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arXiv:2609.25219

A Unitary Fixed Point Away from Threshold: Momentum-Surface EFT for Strong Mixing

Lorenzo De Ros, Javier Reig Navarro

Published Sep 21, 2026• 0 citations
arXivHTMLPDF

Abstract

Radiative capture in a non-relativistic system can become non-perturbative even when the underlying transition interaction is weak. We demonstrate this mechanism in a simple quantum-mechanical two-channel model with a systematic power counting, where strong mixing between scattering and bound states develops in a narrow region around a finite momentum $k_0$, leading to a perturbative violation of unitarity. In this regime, the enhanced contributions factorize, reducing the dynamics to a free scattering state interacting through a strong local coupling. Under RG evolution in the factorization scale, this local interaction approaches a unitary fixed point, analogous to that of systems with an anomalously large scattering length. This motivates an EFT organized around the finite-momentum surface $|\mathbf{k}|=k_0$, describing fermions at unitarity with a linear dispersion relation. The resummation resulting from the EFT restores unitarity and provides a systematic expansion for both elastic scattering and radiative capture.

DOI
10.48550/arxiv.2609.25219

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The usual treatment of a Bose-Fermi mixture relies on weak-coupling Gross-Pitaevskii (GP) and density-functional (DF) Lagrangians, often including the more realistic perturbative Lee-Huang-Yang (LHY) corrections. We suggest analytic non-perturbative beyond-mean-field Bose and Fermi Lagrangians valid along the crossover from weak- to strong-coupling limits of intraspecies interactions consistent with the LHY corrections and the strong-coupling (unitarity) limit for small and large scattering lengths ∣a∣|a|∣a∣, respectively, and use these to study the Bose-Fermi mixture. We study numerically mixing-demixing and spontaneous symmetry breaking in Bose-Fermi mixtures in spherically symmetric and quasi-one-dimensional traps, while the intraspecies Bose and Fermi interactions are varied from weak-coupling to strong-coupling limits. The LHY correction is appropriate for medium to weak atomic interactions and diverges for stronger interactions (large scattering length ∣a∣|a|∣a∣), whereas the present beyond-mean-field Lagrangian is finite in the unitarity limit ($|a|\ensuremath{\rightarrow}\ensuremath{\infty}$). We illustrate our results using the Bose-Fermi ${}^{7}\mathrm{Li}{\text{\ensuremath{-}}}^{6}\mathrm{Li}$ mixture under a spherically-symmetric and a quasi-one-dimensional trap. The results obtained with the present model for density distribution of the Bose-Fermi mixture along the crossover could be qualitatively different from the usual GP-DF Lagrangian with or without LHY corrections. Specifically, we identified spontaneous symmetry breaking and demixing in the present model not found in the usual model with the same values of the parameters.
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