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Placing bright sub-millimetre galaxies (SMGs) within the broader context ofgalaxy formation and evolution requires accurate measurements of theirclustering, which can constrain the masses of their host dark matter halos.Recent work has shown that the clustering measurements of these galaxies may beaffected by a `blending bias,' which results in the angular correlationfunction of the sources extracted from single-dish imaging surveys beingboosted relative to that of the underlying galaxies. This is due to confusionintroduced by the coarse angular resolution of the single-dish telescope andcould lead to the inferred halo masses being significantly overestimated. Weinvestigate the extent to which this bias affects the measurement of thecorrelation function of SMGs when it is derived via a cross-correlation with amore abundant galaxy population. We find that the blending bias is essentiallythe same as in the auto-correlation case and conclude that the best way toreduce its effects is to calculate the angular correlation function using SMGsin narrow redshift bins. Blending bias causes the inferred host halo masses ofthe SMGs to be overestimated by a factor of $\sim6$ when a redshift interval of$\delta z=3$ is used. However, this reduces to a factor of $\sim2$ for $\deltaz=0.5$. The broadening of photometric redshift probability distributions withincreasing redshift can therefore impart a mild halo `downsizing' effect ontothe inferred host halo masses, though this trend is not as strong as seen inrecent observational studies.

Blending bias impacts the host halo masses derived from a cross-correlation analysis of bright sub-millimetre galaxies