Generalized Heavy Baryon Chiral Perturbation Theory

Abstract

Standard SU(2) Heavy Baryon Chiral Perturbation Theory is extended in order to include the case of small or even vanishing quark condensate. The effective lagrangian is given to ${\cal O}(p^2)$ in its most general form and to ${\cal O}(p^3)$ in the scalar sector. A method is developed to efficiently construct the relativistic baryonic effective lagrangian for chiral SU(2) to all orders in the chiral expansion. As a first application, mass- and wave-function renormalization as well as the scalar form factor of the nucleon is calculated to ${\cal O}(p^3)$. The result is compared to a dispersive analysis of the nucleon scalar form factor adopted to the case of a small quark condensate. In this latter analysis, the shift of the scalar form factor between the Cheng-Dashen point and zero momentum transfer is found to be enhanced over the result assuming strong quark condensation by up to a factor of two, with substantial deviations starting to be visible for $r=m_s/\hat{m}\lesssim 12$.