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The Leggett collective excitations for a two-band Fermi gas with s-wavepairing and Josephson interband coupling in the BCS-BEC crossover at finitetemperatures are investigated within the Gaussian pair fluctuation approach.Eigenfrequencies and damping factors for Leggett modes are determined in anonperturbative way, using the analytic continuation of the fluctuationpropagator through a branch cut in the complex frequency plane, as in Phys.Rev. Lett. 122, 093403 (2019). The treatment is performed beyond the low-energyexpansion, which is necessary when the collective excitation energy reaches thepair-breaking continuum edge. The results are applied in particular to coldatomic gases at the orbital Feshbach resonance and in a regime far from BEC,which can be relevant for future experiments.

Leggett collective excitations in a two-band Fermi superfluid at finite temperatures