Functional renormalisation group for few-nucleon systems: SU(4) symmetry and its breaking

Abstract

We apply the functional renormalisation group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalisation group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalisation flow equations decouple, and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for fermions with spin degrees only. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and quintet channels.

References in corpus (6)

• Exact evolution equation for the effective potential
• Flow Equations for the BCS-BEC Crossover
• Efimov effect from functional renormalization
• Three-body scattering from nonperturbative flow equations
• Functional renormalisation group for two-body scattering
• Convergence of a renormalization group approach to dimer-dimer scattering

Cited by in corpus (5)

• New applications of renormalization group methods in nuclear physics
• Functional renormalization group studies of nuclear and neutron matter
• Nuclear Symmetries of the similarity renormalization group for nuclear forces
• Universal behaviour of four-boson systems from a functional renormalisation group
• Few-body hierarchy in non-relativistic functional renormalization group equations and a decoupling theorem