Effective mass of composite fermion: a phenomenological fit in with anomalous propagation of surface acoustic wave

We calculate the conductivity associated with the anomalous propagation of a surface acoustic wave above a two-dimensional electron gas at $\nu=1/2$. Murthy-Shankar's middle representation is adopted and a contribution to the response functions beyond the random phase approximation has been taken into account. We give a phenomenological fit for the effective mass of composite fermion in with the experimental data of the anomalous propagation of surface acoustic wave at $\nu=1/2$ and find the phenomenological value of the effective mass is several times larger than the theoretical value $m_{th}^*=6\epsilon/e^2l_{1/2}$ derived from the Hartree-Fock approximation. We compare our phenomenologically fitting composite fermion effective mass with those appeared in the measurements of the activation energy and the Shubnikov-de Haas effect and find that our result is fairly reasonable.