Run 9 200GeV Dijet Cross Section: Integrated Luminosity Systematic

Hopefully the last discussion on how to quantify the systematic error associated with the extraction of the integrated luminosity ...

As has been documented in previous blogs and presentations, the number of reconstructed dijets per unit of integrated luminosity as measured by the BBC changes during the course of the run. It appears that there is a discreet change in this relationship which starts between days 152 and 154 when the accelerator delivered several transverse fills to STAR. Also around this time (day 155) sector 18-1 died, causing a slight change in the invariant mass spectrum.

The period before day 152 exhibits rather large inter-fill variation in the dijet/BBC ratio (see for example figure 1 here) as compared to the period after day 152. Because of this it was decided to extract the cross section from the later part of the run. However, without knowing the cause of the abrupt change in between days 152 and 154, it is imposible to say for which period the integrated luminosity determination is correct (if either is). It is possible for example, that whatever change eliminated the inter-fill variation, also moved the number of dijets seen per number of BBC counts away from the 'correct' relationship.

The systematic error on the integrated luminosity determination should reflect this uncertainty on which period has the 'correct' integrated luminosity. I think the most straight forward way of doing that is to look at the raw yields and cross sections from before and after the day 152-154 split and use the difference as a systematic. I present several different 'before and after' comparisons as a way to estimate the difference between periods including a comparison of the raw dijet yield from the EMC only branch (this is how I arrived at the 17% number I have often quoted), a comparison of the unfolded dijet cross sections from the two periods, and a comparison of the (data-theory)/theory values for the two periods.

In this blog post, I estimated the size of the scale systematic due to the change in integrated luminosity determination to be 17%, which is the preliminary estimation of this systematic which I have been quoting for some time. I did this by looking at the ratio of the dijet yield from the EMC only branch from before and after day 155. I originally split at day 155 to see the difference caused by sector 18-1 dying, but there are only a handful of runs between the day 152-154 split and day 155 that looking at this difference should be quite similar to looking at pre/post day 152-154. Looking at the EMC only branch removes any mass dependence and leaves only the effects due to the change in integrated luminosity determination.

The integrated luminosity systematic quoted above does not include any possible mitagation which may come from the unfolding procedure so I wanted to compare the unfolded yields (normalized by the BBC determined integrated luminosity) from before and after the day 152-154 split.

Figure 1: Ratio of the unfolded cross section from days 120-152 over the cross section from days 154-180. The data ratio is in red and the theory ratio is in blue. The data cureve is fit with a p0 over 19-100 GeV.

Figure 2: Ratio of (Data-Theory)/Theory for the period before day 153 (red) and after day 153 (blue). The ratio for the entire period is in black. The data for each period (and the UEH corrections to the theory) were unfolded using the embedding sample appropriate for that period.

Figure 3: Difference between the (Data-Theory)/Theory ratios from the pre and post day 152-154 split (red curve - blue curve from figure 2).

If we assume that the integrated luminosity is calculated correctly for either the pre or post day 152-154 period, then the cross sections extracted for those two periods should represent upper and lower bounds on where the true cross section sits. Since it is not known which period is correct, it may be most prudent to calculate the cross section from the entire data set and use the deviation from that 'average' cross section to the pre/post day 152-154 limiting case cross sections as the systematic. Figure 2 shows roughly what this would look like.

As the uncertainty on the integrated luminosity is a scale uncertainty, we need one value to assign to all points. The mass independent EMC branch determination gave an uncertainty of 17%. The average values of the unfolded comparisons sit around 10%, but there is statistical scatter and mass dependence with some of the high mass points reaching ~15%  or more. We may also want to consider giving ourselves some extra wiggle room.

If we use the entire run to extract the cross section central value, then I think its reasonable to take half of the difference between the pre and post day 152-154 cross sections as a systematic. If we assume an average difference of between 15% and 20% (giving a little extra bump in uncertainty on the high end) between the two periods, that would translate to a systematic uncertainty of 7.5% to 10%. This uncertainty would then need to be added (in quadrature?) to the uncertainty on the actual effective BBC cross section as extracted by Angelika.