Phenomenolgical two-branch model for the long-wavelength excitation spectrum of superfluid<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">He</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>4</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

It is suggested that the long-wavelength excitation spectrum of superfluid $^{4}\mathrm{He}$ may consist of a branch of quasiparticle excitations which has a gap at zero momenta in addition to a branch of hydrodynamic phonons. A phenomenological two-branch spectrum is constructed. The model is suggested by the structure of a theory of boson pairing similar to the BCS theory of fermions. The low-temperature specific heat of $^{4}\mathrm{He}$ is calculated within the model and compared with experimental data. It is found that a two-branch-model excitation spectrum can describe the low-temperature anomaly in the specific heat without contradicting existing direct measurement of the excitation spectrum. Some features of a possible microscopic theory of the two-branch spectrum are discussed, and the possibilities of making direct measurements testing the idea of a two-branch excitation spectrum are considered.

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