Summation of two-pion inserts to the sigma-meson propagator and nucleon forces

Journal Article · Mon Nov 01 04:00:00 EST 1976 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.14.2402· OSTI ID:7335309

Lomon, E L

Each pion-pair insert into a sigma-meson propagator leads to a factorizable contribution, a function of the magnitude of the sigma-meson four-momentum. The sum of the resulting geometric series produces a modified propagator with a mass shift and a width which are determined by the physical mass and decay rate of the sigma meson. The modified propagator is used to calculate the contribution of all nucleon-nucleon scattering diagrams in which the nucleons can be separated by cutting only a sigma-meson line. This replaces the treatment of F. Partovi and E. L. Lomon in which the effect of the sigma-meson width was approximated by averaging the potential obtained from an unmodified propagator over the sigma-meson mass distribution. The new potential, when the general chiral constraint is imposed on the coupling constants, is small, in spite of large coupling strengths, due to cancellations between terms. It is similar to the previous approximate result and is less sensitive to the sigma-meson width. The size of the potential is reasonable for widths greater than 300 MeV. As before, the Weinberg-model prediction of a sigma meson which has a rho-meson mass and a width of 620 MeV leads to the best cancellation of nucleon-pair terms away from zero four-momentum transfer. The addition of this contribution to the theoretical potential of M. Hossein Partovi and E. L. Lomon tends to decrease the agreement with several realistic potentials. The size of the sigma-meson-exchange contribution is decreased if the sigma-meson width is increased; but neglecting exchange contributions a zero-isospin two-pion bound state also arises. (AIP)

• Research Organization: Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
• OSTI ID: 7335309
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 14:9; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645204* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON-BARYON INTERACTIONS
BOSON-EXCHANGE MODELS
BOSONS
BOUND STATE
COUPLING CONSTANTS
ELEMENTARY PARTICLES
FIELD THEORIES
HADRON-HADRON INTERACTIONS
HADRONS
INTERACTIONS
ISOSPIN
MASS FORMULAE
MATHEMATICAL MODELS
MESONS
NUCLEON-NUCLEON INTERACTIONS
OBE MODEL
PARTICLE INTERACTIONS
PARTICLE MODELS
PARTICLE PROPERTIES
PERIPHERAL MODELS
PIONS
PROPAGATOR
PSEUDOSCALAR MESONS
QUANTUM FIELD THEORY
SIGMA MODEL