Hi,
I have understood the issue, as I said, it is a technical artefact due to the introduction of systematics.
To compute the p-value (CL(s+b) ) used to get the limit (the red points in your scan plot) you count the number of toy events the test statistics for the given s is larger or equal than the data value. Now when you don’t have systematics, if you observe 0 events, you will have a large fraction of toys also with zero events. In that case the test statistics in the data is exactly the same as the test statistics in the toys when generated with N=0. If you have a very small systematics, around 50% of the toys with N=0 will have a test statistics smaller than the data, decreasing then the obtained p-value.
I am not sure what is the correct value to quote, since this is just a procedure to compute limit.
We could maybe add an option to consider all the toys within an interval of the given test statistics value in the data, to avoid this effect. In this case we would get basically the same value without systematics.
However, if the systematic is small, (10% for 0.6 is small) , I think it is better to quote the value without systematics.
Note that Feldman-Cousins has also the weird property to have a better (lower) upper limit when you increase the background.
Lorenzo