Narrow resonances and short-range interactions

Abstract

Narrow resonances in systems with short-range interactions are discussed in an effective field theory (EFT) framework. An effective Lagrangian is formulated in the form of a combined expansion in powers of a momentum Q << Lambda--a short-distance scale--and an energy difference delta epsilon = |E-epsilon_0| << epsilon_0--a resonance peak energy. At leading order in the combined expansion, a two-body scattering amplitude is the sum of a smooth background term of order Q^0 and a Breit-Wigner term of order Q^2 (delta epsilon)^{-1} which becomes dominant for delta epsilon <~ Q^3. Such an EFT is applicable to systems in which short-distance dynamics generates a low-lying quasistationary state. The EFT is generalized to describe a narrow low-lying resonance in a system of charged particles. It is shown that in the case of Coulomb repulsion, a two-body scattering amplitude at leading order in a combined expansion is the sum of a Coulomb-modified background term and a Breit-Wigner amplitude with parameters renormalized by Coulomb interactions.

9 pages, 4 figures, references added

References in corpus (31)

• Renormalization Group Approach to Interacting Fermions
• Effective Field Theory for Few-Nucleon Systems
• A New Expansion for Nucleon-Nucleon Interactions
• Two-Nucleon Systems from Effective Field Theory
• The Two-Nucleon Potential from Chiral Lagrangians
• Few-Nucleon Forces and Systems in Chiral Effective Field Theory
• Three-Body Interactions Among Nucleons and Pions
• Effective Field Theory for Short-Range Forces
• Introduction to Effective Field Theory
• Effective Field Theory for Halo Nuclei: Shallow p-Wave States
• More Effective Field Theory for Nonrelativistic Scattering
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• Resonance Superfluidity: Renormalization of Resonance Scattering Theory
• A renormalisation-group treatment of two-body scattering
• Narrow Resonances in Effective Field Theory
• Resonant Fermi gases with a large effective range
• Coulomb Effects in Low Energy Proton-Proton Scattering
• alpha-alpha Scattering in Halo Effective Field Theory
• A renormalisation group approach to two-body scattering in the presence of long-range forces
• Proton-Proton Scattering Lengths from Effective Field Theory
• Scattering Models for Ultracold Atoms
• Proton-Proton Fusion in Effective Field Theory
• Perturbative nuclear physics
• Universality in Phase Transitions for Ultracold Fermionic Atoms
• Renormalisation Flow and Universality for Ultracold Fermionic Atoms
• Low energy proton-proton scattering in effective field theory
• Hadronic Atoms and Effective Interactions
• Functional Integral for Ultracold Fermionic Atoms
• Scheming in Dimensional Regularization
• Systematic Power Counting in Cutoff Effective Field Theories for Nucleon-Nucleon Interactions and the Equivalence With PDS
• Renormalization-group analysis for low-energy scattering of charged particles

Cited by in corpus (16)

• Nuclear effective field theory: status and perspectives
• Resonance Contribution to Radiative Neutron Capture on Lithium-7
• Radiative Neutron Capture on Carbon-14 in Effective Field Theory
• Coupled-channel effective field theory and proton-${}^7$Li scattering
• Elastic $\alpha$-${}^{12}$C scattering at low energies in cluster effective field theory
• Weinberg's Compositeness
• Nonrelativistic Effective Field Theory with a Resonance Field
• Effective Field Theory for Two-Body Systems with Shallow S-Wave Resonances
• Effective field theory for shallow P-wave states
• The $S$ matrices of elastic $\alpha$-${}^{12}$C scattering at low energies in effective field theory
• Short-range interactions and narrow resonances in effective field theory
• Radiative proton capture on ${}^{15}\mathrm{N}$ within effective field theory
• Elastic $\alpha$-${}^{12}$C scattering at low energies with the sharp resonant $0_3^{+}$ state of ${}^{16}$O
• Chiral dynamics of S-wave baryon resonances
• Matching effective few-nucleon theories to QCD
• Exploring universality in nuclear clusters with Halo EFT