Fried-Yennie gauge in dimensionally regularized QED

The Fried-Yennie gauge in QED is a covariant gauge with agreeable infrared properties. That is, the mass-shell renormalization scheme can be implemented without introducing artificial infrared divergences, and terms having spuriously low orders in $\alpha$ disappear in certain bound-state calculations. The photon propagator in the Fried-Yennie gauge has the form $D_{\beta }^{\mu \nu }\mathrm{}\left(k\right)=(-\frac{1}{k^2})[g^{\mu \nu }+\frac{\beta k^{\mu }{k}^{\nu }}{k^2}]$, where $\beta$ is the gauge parameter. In this work, I show that the Fried-Yennie gauge parameter is $\beta =\frac{2}{(1-2\mathrm{}\epsilon )}$ when dimensional regularization (with $n=4-2\mathrm{}\epsilon$ dimensions of spacetime) is used to regulate the theory.