On estimates of the pion-nucleon sigma term by the dispersion relations and taking into account the interrelation between the chiral and scale invariance breaking

Possible reasons of disagreement between estimates of the pion-nucleon σ term obtained by the method of dispersion relations with extrapolation to the Chang-Dashen point and by alternative methods, making no use of such extrapolation are investigated. One of the reasons may be, that the πN amplitude is not analytic in the variable t at ν=0. A method, which is not so strongly influenced by the nonanalyticity, is suggested to estimate the σ term making use of the threshold data for the πN amplitude. Relation between the scale and chiral invariance breakings is discussed and the resulting estimate of the σ term is presented. Both estimates give close results (42 and 34 MeV) which do not contradict one another within the uncertainties of the methods