The axial form factor in the Nambu-Jona-Lasinio model

We give a general expression for the expectation value of the axial vector currentA _µ ^a in a system with baryon numberB=1, which arises as solution of theSU(2)—flavour Nambu-Jona-Lasinio model in the fermion-1-loop approximation. States with good spin and isospin quantum numbers are constructed by using the lowest order cranking approximation. Taking the self consistent solutions for such a system we calculate the axial form factorg _A(q ²) and the axial coupling constantg _A . The results can be checked by comparing the value of g_A with the one obtained from the radial integral or the asymptotic tail of the self consistent pion field by means of the PCAC relation.