Update:I determined the electron peak positions in the p < 3.00 bins by letting that parameter float instead of fixing it to the Bichsel value. The difference was about 0.75σ in the lowest bin. The χ2 for that bin is dramatically better. Some of the other higher momentum slices in the first bin still have large χ2 values, but for the moment I’m working under the assumption that the background fractions are basically correct. So that bin’s back in. I’ve updated the PDF with the new fits.

Historically, I’ve used separate triple-Gaussian fits for positively- and negatively-charged tracks (18 free parameters in total) to extract the pion, proton/kaon, and electron yields for my A_{LL} analyses. There are several problems with that approach

1. To first order, dE/dx resolution is independent of particle species.
2. The peak positions for pions, kaons, protons, and electrons are not charge-dependent.
3. Those peak positions (or at least the separations between them) have been determined with a great deal of accuracy in other analyses.
4. dE/dx scales with momentum, not p_{T}. At y = 1.0, p ~ 1.5*p_{T}. This difference was not being taken into account.

I set out to address those three points by redoing the fits in the manner employed by the lfspectra working group. I fill a 3D histogram of p_{T} vs. p vs. (nσ(π) + 6*track.charge()), and then fit individual xy slices of this histogram with a function comprised of 8 Gaussians. That function is subject to the following constraints:

• all Gaussian widths are identical
• π+ mean == π- mean (after subtracting imposed offset of 12)
• K+ mean == K- mean (ditto)
• proton mean == pbar mean (ditto)
• positron mean == electron mean (ditto)
• π mean - K mean is a fixed function of momentum
• π mean - p mean is a fixed function of momentum
• π mean - e mean is a fixed function of momentum

That leaves 24-14 = 10 free parameters for each fit. I received the momentum-dependent particle separations from Yichun Xu. Her work is documented in this NIM draft, and the actual values for the separation are posted at (columns are p, p/mass, and separation):

π - electron separations
π - kaon separations
π - proton separations

The results of the fits are attached as a PDF. The fits in the first p_{T} bin (2.00 - 3.18) are not good. Part of the reason is that Yichun’s analysis doesn’t go below 3.0 GeV/c, so I used a Bichsel parameterization for the particle separations instead of taking them from data. This bin is complicated because at the low momenta the protons are entering the 1/β^2 region. I think the sensible choice may be to drop the bin from the A_{LL} analysis.

The fits for the higher p_{T} bins are much better, particularly at mid-rapidity. I don’t really believe in the p/π and K/π ratios that come out, but in the end I think the only important thing for my analysis is that the (p+K)/π ratio is correct. I’ll explore the effect of these new fits on A_{LL} in a separate post.