Fixed scalar greybody factors in five and four dimensions

We perform the classical gravity calculations of the fixed scalar absorption cross sections by $D$=5 black holes with three charges and by $D=4\mathrm{}$ black holes with four charges. We obtain analytic results for the cases where the energy and the left- and right-moving temperatures are sufficiently low but have arbitrary ratios. In $D=5\mathrm{}$ the greybody factor is in perfect agreement with the recent calculation performed in the context of the effective string model for black holes. In $D=4\mathrm{}$ the formula for the greybody factor in terms of the energy and the temperatures differs from that in $D=5\mathrm{}$ only by the overall normalization. This suggests that the fixed scalar coupling to the effective string in $D=4\mathrm{}$ is identical to that in $D=5\mathrm{}$.