Efimov States in Nuclear and Particle Physics

Abstract

Particles with resonant short-range interactions have universal properties that do not depend on the details of their structure or their interactions at short distances. In the three-body system, these properties include the existence of a geometric spectrum of three-body Efimov states and a discrete scaling symmetry leading to log-periodic dependence of observables on the scattering length. Similar universal properties appear in the four-body system and possibly higher-body systems as well. For example, universal four-body states have recently been predicted and observed in experiment. These phenomena are often referred to as "Efimov Physics". We review their theoretical description and discuss applications in different areas of physics with a special emphasis on nuclear and particle physics.Comment: Invited review for Annual Review of Nuclear and Particle Scienc

Effective field theory of3He

“…This differs from the triton energy for the same three-body force by 0.82 MeV. It is within 1% of the observed 3 He energy, indicating that the isospin-violating three-body force is indeed a higher-order contribution. This is as expected, given the absence of any modification of the renormalization, since the isospin-violating term is suppressed by one power of the inverse Bohr radius κ relative to the LO force.…”

“…We find that a three-body interaction is required at leading order in 3 He, as in the triton. This force also exhibits the same limit-cycle behavior as a function of the cutoff Λ as found by Bedaque et al [2] for systems with purely short-range interactions.…”

“…We have studied 3 He within the framework of the pionless EFT, treating the Coulomb interaction nonperturbatively. We solve the set of integral equations developed by Kok et al [8], which can be thought of as extending the equation of Skornyakov and ter-Martirosian [17] to include the full offshell Coulomb T -matrix.…”

“…corresponding to a scale α = 85.127 MeV Firstly, assuming the isospin symmetry in the three-body contact interaction and using the Λ 0 value fixed by tritium binding energy above, we get α = 84.8084 MeV, or a binding energy of B 3 = 7.66038 MeV for 3 He. This differs from the triton energy for the same three-body force by 0.82 MeV.…”

“…For the 3 He channel, we need to the pp Coulomb scattering length as a two-body input parameter, a C = −7.8063 ± 0.0026 fm [16].…”