Documentation for a systematic uncertainty in the Run 5 charged pion A_{LL} based on contamination from non-pions in the PID selection window.

Background Contamination Fraction

In my analysis I look at nσ(π) distributions for each fill and choose a PID selection window based on the result of a triple-Gaussian fit for that fill. Details of that analysis can be found here. On this page I use the fit results to recalibrate the cumulative nσ(π) distributions, that is for each track I do

nSigmaPion = (track.nSigmaPion() - pidFit.mean()) / pidFit.sigma()

The result should be that any fill-to-fill variations are removed, and nσ(π) summed over all fills will have a pion Gaussian with a mean of 0 and sigma of 1. The increase in statistics by summing over all fills allows me to investigate the pT-dependence of the fits. First, here’s the pT-integrated, charge-summed nσ(π) distribution:

The χ^2 could be a little better given the ~90 dof, but generally speaking the fit looks good. Now here are the fits for each pT bin in the Run 5 analysis:

I think the most dramatic effect is the way the electron Gaussian moves underneath the pion peak at high pT. Note: I forced the electron mean to be > 1.5 in the 8-10 fit — if I don’t, the result is a fit with an equivalent χ^2/dof (1.07 instead of 1.08) but an electron contribution that is far too large. I linked the plot here.

Background Asymmetries

Using the above fits I get f_{bg}(pT) = {10, 9, 10, 16} x 10^-2. The next step is to calculate the asymmetry of the background, which I did by collecting all charged tracks that passed my cuts but fell 2 sigma away from the mean of the recalibrated nσ(π) and plotting their A_{LL}:

Run 6 Background Asymmetries

Well, the lack of statistics at high p_{T} was really making this systematic uncertainty annoyingly large, so I decided to also calculate the background asymmetry using 2006 long2 data. I selected only runs that passed Murad’s QA and had good relative luminosities (board 5 or 6) from Tai, and integrated over BBC timebins 6-9. Other than that, the cuts remain the same as for the 2005 analysis. Here’s the results for the BJP1 trigger:

In the final analysis I combine these Run 5 and Run 6 measurements to obtain a more precise estimate of the background A_{LL}.

Assignment of the Uncertainty

The relation between measured A_{LL} and the “true” background-free charged pion A_{LL} is

so the systematic uncertainty we assign is given by

In this analysis I actually use max(δA_{LL,bg}, |A_{LL,meas} - A_{LL,bg}|) to account for situations where the signal and background A_{LL} are statistically compatible. The final p_{T}-dependent systematics from this analysis are then

π+: {2.11, 2.92, 1.66, 4.46} e-3
π-: {0.76, 1.09, 3.02, 5.70} e-3

NB: In my SPIN 2006 preliminary result, I did not consider the pT-dependence of the background asymmetry, but instead used a pT-integrated background asymmetry + 1 sigma to assign a systematic. As a result, the uncertainty assigned via this final analysis is still larger in certain bins than the preliminary value of 1.7e-3.

Possibilities for Improvement

1. Calculate background fractions and asymmetries for electrons and protons/kaons separately. This won’t reduce the size of the uncertainty, but it just seems like the right thing to do in my book.

2. Be really, really sure that the increase in background fraction from 10% to 16% in the last bin isn’t just an artifact of the fit. There is physics going on here, of course — the dE/dx bands get much closer together at high momentum.