drach09's blog

I have finally applied polarization-correction to the Sivers asymmetries for the "all triggers" sample. I utilized a weighted-average techniqe as follows:

Calculate raw asymmetries in p_T-bins separately for the different fills
Correct the raw asymmetries for each fill by dividing by the polarization for the appropriate fill
For each p_T-bin, calculate the weighted mean:

$\langle A_{N}\rangle=\frac{\sum_{i}\left[\left(\epsilon_{i}/P_{i}\right)/\left(\sigma_{\epsilon_{i}}/P_{i}\right)^{2}\right]}{\sum_{i}\left[1/\left(\sigma_{\epsilon_{i}}/P_{i}\right)^{2}\right]}$

$\sigma_{\langle A_{N}\rangle}=\sqrt{\frac{1}{\sum_{i}\left[1/\left(\sigma_{\epsilon_{i}}/P_{i}\right)^{2}\right]}}$

Note, for these calculations I have left out the polarization uncertainty. I have also performed the calculations under the assumption

$\sigma_{A_{N,i}}=|A_{N,i}|\sqrt{ \left(\frac{\sigma_{\epsilon_{i}}}{\epsilon_{i}}\right)^{2} + \left(\frac{\sigma_{P_{i}}}{P_{i}}\right)^{2} }$

and found no significant difference. One reason for excluding the uncertainty is that it includes a systematic piece correlated across all bins. It is trivial to include the polarization uncertainty in the calculation, so I am certainly open to suggestions.

With these asymmetries I have implemented a requirement that I require at least six non-zero φ_S bins for the calculation. Since I, now, perform the calculation separately for each fill, this will sacrifice a few events from my previous update, which sums over the fills prior to calculating the asymmetries. Additionally, I have only considered fills deemed "physics" on the CNI webpage. This excludes a few fills considered in my previous update. All told, the loss of data is quite minimal.

Figure 1: Polarization-corrected Sivers Asymmetry (All Triggers)

In Fig. 1 I show the Sivers asymmetries summing over triggers and eta bins. On the right I post a zoomed-out version, and on the left I zoom in to show the most significant bins. Qualitatively, the situation looks much like my previous update. As before, the lowest bin of x_F < 0 appears to be a bit high (2.57σ).

Figure 2: Polarization-corrected Sivers Asymmetry in η-bins (All Triggers)

In Fig. 2 I show the asymmetries binned in η. Again, the fluctuations for the lowest bin of x_F < 0 appear to derive from the 0 < η < 0.5 bin where there exists a 2.48σ offset from zero and χ²/ν = 24.066/14 (2.00σ).

Bin-by-bin Asymmetries

In Fig. 3 I show the individual asymmetry calculations for the bins of Fig. 1. I note that for the lowest bin of x_F < 0 the fit quality is not very good (2.5σ). It appeasr that a good portion of this may come from the early fills. It may be worth digging into these fills a bit deeper.