On Goldstone bosons decoupling from high-lying hadrons

In thispaper,wediscussa decoupling oftheG oldstonebosonsfrom highly excited hadrons in relation to the restoration ofchiralsym m etry in such hadrons. W e use a generalised N am bu{Jona-Lasinio m odelwith the interaction between quarks in the form of an instantaneous Lorentz{vector con(cid:12)ning potential. This m odel is known to provide spontaneous breaking ofchiralsym m etry in the vacuum via the standard selfenergy loopsforvalence quarks.Forhighly excited hadrons,where the typicalm om entum ofvalence quarksis large,the loop contributions representonly a sm allcorrection to the chiral{invariant classicalcontributionsand asym ptotically vanish.Consequently the chiralsym m etry violating Lorentz{scalar dynam icalm ass ofquarks vanishes. Then the conservation ofthe axialvector current in the chiral lim itrequires,viatheG oldberger{Treim an relation,thatthevalencequarksdecouple from the G oldstone boson.A sa consequence,the whole hadron decouplesfrom the G oldstone boson aswell,which im pliesthatitsaxialconstantalso vanishes.