The Delta(1232) Resonance in Chiral Effective Field Theory

Abstract

I discuss the problem of formulating the baryon chiral perturbation theory ($\chi$PT) in the presence of a light resonance, such as the $\Delta (1232)$, the lightest nucleon resonance. It is shown how to extend the power counting of $\chi$PT to correctly account for the resonant contributions. Recent applications of the resulting chiral effective-field theory to the description of pion production reactions in $\Delta$-resonance region are briefly reviewed.

arXiv comment8 pages, 8 figs; prepared for the proceedings of the Intl Erice School ``Quarks in Hadrons and Nuclei'', 29th Course, 16--24 Sep 2007, Sicily, Italy

References in corpus (32)

• Mass and width of the lowest resonance in QCD
• Electromagnetic excitation of the Delta(1232)-resonance
• Meson-exchange Model for $\pi N$ scattering and $\gamma N->\pi N$ reaction
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Dynamical Study of the Delta Excitation in N(e,e' pi) Reactions
• Narrow Resonances in Effective Field Theory
• Systematic 1/M Expansion for Spin 3/2 Particles
• Pion cloud and the $Q^2-$dependence of ${\gamma }^{\ast }N\leftrightarrow \Delta$ transition form factors
• gamma* N -> Delta transition form factors: a new analysis of the JLab data on p(e,e'p)pi0 at Q^2=2.8 and 4.0 (GeV/c)^2
• Search for Quadrupole Strength in the Electro-excitation of the Delta(1232)
• The reaction $\gamma p\to {\pi }^{\circ }{\gamma }^{\prime }p$ and the magnetic dipole moment of the ${\Delta }^{+}(1232)$ resonance
• Investigation of the conjectured nucleon deformation at low momentum transfer
• Chiral Effective-Field Theory in the Delta(1232) Region: Pion Electroproduction on the Nucleon
• The N to Delta electromagnetic transition form factors from Lattice QCD
• Measurement of the recoil polarization in the p (\vec e, e' \vec p) pi^0 reaction at the Δ(1232) resonance
• Magnetic moment of the Delta(1232)-resonance in chiral effective field theory
• Electromagnetic Nucleon-to-Delta Transition in Chiral Effective-Field Theory
• Signatures of chiral dynamics in the Nucleon to Delta transition
• Chiral symmetry and the Delta-Nucleon transition form factors
• Pion-nucleon interaction in a covariant hadron-exchange model
• Magnetic dipole moment of the ${\Delta }^{+}$(1232) from the $\gamma p\to \gamma {\pi }^{0}p$ reaction
• Measurement of the Transverse-Longitudinal Cross Sections in the p (e,e'p)pi0 Reaction in the Delta Region
• Chiral effective-field theory in the Delta(1232) region: II. radiative pion photoproduction
• Inelastic photon scattering and the magnetic moment of the $\Delta$ (1232) resonance
• Pion photoproduction on nucleons in a covariant hadron-exchange model
• ${\gamma }^{\ast }N\Delta$ Form Factors from a Relativistic Dynamical Model of Pion Electroproduction
• Magnetic dipole moment of the $\Delta (1232)$ in chiral perturbation theory
• A dynamical model for pion electroproduction on the nucleon
• Two-photon-exchange effects in the electro-excitation of the $\Delta$ resonance
• Calculation of two-photon exchange effects for $\Delta$ production in electron-proton collisions
• Effective Field Theories of Light Nuclei
• The lifetime of unstable particles in electromagnetic fields

Cited by in corpus (12)

• Photon- and pion-nucleon interactions in a unitary and causal effective field theory based on the chiral Lagrangian
• Neutrinoproduction of Photons and Pions From Nucleons in a Chiral Effective Field Theory for Nuclei
• $\pi N$ Scattering in the $\Delta (1232)$ Region in an Effective Field Theory
• πN scattering in relativistic baryon chiral perturbation theory revisited
• Heavy-particle formalism with Foldy-Wouthuysen representation
• The Role of the Roper in Chiral Perturbation Theory
• Pion photoproduction off nucleons in covariant chiral perturbation theory
• Pseudoscalar Meson and Decuplet Baryon Scattering Lengths
• Threshold pion electro- and photoproduction off nucleons in covariant chiral perturbation theory
• Chiral Lagrangians with $\Delta (1232)$ to one loop
• Baryon Chiral Perturbation Theory combined with the $1/{\mathbf{N}}_{\mathbf{c}}$ Expansion in SU(3) I: Framework
• Effects of consistent and inconsistent isobar coupling in the nuclear medium