Renormalization in the Three-body Problem with Resonant P-wave Interactions

Abstract

Resonant P-wave interactions can be described by a minimal zero-range model defined by a truncated effective range expansion, so that the only 2-body interaction parameters are the inverse scattering volume 1/a_P and the P-wave effective range r_P. This minimal model can be formulated as a local quantum field theory with a P-wave interaction between atom fields and a molecular field. In the two-atom sector, the model is renormalizable, but it has unphysical behavior at high energies, because there are negative-probability states with momentum scale r_P. In the sector with three atoms, two of which are identical, renormalization in some parity and angular-momentum channels involves an ultraviolet limit cycle, indicating asymptotic discrete scale invariance. The Efimov effect occurs in the unitary limit a_P^(-1/3), r_P \to 0, but this limit is unphysical because there are low-energy states with negative probability. The minimal model can be of physical relevance only at energies small compared to the energy scale set by r_P, where the effects of negative-probability states are suppressed.

16 pages, 3 figures, major changes in interpretation of results, final version

References in corpus (12)

• Theory of ultracold Fermi gases
• Resonantly-paired fermionic superfluids
• Nonrelativistic conformal field theories
• Anisotropic Fermi Superfluid via p-wave Feshbach Resonance
• Collisional Properties of p-Wave Feshbach Molecules
• Binding Energies of 6Li p-wave Feshbach Molecules
• Three fully polarized fermions close to a p-wave Feshbach resonance
• Fermion Superfluids of Non-Zero Orbital Angular Momentum near Resonance
• Scattering Models for Ultracold Atoms
• Strongly-resonant p-wave superfluids
• Modeling interactions for resonant p-wave scattering
• Impossibility of the Efimov effect for p-wave interactions

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