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.

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

References in corpus (7)

• Electromagnetic excitation of the Delta(1232)-resonance
• Nuclear forces with Delta-excitations up to next-to-next-to-leading order I: peripheral nucleon-nucleon waves
• Relativity constraints on the two-nucleon contact interaction
• 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 (4)

• Short-range nuclear forces in singlet channels
• The reaction pi N -> pi pi N in chiral effective field theory with explicit Delta(1232) degrees of freedom
• Chiral Lagrangians with $\Delta (1232)$ to one loop
• Renormalization of proton-proton fusion in chiral effective field theory