Loop Corrections and Naturalness in a Chiral Effective Field Theory

Abstract

The loop expansion is applied to a chiral effective hadronic lagrangian; with the techniques of Infrared Regularization, it is possible to separate out the short-range contributions and to write them as local products of fields that are already present in our lagrangian. (The appropriate field variables must be re-defined at each order in loops.) The corresponding parameters implicitly include short-range effects to all orders in the interaction, so these effects need not be calculated explicitly. The remaining (long-range) contributions that must be calculated are nonlocal and resemble those in conventional nuclear-structure calculations. Nonlinear isoscalar scalar $(\sigma )$ and vector $(\omega )$ meson interactions are included, which incorporate many-nucleon forces and nucleon substructure. Calculations are carried out at the two-loop level to illustrate these techniques at finite nuclear densities and to verify that the coupling parameters remain natural when fitted to the empirical properties of equilibrium nuclear matter. Contributions from the $\omega N$ tensor coupling are also discussed.

22 pages, 6 figures

References in corpus (19)

• Recent Progress in Quantum Hadrodynamics
• Neutron Radii in Mean-Field Models
• A Chiral Effective Lagrangian for Nuclei
• Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form
• Generalized Dimensional Analysis
• Pion--Nucleon Scattering in a New Approach to Chiral Perturbation Theory
• Parameter Counting in Relativistic Mean-Field Models
• Infrared regularization of baryon chiral perturbation theory reformulated
• QCD Scales in Finite Nuclei
• Power counting in baryon chiral perturbation theory including vector mesons
• Dimensional Power Counting in Nuclei
• Infrared and extended on-mass-shell renormalization of two-loop diagrams
• Probing the convergence of perturbative series in baryon chiral perturbation theory
• Two-loop Corrections for Nuclear Matter in a Covariant Effective Field Theory
• Effective lagrangian approach to structure of selected nuclei far from sta bility
• Two-Loop Calculations with Vertex Corrections in the Walecka Model
• On the Surface Structure of Strange Superheavy Nuclei
• Recent Developments in the Nuclear Many-Body Problem
• Manifestly Lorentz-Invariant Baryon Chiral Perturbation Theory

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• Incoherent Neutrinoproduction of Photons and Pions in a Chiral Effective Field Theory for Nuclei
• Two-loop Corrections for Nuclear Matter in a Covariant Effective Field Theory
• Hot and dense matter beyond relativistic mean field theory
• A Field-Theoretic Parametrization of Low-Energy Nucleon Form Factors
• Three-loop Corrections in a Covariant Effective Field Theory