  We present a study of the effect of High Column Density (HCD) systems on the
Lyman \alpha forest correlation function on large scales. We study the effect
both numerically, by inserting HCD systems on mock spectra for a specific
model, and analytically, in the context of two-point correlations and linear
theory. We show that the presence of HCDs substantially contributes to the
noise of the correlation function measurement, and systematically alters the
measured redshift-space correlation function of the Lyman \alpha forest,
increasing the value of the density bias factor and decreasing the redshift
distortion parameter $\beta_\alpha$ of the Lyman \alpha forest. We provide
simple formulae for corrections on these derived parameters, as a function of
the mean effective optical depth and bias factor of the host halos of the HCDs,
and discuss the conditions under which these expressions should be valid. In
practice, precise corrections to the measured parameters of the Lyman \alpha
forest correlation for the HCD effects are more complex than the simple
analytical approximations we present, owing to non-linear effects of the damped
wings of the HCD systems and the presence of three-point terms. However, we
conclude that an accurate correction for these HCD effects can be obtained
numerically and calibrated with observations of the HCD-Lyman \alpha
cross-correlation. We also discuss an analogous formalism to treat and correct
for the contaminating effect of metal lines overlapping the Lyman \alpha forest
spectra.
