POINT-COUPLING AND NONLINEAR WALECKA MODELS CONNECTION

In the context of infinite nuclear matter, the equation of states obtained from the Walecka model turn out to be the same as those constructed from point-coupling models in which the nucleons interact with each other only when they are in contact.1 Nonlinear point-coupling models have been applied sucessfully to describe infinite nuclear matter and finite nuclei spectra properties.2 A theoretical support for this was presented on the basis of naturalness and naive dimensional analysis.3 For the usual linear Walecka model the infinite meson masses limit leads to a point-coupling model. From this, a quite natural question arises, whether the same kind of masses limit taken in a nonlinear Walecka model would provide a point-coupling model. We construct a modified nonlinear Walecka model Lagrangian in which the infinite meson masses limit can be taken exactly and leads to the contact nonlinear model. This modified nonlinear Walecka model includes higher order couplings. Although the modified and the nonlinear Walecka model at a mean field approach lead to distinct equations of state, the physically relevant content of the models are the same.

NATURALNESS IN AN EFFECTIVE FIELD THEORY FOR NEUTRON STAR MATTER

High density hadronic matter is studied in a generalized relativistic multi-baryon Lagrangian density mean field approach which contains nonlinear couplings of the σ, ω, ϱ fields. We compare the predictions of our model with estimates obtained within a phenomenological naive dimensional analysis based on the naturalness of the coefficients of the theory. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as the ones found in the interior of neutron stars. Moreover, we show that naturalness play a major role in effective field theory and, in combination with experiment, could represent a relevant criterium to select a model among others in the description of global static properties of neutron stars.

NÄIVE DIMENSIONAL ANALYSIS IN AN EFFECTIVE FIELD THEORY FOR NEUTRON STARS

In the investigation of the role of naturalness in effective theory, we focus on dense hadronic matter in a generalized relativistic multi-baryon Lagrangian density mean field approach which contains nonlinear self-couplings of the σ and δ meson fields interacting with the fundamental baryon octet and with the ω and ϱ meson fields and compare its predictions with estimates obtained within a phenomenological naive dimensional analysis based on the naturalness of the coupling constants of the Lagrangian model; our investigation is limited however to the scalar sector of the theory. Upon adjusting the model parameters to describe bulk static properties of ordinary nuclear matter, we show that our approach represents a natural modelling of nuclear matter under the extreme conditions of density as found in the interior of neutron stars.

ON FERMION NUMBER VIOLATION AT HIGH ENERGIES

By considering the back reaction of the scattered particles on instantons, the explicit high energy behavior of fermion number violating amplitudes in the standard electroweak model is obtained to the leading order in the coupling constant. The amplitudes decay faster than what is expected from naive dimensional analysis due to the renormalization group flow of the coupling constant and this is consistent with unitarity. Also, it is shown that the constrained instanton approach is valid at low energies, while the high energy behavior is governed by the back reaction of the external particles.