LOW-MASS SCALAR MESONS IN NUCLEAR PHYSICS: MULTILOOP EFFECTS IN THE BOSONIZATION OF THE NAMBU-JONA-LASINIO MODEL

Abstract

We review a momentum-space bosonization of the Nambu-Jona-Lasinio model performed at the one-loop level by Bernard, Osipov and Meissner. At that level of approximation, the theory predicts a low-mass sigma meson where [Formula: see text] with mq being the constituent quark mass. Such a meson is not seen in experiment. We therefore extend the bosonization procedure to include a multiple-loop diagram describ-ing the coupling of the sigma to the two-pion channel. We find that for spacelike values of the momentum p2 (p2 ≤ 0), the sigma propagator behaves as if there were a pole at a small value of the mass, m eff ≃460 MeV. However, we see that the channel coupling is very large for timelikep2. That limits the applicability of a perturbative bosonization scheme in the timelike regime where a theory with explicit multichannel unitarity is to be preferred. We extend our analysis to include unitarity corrections to the self-energy in the isoscalar-scalar channel. Quite satisfactory results are obtained in that case. Again for spacelikep2, the dynamics is governed by a small value of m eff (m eff ≃500 MeV ); however, the theory no longer predicts a physical low-mass a meson. This analysis clarifies the nature of the low-mass sigma meson used in relativistic nuclear physics and in the one-boson exchange model of the nucleon-nucleon force. It is also seen that the low-mass (effective) sigma is predominantly of [Formula: see text] character with some admixture of [Formula: see text] (correlated two-pion components).