CALCULATION OF THE PROPERTIES OF THE SIGMA-MESON IN A GENERALIZED NAMBU-JONA-LASINIO-MODEL WITH LORENTZ-VECTOR-CONFINEMENT

A recent analysis by Tornqvist and Roos suggests that the a meson has a mass of 860 MeV with a width of 880 MeV. In this work we calculate t he properties of the a meson using a generalized Nambu-Jona-Lasinio mo del that includes a model of confinement. We describe, in some detail, how the a coupling to states in the two-pion continuum may be calcula ted, when using a Lorentz-vector confining interaction. As part of our work we provide a general procedure for calculating various loop diag rams in Minkowski momentum space for quarks in the presence of the con fining interaction. We study the properties of the a meson by consider ing t-channel scalar-isoscalar exchange between two quarks. The result ing quark-quark T matrix t(qq)(q(2)) has Re t(qq)(q(2))=0 for q(2)=(0. 823 GeV)(2). Thus, we have m(sigma)=0.823 GeV. However, the coupling o f the a to the two-pion states is so large as to make \t(qq)(q(2))\ a rather smooth function over a broad range of q(2). Therefore, we do no t attempt to assign a width for the resonance.