Rob made plots of the Collins angle (phiC)  for the sum of the luminosity weighted spin up and spin down events for both positive and negatively charged pions.  The distributions show periodic inefficiencies tied to a combination of the TPC sectors and BEMC trigger sectors.  The spectra is shifted by a few degrees from positive to negative and this accounts for the opposite bending within the TPC.

To estimate the effect of this acceptance (D) on the calculated asymmetry we take a known asymmetry (A_physics) and multiply by the detector distributions as we integrate over the phiC bins:

Spin up yields per phiC bin = Y+ =  D(phiC) * (1 + A_physics sin(phiC))

Spin down yields per phiC bin = Y- = D(phiC) * (1 + A_physics sin(phiC))

Then we integrate over the phiC bins to get the final Asymmetry:

A_calculated= 2  SUM { (Y+ + Y-)*sin(phiC)} / SUM{ Y+ + Y- } 

Comparing A_physics and A_calculated  quantifies the effect of the acceptance. 

First we start with a completely flat acceptance, D =1, and an asymmetry A =0.03.   The plot below shows the spin up and spin down yields as well as the input acceptance distribution (black).

For an ideal and flat acceptance distribution and  input Asymmetry =0.03

Output Asymmetry pi+ = 0.03 %diff = 0

Output Asymmetry pi- = 0.03 %diff = 0

The output asymmetry is the same as the input.

Using the real data acceptance distribution and input Asymmetry =0.03

Output A pi+ = 0.0241392 diff = 0.00586077  %diff =19.5359
Output A pi- = 0.0212484 diff = 0.00875161  %diff =29.172
 

The effect on the data is 19% for the pi+ and 29% for the pi-, or 6 (9) x 10-3 in magnitude, which is less than half of our current leading systematic.