realistic estimate of the errors, except for errors of the partial wave solution and of the ππ $$ - N\bar N$$ amplitudes assumed at t < 4μ2 —If our ππ $$ - N\bar N$$ partial waves are used, which are based on the ππs-wave scattering length a 0 0 =0.28 μ-1, the result for the sigma term is 64±8 MeV, in agreement with earlier determinations.—The discrepancy with the theoretical prediction σπN≈ 30 MeV is smaller by only 8 MeV, if our $$ - N\bar N$$ amplitudes are modified in such a way that the threshold behaviour of the ππs-wave agrees with Weinberg's prediction a 0 0 =0.16 μ-1. Further progress depends on new accurate experimental π±p scattering data in the Coulomb interference region at low energies.