A chiral effective lagrangian for nuclei

Abstract

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.

Relativistic nuclear model with point-couplings constrained by QCD and chiral symmetry

“…[1,3,4], the effective hadronic Lagrangians of QHD and related models are consistent with the symmetries of QCD: Lorentz invariance, parity invariance, electromagnetic gauge invariance, isospin and chiral symmetry. However, QHD calculations do not include pions explicitly.…”

Accurate calibration of relativistic mean-field models: Correlating observables and providing meaningful theoretical uncertainties

“…A meaningful criterion used to construct an effective Lagrangian for nuclear-physics calculations has been proposed by Furnstahl and collaborators based on the concept of "naive dimensional analysis" and "naturalness" [22][23][24][25][26]. The basic idea behind naturalness is that once the dimensionful meson fields (having units of mass) have been properly scaled using strong-interaction mass scales, the remaining dimensionless coefficients of the effective Lagrangian should all be "natural"; that is, neither too small nor too large [22,27]. Such an approach is both useful and powerful as it allows an organizational scheme based on an expansion in powers of the meson fields.…”

“…In practice, however, many successful theoretical models-such as NL3 [16,17] and FSUGold [19]-arbitrarily set some of these parameters to zero. The "justification" behind these fairly ad-hoc procedure is that whereas the neglected terms are of the same order in a power-counting scheme, the full set of parameters is poorly determined by existing data, so ignoring a subset model parameters does not compromise the quality of the fit [10,22].…”

The nuclear spin-orbit force in chiral effective field theories

“…The concepts and methods of effective field theory (EFT) [1][2][3][4][5] have recently elucidated the successful nuclear phenomenology of relativistic field theories of hadrons, called quantum hadrodynamics (QHD) [6][7][8][9]. 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.…”