A Model Study of Discrete Scale Invariance and Long-Range Interactions

Abstract

We investigate the modification of discrete scale invariance in the bound state spectrum by long-range interactions. This problem is relevant for effective field theory descriptions of nuclear cluster states and manifestations of the Efimov effect in nuclei. As a model system, we choose a one dimensional inverse square potential supplemented with a long-range Coulomb interaction. We study the renormalization and bound-state spectrum of the system as a function of the Coulomb interaction strength. Our results indicate, that the counterterm required to renormalize the inverse square potential alone is sufficient to renormalize the full problem. However, the breaking of the discrete scale invariance through the Coulomb interaction leads to a modified bound state spectrum. The shallow bound states are strongly influenced by the Coulomb interaction while the deep bound states are dominated by the inverse square potential.

8 pages, 6 figures, EPJ style, published version

References in corpus (15)

• Universality in Few-body Systems with Large Scattering Length
• Evidence for Efimov quantum states in an ultracold gas of cesium atoms
• Effective Field Theory for Few-Nucleon Systems
• Renormalization of the Three-Body System with Short-Range Interactions
• Effective Field Theory for Halo Nuclei: Shallow p-Wave States
• Narrow Resonances in Effective Field Theory
• Singular Potentials and Limit Cycles
• Efimov States in Halo Nuclei
• Renormalization of Singular Potentials and Power Counting
• The singular inverse square potential, limit cycles and self-adjoint extensions
• The Renormalization Group Limit Cycle for the 1/r^2 Potential
• A renormalized equation for the three-body system with short-range interactions
• Effective theories of scattering with an attractive inverse-square potential and the three-body problem
• On the limit cycle for the 1/r^2 potential in momentum space
• Virtual states of light non-Borromean halo nuclei

Cited by in corpus (23)

• Modern Theory of Nuclear Forces
• Efimov Physics: a review
• Conformality Lost
• Effective field theory description of halo nuclei
• Heavy-quark spin and flavour symmetry partners of the X(3872) revisited: what can we learn from the one boson exchange model?
• Efimov States in Nuclear and Particle Physics
• Universal properties and structure of halo nuclei
• Nonrelativistic inverse square potential, scale anomaly, and complex extension
• Effective field theory of 3He
• Scale Invariance in Heavy Hadron Molecules
• Below the Breitenlohner-Freedman bound in the nonrelativistic AdS/CFT correspondence
• The $D^{\ast }{D}^{\ast }\bar{D}$ and $D^{\ast }{D}^{\ast }{\bar{D}}^{\ast }$ Three-Body Systems
• Three-body forces and Efimov physics in nuclei and atoms
• Renormalization group procedure for potential $-g/r^2$
• Few-body universality in the deuteron-alpha system
• Nonrelativistic scale anomaly, and composite operators with complex scaling dimensions
• Nuclear clusters with Halo Effective Field Theory
• Universal bound states and resonances with Coulomb plus short-range potentials
• Triple-X and beyond: hadronic systems of three and more X(3872)
• Efimov universality with Coulomb interaction
• Efimovian states of three charged particles
• Bound-like State in a 1D Self-Similar Delta-Barrier Array
• Neural-network solution of subtracted three-body Faddeev integral equations near the Efimov limit