Dimensional Power Counting in Nuclei

Abstract

Weinberg's dimensional power counting for nuclei is reprised in this primer. The role of QCD and chiral symmetry in constructing effective Lagrangians is discussed. The two-scale hypothesis of Manohar and Georgi is combined with power counting in amplitudes to shed light on the scales of nuclear kinetic and potential energies, the size of strong-interaction coupling constants, the size of meson-exchange currents, and the relative sizes of $N$-nucleon forces. Numerous examples are worked out and compared to conventional nuclear models.

38 pages, latex, 10 figures -- submitted to Few-Body Systems -- epsfig.sty and fbssuppl.sty required

Cited by in corpus (45)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Three-Nucleon Forces from Chiral Effective Field Theory
• Neutron Radii in Mean-Field Models
• Nuclear effective field theory: status and perspectives
• Effective Field Theory for Short-Range Forces
• Effective Field Theory of Nuclear Forces
• The nucleon-nucleon interaction
• Uncertainty analysis and order-by-order optimization of chiral nuclear interactions
• Resonance saturation for four-nucleon operators
• The Effective Chiral Lagrangian From Dimension-Six Parity and Time-Reversal Violation
• Four-nucleon force in chiral effective field theory
• How low-energy weak reactions can constrain three-nucleon forces and the neutron-neutron scattering length
• Electromagnetic Corrections to the One-Pion-Exchange Potential
• Lambda-nuclear interactions and hyperon puzzle in neutron stars
• Power Counting of Contact-Range Currents in Effective Field Theory
• Nuclear Octupole Correlations and the Enhancement of Atomic Time-Reversal Violation
• Charge-dependent nucleon-nucleon potential from chiral effective field theory
• Compton scattering on the proton, neutron, and deuteron in chiral perturbation theory to O(Q^4)
• Charge-Symmetry Breaking and the Two-Pion-Exchange Two-Nucleon Interaction
• The $A_y$ Puzzle and the Nuclear Force
• Charge-Independence Breaking in the Two-Pion-Exchange Nucleon-Nucleon Force
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Large Lorentz Scalar and Vector Potentials in Nuclei
• Deuteron electromagnetic properties and the viability of effective field theory methods in the two-nucleon system
• The pion-nucleon scattering lengths from pionic deuterium
• Power counting in chiral effective field theory and nuclear binding
• Density-dependent effective baryon-baryon interaction from chiral three-baryon forces
• Charge-Symmetry-Breaking Three-Nucleon Forces
• Nuclear Corrections to Hyperfine Structure in Light Hydrogenic Atoms
• Compton Scattering on the Deuteron in Baryon Chiral Perturbation Theory
• Implications of Efimov physics for the description of three and four nucleons in chiral effective field theory
• Ab-initio electroweak corrections to superallowed $\beta$ decays and their impact on $V_{ud}$
• Improved analysis of neutral pion electroproduction off deuterium in chiral perturbation theory
• Can one extract the pi-neutron scattering length from pi-deuteron scattering?
• Nuclear Effective Field Theories: Reverberations of the early days
• The Structure of Light Nuclei and Its Effect on Precise Atomic Measurements
• The Nuclear Physics of Hyperfine Structure in Hydrogenic Atoms
• Natural Units For Nuclear Energy Density Functional Theory
• Loop Corrections and Naturalness in a Chiral Effective Field Theory
• Electromagnetic Interactions in a Chiral Effective Lagrangian for Nuclei
• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
• Scattering Observables from One- and Two-Body Densities: Formalism and Application to $\gamma {}^3$He Scattering
• Chiral Symmetry and Low Energy Pion-Nucleon Scattering
• Weinberg and few-nucleon forces