1 research outputs found
Nucleon mass and pion loops: Renormalization
Using Dyson--Schwinger equations, the nucleon propagator is analyzed
nonperturbatively in a field--theoretical model for the pion--nucleon
interaction. Infinities are circumvented by using pion--nucleon form factors
which define the physical scale. It is shown that the correct, finite,
on--shell nucleon renormalization is important for the value of the mass--shift
and the propagator. For physically acceptable forms of the pion--nucleon form
factor the rainbow approximation together with renormalization is inconsistent.
Going beyond the rainbow approximation, the full pion--nucleon vertex is
modelled by its bare part plus a one--loop correction including an effective
. It is found that a consistent value for the nucleon mass--shift can
be obtained as a consequence of a subtle interplay between wave function and
vertex renormalization. Furthermore, the bare and renormalized pion--nucleon
coupling constant are approximately equal, consistent with results from the
Cloudy Bag Model.Comment: 14 pages, 6 figure