Heavy-particle formalism with Foldy-Wouthuysen representation

Abstract

Utilizing the Foldy-Wouthuysen representation, we use a bottom-up approach to construct heavy-baryon Lagrangian terms, without employing a relativistic Lagrangian as the starting point. The couplings obtained this way feature a straightforward $1/m$ expansion, which ensures Lorentz invariance order by order in effective field theories. We illustrate possible applications with two examples in the context of chiral effective field theory: the pion-nucleon coupling, which reproduces the results in the literature, and the pion-nucleon-delta coupling, which does not employ the Rarita-Schwinger field for describing the delta isobar, and hence does not invoke any spurious degrees of freedom. In particular, we point out that one of the subleading $\pi N\Delta$ couplings used in the literature is, in fact, redundant, and discuss the implications of this. We also show that this redundant term should be dropped if one wants to use low-energy constants fitted from $\pi N$ scattering in calculations of $NN\to NN\pi$ reactions.

arXiv comment28 pages, 2 figures, RevTeX4, appendix added, version published in Phys. Rev. C

References in corpus (31)

• Modern Theory of Nuclear Forces
• Chiral Dynamics in Nucleons and Nuclei
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• The Two-Nucleon Potential from Chiral Lagrangians
• Mass and width of the lowest resonance in QCD
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Electromagnetic excitation of the Delta(1232)-resonance
• Heavy Baryon Chiral Perturbation Theory with Light Deltas
• Effective Field Theory of Nuclear Forces
• The chiral effective pion-nucleon Lagrangian of order p^4
• The HQET/NRQCD Lagrangian to order alpha/m^3
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Meson production in nucleon--nucleon collisions close to the threshold
• Quantization of an interacting spin-3/2 field and the Delta isobar
• Systematic 1/M Expansion for Spin 3/2 Particles
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• The $pp\to pp{\pi }^0$ Reaction near Threshold: A Chiral Power Counting Approach
• Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields
• Low-energy expansion of the pion-nucleon Lagrangian
• Chiral Three-Nucleon Forces from p-wave Pion Production
• Redundance of $\Delta$-isobar Parameters in Effective Field Theories
• Equivalence of Nonstatic Two-Pion-Exchange Nucleon-Nucleon Potentials
• Redundancy of the off-shell parameters in chiral effective field theory with explicit spin-3/2 degrees of freedom
• $\pi N$ Scattering in the $\Delta (1232)$ Region in an Effective Field Theory
• Relativity constraints on the two-nucleon contact interaction
• p-Wave pion production from nucleon-nucleon collisions
• Poincare' invariance and the heavy-quark potential
• On-shell consistency of the Rarita-Schwinger field formulation
• Bridging over p-wave pi-production and weak processes in few-nucleon systems with chiral perturbation theory
• The Delta(1232) Resonance in Chiral Effective Field Theory
• Comparison of the heavy-fermion and Foldy-Wouthuysen formalisms at third order

Cited by in corpus (16)

• The chiral representation of the $\pi N$ scattering amplitude and the pion-nucleon sigma term
• Local chiral potentials and the structure of light nuclei
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Renormalizing Chiral Nuclear Forces: Triplet Channels
• Delta isobars and nuclear saturation
• Short-range nuclear forces in singlet channels
• The nucleon mass and pion-nucleon sigma term from a chiral analysis of lattice QCD world data
• Lorentz invariance in heavy particle effective theories
• Microscopically-based energy density functionals for nuclei using the density matrix expansion: Full optimization and validation
• Weak pion production off the nucleon in covariant chiral perturbation theory
• Do we know how to count powers in pionless and pionful effective field theory?
• The Role of the Roper in Chiral Perturbation Theory
• The reaction pi N -> pi pi N in chiral effective field theory with explicit Delta(1232) degrees of freedom
• Cutoff regulators in chiral nuclear effective field theory
• Chiral Lagrangians with $\Delta (1232)$ to one loop
• Renormalization of proton-proton fusion in chiral effective field theory