Four-Body Scale in Universal Few-Boson Systems

Abstract

The role of an intrinsic four-body scale in universal few-boson systems is the subject of active debate. We study these systems within the framework of effective field theory. For systems of up to six bosons we establish that no four-body scale appears at leading order (LO). However, we find that at next-to-leading (NLO) order a four-body force is needed to obtain renormalized results for binding energies. With the associated parameter fixed to the binding energy of the four-boson system, this force is shown to renormalize the five- and six-body systems as well. We present an original ansatz for the short-distance limit of the bosonic $A$-body wave function from which we conjecture that new $A$-body scales appear at N${}^{A-3}$LO. As a specific example, calculations are presented for clusters of helium atoms. Our results apply more generally to other few-body systems governed by a large scattering length, such as light nuclei and halo states, the low-energy properties of which are independent of the detailed internal structure of the constituents.

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• What hath Weinberg wrought? Reflections on what Weinberg's papers on 'Nuclear Forces from Chiral Lagrangians' did and did not accomplish
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• Regulator constraints for the perturbative renormalizability of attractive triplets
• Worldline Monte Carlo method for few body nuclear physics
• Four-Body Systems at Large Cutoffs in Effective Field Theory
• Emergent four-body parameter in universal two-species bosonic systems
• Few-Nucleon Systems within Finite-Cutoff Pionless EFT
• Les Houches Lectures on Effective Field Theories for Nuclear and (some) Atomic Physics
• The Four-Boson First-Excited State Near Two-Body Unitarity
• Synergy between deep neural networks and the variational Monte Carlo method for small ${}^{4}H{e}_N$ clusters
• NuLattice: Ab initio computations of atomic nuclei on lattices
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• Perturbative application of next-to-leading order pionless EFT for $A\le 3$ nuclei in a finite volume
• Efimov physics beyond three particles
• Emergence of N-body tunable interactions in universal few-atom system
• Van der Waals five-body size-energy universality
• Improved Actions for Nuclear Effective Field Theories