Here we look at the constraints on the BTT three-point function with S4. For more on the BTT three-point function see http://lanl.arxiv.org/abs/1603.02243 (paper) http://lanl.arxiv.org/abs/1605.04431 (shorter conference proceedings)
These forecasts are with
-Fixed effort with corresponding to noise of 1 uK-arcmin
-No cosmic variance in B
Main conclusion; since B noise is the limiting factor in this correlation (and not T), roughly cancels. Only for very small sky fraction, there seems to be some effect. The conclusion should not hold when we detect r at some level (e.g. 0.01). I can make plots for that as well.
For equilateral NGs in BTT the beam effect is small, however the sky fraction effect is even smaller.