Calculation of the properties of the {sigma} meson in a generalized Nambu{endash}Jona-Lasinio model with Lorentz-vector confinement
- Department of Physics and Center for Nuclear Theory, Brooklyn College of the City University of New York, Brooklyn, New York 11210 (United States)
A recent analysis by T{umlt o}rnqvist and Roos suggests that the {sigma} meson has a mass of 860 MeV with a width of 880 MeV. In this work we calculate the properties of the {sigma} meson using a generalized Nambu{endash}Jona-Lasinio model that includes a model of confinement. We describe, in some detail, how the {sigma} coupling to states in the two-pion continuum may be calculated, when using a Lorentz-vector confining interaction. As part of our work we provide a general procedure for calculating various loop diagrams in Minkowski momentum space for quarks in the presence of the confining interaction. We study the properties of the {sigma} meson by considering t-channel scalar-isoscalar exchange between two quarks. The resulting quark-quark T matrix t{sub qq}(q{sup 2}) has Ret{sub qq}(q{sup 2})=0 for q{sup 2}=(0.823GeV){sup 2}. Thus, we have m{sub {sigma}}=0.823GeV. However, the coupling of the {sigma} to the two-pion states is so large as to make {vert_bar}t{sub qq}(q{sup 2}){vert_bar} a rather smooth function over a broad range of q{sup 2}. Therefore, we do not attempt to assign a width for the resonance. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 509108
- Journal Information:
- Physical Review, C, Vol. 55, Issue 6; Other Information: PBD: Jun 1997
- Country of Publication:
- United States
- Language:
- English
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