Multi-fermion systems with contact theories

• Main Authors: M. Schäfer, L. Contessi, J. Kirscher, J. Mareš
• Format: Article
• Language: English
• Published: Elsevier 2021-05-01
• Series: Physics Letters B
• Subjects: Universality; Contact effective field theory; Unitarity; Renormalization; Pionless
• Online Access: http://www.sciencedirect.com/science/article/pii/S0370269321001349

We address the question of minimal requirements for the existence of quantum bound states. In particular, we demonstrate that a few-body system with zero-range momentum-independent two-body interactions is unstable against decay into clusters, if mixed-symmetry of its wave function is enforced. We claim that any theory in which the two-body scattering length is much larger than any other scale involved exhibits such instability. We exemplify this with the inability of the leading-order pionless effective field theory to describe stable states of A>4 nuclei. A finite interaction range is identified as a sufficient condition for a bound mixed-symmetry system. The minimal value of this range depends on the proximity of a system to unitarity, on the number of constituents, and on the particular realization of discrete scale invariance of the three-body spectrum.