Note on BG correction dependence on Pion Purity Variations

The following figure shows the pion purity for each pT bin used in the A_LL analysis; this was copied from the analysis note.
The uncertainty is the MLM purity uncertainty, given the uncertainties for each runset's purity fit

Question: how much do the nominal A_LL values change, given reasonable changes in pion purity?

Test: recalculate BG-corrected A_LL for 2 cases:
-- HIGHER PURITY VARIATION:  purity --> purity + purityErr
-- LOWER PURITY VARIATION:  purity --> purity - purityErr

- blue points: A_LL with nominal purity
- red points: A_LL varied purity (either varied lower (left panel) or higher (right panel))
- black points: A_LL with varied purity minus A_LL with nominal purity



Conclusion: variations in A_LL due to reasonable variations in purity are no more than the relative luminosity systematic (~3e-4)