Two-loop corrections with scalar and vector form factors are calculated for nuclear matter in the Walecka model. The on-shell form factors are derived from vertex corrections within the framework of the model and are highly damped at large spacelike momenta. The two-loop corrections are evaluated first by using the one-loop parameters and mean fields and then by refitting the total energy/baryon to empirical nuclear matter saturation properties. The modified two-loop corrections are significantly smaller than those computed with bare vertices. Contributions from the anomalous isoscalar form factor of the nucleon are included for the first time. The effects of the implicit density dependence of the form factors, which arise from the shift in the baryon mass, are also considered. Finally, necessary extensions of these calculations are discussed.Typeset using REVT E X where F µν = ∂ µ V ν − ∂ ν V µ and δL contains the counterterms. We observe that the off-shell vertex functions should be used in a fully satisfactory calculation with loops. A full offshell calculation is quite complicated, however, as one needs to know the off-shell behavior of the vertices at all spacelike momenta, as well as the modification of the vertices in the presence of valence nucleons at finite density. Calculations exploring these off-shell vertex functions are in progress [19]. Here, as a first step, we use an on-shell approximation, in which the off-shell vertex functions are replaced by their on-shell forms at zero density. This procedure is analogous to that used in Refs. [15] and [16], where parametrized, on-shell form factors were used at the vertices, except that we use form factors obtained from within our model. Note also that the form factors used in Refs. [15] and [16] were chosen to have

An effective hadronic lagrangian consistent with the symmetries of quantum chromodynamics and intended for applications to finite-density systems is constructed. The degrees of freedom are (valence) nucleons, pions, and the low-lying non-Goldstone bosons, which account for the intermediate-range nucleon-nucleon interactions and conveniently describe the nonvanishing expectation values of nucleon bilinears. Chiral symmetry is realized nonlinearly, with a light scalar meson included as a chiral singlet to describe the mid-range nucleon-nucleon attraction. The low-energy electromagnetic structure of the nucleon is described within the theory using vector-meson dominance, so that external form factors are not needed. The effective lagrangian is expanded in powers of the fields and their derivatives, with the terms organized using Georgi's "naive dimensional analysis". Results are presented for finite nuclei and nuclear matter at one-baryon-loop order, using the single-nucleon structure determined within the model. Parameters obtained from fits to nuclear properties show that naive dimensional analysis is a useful principle and that * Present address: School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455.

An analysis of nuclear properties based on a relativistic energy functional containing Dirac nucleons and classical scalar and vector meson fields is discussed. Density functional theory implies that this energy functional can include many-body effects that go beyond the simple Hartree approximation. Using basic ideas from effective field theory, a systematic truncation scheme is developed for the energy functional, which is based on an expansion in powers of the meson fields and their gradients. The utility of this approach relies on the observation that the large scalar and vector fields in nuclei are small enough compared to the nucleon mass to provide useful expansion parameters, yet large enough that exchange and correlation corrections to the fields can be treated as minor perturbations. Field equations for nuclei and nuclear matter are obtained by extremizing the energy functional with respect to the field variables, and inversion of these field equations allows one to express the unknown coefficients in the energy functional directly in terms of nuclear matter properties near equilibrium. This allows for a systematic * Present address: School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455.1 and complete study of the parameter space, so that parameter sets that accurately reproduce nuclear observables can be found, and models that fail to reproduce nuclear properties can be excluded. Chiral models are analyzed by considering specific lagrangians that realize the spontaneously broken chiral symmetry of QCD in different ways and by studying them at the Hartree level. The resulting energy functionals are special cases of the general functional considered earlier. Models that include a light scalar meson playing a dual role as the chiral partner of the pion and the mediator of the intermediate-range nucleon-nucleon interaction, and which include a "Mexican-hat" potential, fail to reproduce basic ground-state properties of nuclei at the Hartree level. In contrast, chiral models with a nonlinear realization of the symmetry are shown to contain the full flexibility inherent in the general energy functional and can therefore successfully describe nuclei.

We study pion-nucleon scattering with a chiral lagrangian of pions, nucleons, and ∆-isobars. The scattering amplitude is evaluated to one-loop Q 3 order, where Q is a generic small momentum, using a new approach which is equivalent to heavy baryon chiral perturbation theory. We obtain a good fit to the experimental phase shifts for pion center-of-mass kinetic energies up to 100 MeV. A sigma term greater than 45 MeV is favored, but the value is not well determined.PACS number(s): 21.30.+y, 21.60.Jz, 21.65.+f Typeset using REVT E X

A relativistic hadronic model for nuclear matter and finite nuclei, which incorporates nonlinear chiral symmetry and broken scale invariance, is presented and applied at the one-baryon-loop level to finite nuclei. The model contains an effective light scalar field that is responsible for the mid-range nucleon-nucleon attraction and which has anomalous scaling behavior. Oneloop vacuum contributions in this background scalar field at finite density are constrained by low-energy theorems that reflect the broken scale invariance of quantum chromodynamics. A mean-field energy functional for nuclear matter and nuclei is derived that contains small powers of the fields and their derivatives, and the validity of this truncation is discussed. Good fits to the bulk properties of finite nuclei and single-particle spectra are obtained.