Simplified calculations of the frequencies of Higgs modes in superfluid ³He-B using N-point Padé approximants

Previous calculations of the frequencies of the Higgs modes in superfluid ³He-B have been done on the real-frequency axis, most recently using the Keldysh formalism. Recently Sauls and Mizushima[1] showed how the unperturbed weak-coupling mode frequencies can be found by solving the imaginary-frequency version of the kinetic equation, followed by standard analytic continuation to real frequencies and evaluation of remaining integrals there. We show that perturbed frequencies due to magnetic fields or strong-coupling effects can be calculated on the imaginary axis and the final results can then be obtained, to high accuracy, by N-point Padé approximants, which greatly simplifies these calculations. [1] J.A. Sauls and Takeshi Mizushima, On the Nambu fermion-boson relations for superfluid 3He, Phys. Rev. B 95, 094515 (2017)