Here, I begin to calculate my needs for an embedding request. I begin with information from Run-6 Monte Carlo as outlined in Pibero's TAMU webpage. I note that the linked webpage does not reflect the final request, and thus following this model may be problematic. It is nonetheless a place to start.

Table 1

Table 1 shows the 2006 simulation request used as the starting point for estimating the 2009 inclusive jet request. For the current request I need to verify that I do not need to go below 3 GeV/c in partonic p_T to cover my needs for the 5-6 GeV/c reconstructed jet bin. If I need to go to 2 GeV/c or below, the numbers could change quite a bit.

Table 2

Table 2 shows the raw jet yields for each bin of partonic and reconstructed p_T. The basic idea is to estimate the uncertainty on the mean "true" p_T for each reconstructed p_T bin given the statistics from Run-6. I can, then, scale the partonic p_T bins to achieve the desired statistics and use the result to estimate the number of events I will need for my study.

ROOT uses the following expression to calculate the uncertainty on the mean:

For the time being I will assume an RMS of 7 GeV/c for a conservative estimate of all reconstructed p_T bins. Table 3 shows the estimated uncertainty of the mean under the current assumption.

Table 3

In each bin, the estimated uncertainty appears to be smaller than my current needs. Thus, it may be possible to request even fewer events than the Run-6 request.

Table 4

Table 4 contains the weighted jet yields according to Pibero's webpage. These are from weighting the yields and combing JP1 and JP2 with relative fractions from the data. This obviously will be different from Run-11 triggers, but perhaps it will suffice to be informative for my request.

Table 5

With a goal of σ(Mean) = 0.05, Table 5 shows the required scales for the reconstructed jet yields.

Table 6

Table 6 shows the weighted jet yields, now, scaled by the values in Table 5. The far-right-hand column reflects the jet yields summed across reconstructed jet bins.

Table 7

Table 7 shows the ratio of scaled to weighted partonic jet yields summed across reconstructed jet bins. The estimated number of required events is then the product of the ratio and the original Run-6 request. The overall total is shown in blue. Again, this table does not include a 2-3 GeV/c bin. One such bin was included for the 2009 analysis, and it would be no surprise if it is needed, here.

Figure 1

In Fig. 1 I show the normalized distribution of reconstructed jet p_T for each bin of partonic p_T. The black points are the 2006 jets as described in Table 4, normalized to sum to unity. The red crosses are the existing embedding data for the 2011 analysis (generated for 2009 dijets), again, normalized to sum to unity. The shapes in the overlapping bins appear to be quite similar, beginning to diverge noticeably by the 55-65 GeV/c bin.