This post contains histograms and plots from the 2006 transversity analysis. As discussed at the analysis meeting, the most interesting result is that which uses all pions in jets (inclusive). That is what this post is dedicated to. NOTE: All averages for all asymmetries are given in the attached table AsymmetryAveragesPDF_Inclusive.pdf.

The first plots below are plots of the cross-ratio histograms used to calculate the asymmetries. There is one histogram for each bin of interest in each of z (pion momentum/jet momentum), pT, and jT. The histograms are fit with a polynomial p₀ + p₁Sin(ϕ_C) and the unpolarized asymmetry is given by the extracted p₁ parameter. Using the average beam polarization we can then calculate the Collins asymmetries.

The leading Collins asymmetries are given in the LeadingCollinsAsymmetry*.pdf plots below. Both π⁺ and π^- asymmetries are given on the same plot for easy comparison. The averages for all of these agree well, as expected when comparing the same data. 

Sivers asymmetries were also calculated from this data set. They are shown in the SiversCombinedAsymmetries*.pdf plots below. These represent true, physical Sivers asymmetries and are calculated in the same way as the Collins asymmetries above. Only when we fit we use the Sivers angle to have a polynomial like p₀ + p₁Sin(ϕ_S). Again the extracted p₁parameter represents the unpolarized asymmetry. The averages measure up well against each other again as we would expect.

I have also calculated asymmetries where I look at “reverse eta”. For these I swap the jet z-momentum direction. For blue beam, I look at negative z jets, and for yellow beam I look at positive z jets. In this way we would expect our asymmetry to be zero, or very approximately so. This is the Collins asymmetry measured for backward scattered jets. These are shown in ReverseEtaCombinedAsymmetry*.pdf below. 

To see how the jet patches affect the result, i.e. how the result is biased by triggers, I calculated the Collins asymmetry for jets that didn’t meet the geometric trigger condition. These jets weren’t matched to a particular jet patch in the barrel. These are shown in UntriggeredCombinedAsymmetry*.pdf below.

Finally the effort to calculate the systematic error for the Collins asymmetry relies on calculating the amount of “leak through” from a Sivers asymmetry. To do this we weight the true yields by the Sivers asymmetry and recalculate our unpolarized asymmetry for this weighting scheme. The result of calculating the unpolarized Collins asymmetry (ε) is that we understand how much leak through that we have.

These plots are shown in SystematicUnpolarizedAsymmetry*.pdf, they’re separated by charge, and each shows both blue and yellow beam asymmetries on the same plot. The previous asymmetries were combined (blue and yellow beam) after polarization was considered. Now we don’t consider polarization, only the raw asymmetry. These all average out to be very small, on the order of ~10^-4 with error larger than the point in all bins.