On Goldstone bosons decoupling from high-lying hadrons

Abstract

In this paper, we discuss a decoupling of the Goldstone bosons from highly excited hadrons in relation to the restoration of chiral symmetry in such hadrons. We use a generalised Nambu-Jona-Lasinio model with the interaction between quarks in the form of an instantaneous Lorentz-vector confining potential. This model is known to provide spontaneous breaking of chiral symmetry in the vacuum via the standard selfenergy loops for valence quarks. For highly excited hadrons, where the typical momentum of valence quarks is large, the loop contributions represent only a small correction to the chiral-invariant classical contributions and asymptotically vanish. Consequently the chiral symmetry violating Lorentz-scalar dynamical mass of quarks vanishes. Then the conservation of the axial vector current in the chiral limit requires, via the Goldberger-Treiman relation, that the valence quarks decouple from the Goldstone boson. As a consequence, the whole hadron decouples from the Goldstone boson as well, which implies that its axial constant also vanishes.