  In recent years, the Lyman-$\alpha$ absorption observed in the spectra of
high-redshift quasars has been used as a tracer of large-scale structure by
means of the three-dimensional Lyman-$\alpha$ forest auto-correlation function
at redshift $z\simeq 2.3$, but the need to fit the quasar continuum in every
absorption spectrum introduces a broadband distortion that is difficult to
correct and causes a systematic error for measuring any broadband properties.
We describe a $k$-space model for this broadband distortion based on a
multiplicative correction to the power spectrum of the transmitted flux
fraction that suppresses power on scales corresponding to the typical length of
a Lyman-$\alpha$ forest spectrum. Implementing the distortion model in fits for
the baryon acoustic oscillation (BAO) peak position in the Lyman-$\alpha$
forest auto-correlation, we find that the fitting method recovers the input
values of the linear bias parameter $b_{F}$ and the redshift-space distortion
parameter $\beta_{F}$ for mock data sets with a systematic error of less than
0.5\%. Applied to the auto-correlation measured for BOSS Data Release 11, our
method improves on the previous treatment of broadband distortions in BAO
fitting by providing a better fit to the data using fewer parameters and
reducing the statistical errors on $\beta_{F}$ and the combination
$b_{F}(1+\beta_{F})$ by more than a factor of seven. The measured values at
redshift $z=2.3$ are $\beta_{F}=1.39^{+0.11\ +0.24\ +0.38}_{-0.10\ -0.19\
-0.28}$ and $b_{F}(1+\beta_{F})=-0.374^{+0.007\ +0.013\ +0.020}_{-0.007\
-0.014\ -0.022}$ (1$\sigma$, 2$\sigma$ and 3$\sigma$ statistical errors). Our
fitting software and the input files needed to reproduce our main results are
publicly available.
