A model field theory in which two Nambu-Goldstone symmetries are realised by one massless pseudoscalar boson

A model field theory is considered consisting of two interacting Nambu-Jona-Lasinio spin 1/2 fields. Solutions are sought in which the symmetries are spontaneously broken by giving the fermions non-zero masses. Each of the two pairs of axial-vector vertex functions in the theory satisfy two coupled integral equations, which are solved in the 'chain approximation'. It is found that all four vertex functions have the same singularity structure, in particular a pole at q2=0 corresponding to a massless pseudoscalar Nambu-Goldstone boson, and another pole corresponding to an axial-vector boson whose mass is cut-off dependent, but which for a certain range of values pf f2 is a stable particle. By considering the coupling of the strings of nucleon-antinucleon pseudoscalar 'bubbles' which generate the massless Nambu-Goldstone bosons associated with fermions 1 and 2, it is shown explicitly that there is only one massless Nambu-Goldstone boson in the theory. (author)