Theory of critical first sound near theλtransition ofHe4. II. Attenuation and dispersion forT≥Tλ

The critical dynamics of the superfluid transition are studied on the basis of a complete stochastic model that includes both the thermal diffusion and the first-sound mode. A two-loop calculation is carried out for the sound attenuation and dispersion above and at $T_{\lambda }$. Static and dynamic effects are properly separated. Renormalized field theory is used to describe the critical behavior. It is shown that the static and dynamic renormalization-group functions of the simpler model $F$ are closely related to those of the present model. This provides the basis for novel quantitative tests of the dynamic renormalization-group theory as a function of frequency.