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

• DOI: 10.1007/bf01571999
• Publication Date: 2005-04-27T17:00:42Z
• Authors: R. Koch
• Keywords: 0103 physical sciences; 01 natural sciences

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.