Recent studies have shown that concepts of effective field theory such as naturalness can be profitably applied to relativistic mean-field models of nuclei. Here the analysis by Friar, Madland, and Lynn of naturalness in a relativistic point-coupling model is extended. Fits to experimental nuclear data support naive dimensional analysis as a useful principle and imply a mean-field expansion analogous to that found for mean-field meson models.
A compelling feature of relativistic mean-field phenomenology has been the reproduction of spin-orbit splittings in finite nuclei after fitting only to equilibrium properties of infinite nuclear matter. This successful result occurs when the velocity dependence of the equivalent central potential that leads to saturation arises primarily because of a reduced nucleon effective mass. The spin-orbit interaction is then also specified when one works in a fourcomponent Dirac framework. Here the nature of the spin-orbit force in more general chiral effective field theories of nuclei is examined, with an emphasis on the role of the tensor coupling of the isoscalar vector meson (ω) to the nucleon.
Recently developed chiral effective field theory models provide excellent descriptions of the bulk characteristics of finite nuclei, but have not been tested with other observables. In this work, densities from both relativistic point-coupling models and mean-field meson models are used in the analysis of meson-nucleus scattering at medium energies. Elastic scattering observables for 790 MeV/c π ± on 208 Pb are calculated in a relativistic impulse approximation, using the Kemmer-Duffin-Petiau formalism to calculate the π ± nucleus optical potential.PACS number(s): 25.80. Dj, 24.10.Jv, 24.10.Ht, The concepts and methods of effective field theory (EFT) [1][2][3] have recently elucidated the successful nuclear phenomenology of relativistic field theories of hadrons, called quantum hadrodynamics (QHD) [4][5][6][7]. The EFT framework shows how QHD models can be consistent with the symmetries of quantum chromodynamics (QCD) and can be extended to accurately reproduce its low-energy features. The EFT perspective accounts for the success of relativistic mean-field models and provides an expansion scheme at the mean-field level and for going beyond it [6,8].A practical outcome of these EFT studies has been new sets of relativistic mean-field models, with parameters determined by global fits to bulk nuclear observables. Here we make the first independent tests of densities from these models by using them as inputs to relativistic impulse approximation (RIA) calculations of elastic π ± nucleus scattering. At energies above the ∆ resonance we expect the impulse approximation to reproduce experiment at forward angles, since the elementary amplitudes incorporate the dominant effects of intermediate ∆'s while medium modifications due to the ∆ should be small.In Ref.[6], an effective hadronic lagrangian consistent with the symmetries of QCD and intended for application to finite density systems was constructed. The goal was to test a systematic expansion for low-energy observables, which included the effects of hadron compositeness and the constraints of chiral symmetry. The degrees of freedom are (valence) nucleons, pions, and the low-lying non-Goldstone bosons. A scalar-isoscalar field with a mass of roughly 500 MeV was also included to simulate the exchange between nucleons of two correlated pions in this channel. The lagrangian was expanded in powers of the fields and their derivatives, with the terms organized using Georgi's "naive dimensional analysis" [9,2,10].The result is a faithful representation of low-energy, non-strange QCD, as long as all nonredundant terms consistent with symmetries are included. In addition, the mean-field framework provides a means of approximately including higher-order many-body and loop effects, since the scalar and vector meson fields play the role of auxiliary KohnSham potentials in relativistic density functional theory [7]. Fits to nuclear properties at the mean-field level showed that the effective lagrangian could be truncated at the first few powers of the fields and their derivatives...
Abstract. The general form of two-point fermion correlation functions at finite density is examined. Examples of particular interest are correlation functions of nucleonic interpolating fields, used in QCD sum-rule studies, and nucleon propagators in hadronic field theories. The constraints of Lorentz covariance, parity, and time-reversal on the form of the correlators are derived by focusing on spectral functions. Discrepancies with other treatments in the literature are discussed.PACS: 24.85+p; 21.65.+f; 12.38.Lg tions. We pattern our discussion after Ref. [4] so that the new features at finite density are manifest.We begin with a review of spectral functions, which will be used to derive results for the various Green's functions. A general Lorentz covariant form is established for the spectral functions and the constraints of parity and time-reversal symmetries are then studied. We work in momentum space for convenience, but all of our conclusions about the form of correlators will apply to the coordinate-space versions. The notation of Bjorken and Drell [4] is followed in general, although we do not assume a specific gamma matrix representation.Two-point fermion correlation functions (or Green's functions) at finite density are fundamental objects for describing the nuclear medium. The nucleon propagator in hadronic field theories of nuclear matter is such a correlation function [1]. Another example arises in QCD sum-rule calculations, where the correlator of two color-singlet fermion interpolating fields is calculated [2]. An example outside of nuclear physics is the electron propagator in an electron gas [3]. It is naturally advantageous to restrict the form of such functions by exploiting symmetries of the system. In this paper, the constraints of Lorentz covariance, parity invariance, and time-reversal invariance on the form of the correlation functions are studied, generalizing the results in Chap. 16 of Ref.[41 to finite density.In many respects this is a straightforward exercise, but there are some subtleties in the details and there is no complete treatment in the literature. Furthermore, the literature is full of incomplete, contradictory, and incorrect statements. For example, there is disagreement in the literature on the possibility of a tensor term (proportional to cru~) in the selfenergies of two-point correlation functions [3,5]. When results for correlation functions are quoted the assumptions made are often too restrictive (as in [6]), or have never been made explicit (for example, [2] and related work on finite-density QCD sum rules), or the reason given is incorrect (e.g., the tensor term vanishes because of translational invariance). In this work, we clarify the conditions under which various properties hold true, with minimal assump- Spectral functionsTo derive results that apply to all of the various Green's functions of interest (time-ordered, advanced, retarded, and so on), we focus on the spectral functions 1which are Fourier transforms of the Wightman functions [8].The ket ](P0(u)) i...
Recently developed chiral effective field theory models provide excellent descriptions of the bulk characteristics of finite nuclei, but have not been tested with other observables. In this work, densities from both relativistic point-coupling models and mean-field meson models are used in the analysis of meson-nucleus scattering at medium energies. Elastic scattering observables for 790 MeV/c π ± on 208 Pb are calculated in a relativistic impulse approximation, using the Kemmer-Duffin-Petiau formalism to calculate the π ± nucleus optical potential.PACS number(s): 25.80. Dj, 24.10.Jv, 24.10.Ht, The concepts and methods of effective field theory (EFT) [1][2][3] have recently elucidated the successful nuclear phenomenology of relativistic field theories of hadrons, called quantum hadrodynamics (QHD) [4][5][6][7]. The EFT framework shows how QHD models can be consistent with the symmetries of quantum chromodynamics (QCD) and can be extended to accurately reproduce its low-energy features. The EFT perspective accounts for the success of relativistic mean-field models and provides an expansion scheme at the mean-field level and for going beyond it [6,8].A practical outcome of these EFT studies has been new sets of relativistic mean-field models, with parameters determined by global fits to bulk nuclear observables. Here we make the first independent tests of densities from these models by using them as inputs to relativistic impulse approximation (RIA) calculations of elastic π ± nucleus scattering. At energies above the ∆ resonance we expect the impulse approximation to reproduce experiment at forward angles, since the elementary amplitudes incorporate the dominant effects of intermediate ∆'s while medium modifications due to the ∆ should be small.In Ref.[6], an effective hadronic lagrangian consistent with the symmetries of QCD and intended for application to finite density systems was constructed. The goal was to test a systematic expansion for low-energy observables, which included the effects of hadron compositeness and the constraints of chiral symmetry. The degrees of freedom are (valence) nucleons, pions, and the low-lying non-Goldstone bosons. A scalar-isoscalar field with a mass of roughly 500 MeV was also included to simulate the exchange between nucleons of two correlated pions in this channel. The lagrangian was expanded in powers of the fields and their derivatives, with the terms organized using Georgi's "naive dimensional analysis" [9,2,10].The result is a faithful representation of low-energy, non-strange QCD, as long as all nonredundant terms consistent with symmetries are included. In addition, the mean-field framework provides a means of approximately including higher-order many-body and loop effects, since the scalar and vector meson fields play the role of auxiliary KohnSham potentials in relativistic density functional theory [7]. Fits to nuclear properties at the mean-field level showed that the effective lagrangian could be truncated at the first few powers of the fields and their derivatives...
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