In the most recent updates, I showed data-to-embedding comparisons of jet-patch triggered events, reconstructed from the new Run-11 embedding sample. Under a new set of trigger definitions, it was apparent that all comparisons but JP0 (and perhaps AJP) appear to be sensible. At the lowest accepted p_T bin (7.1 < p_T < 8.4 GeV/c), the embedding sample appears to continue to rise while the data appears to level off near the trigger threshold. I have since run a few studies to try to locate whence this behavior arises. As a reminder the current trigger definition is as follows:

• VPDMB:
  • VPDMB fires in the hardware
  • jet p_T > 5 GeV/c
  • data only: |z_{vertex, TPC}-z_{vertex, VPD}| < 6 cm
  • embedding only: |z_{vertex, TPC}-z_{vertex, thrown}| < 2 cm
  • embedding only: jet p_T < 16.3 GeV/c
• JP0:
  • JP0 fires in the hardware and software
  • jet matches to JP0 patch
  • jet p_T > 7.1 GeV/c
• JP1:
  • JP1 fires in the hardware and software
  • jet matches to JP1 patch
  • jet p_T > 9.9 GeV/c
• JP2:
  • JP2 fires in the hardware and software
  • jet matches to JP2 patch
  • jet p_T > 16.3 GeV/c
• AJP:
  • AJP fires in the hardware and software
  • jet matches to AJP patch
  • jet p_T > 16.3 GeV/c

In the data, jets are assigned to the first and only the first category satisfied. In the simulation, jets are assigned to any of the above categories satisfied. The bins of p_T are as follows:

    const int nbins = 18;
    const double ptbins[nbins+1] = { 5.0, 6.0, 7.1, 8.4, 9.9, 11.7, 13.8, 16.3, 19.2, 22.7, 26.8, 31.6, 37.3, 45., 55., 65., 80., 100., 250. };

Note: I have no illusions of using jets as high as 250 GeV. I will tune an upper limit with the new simulation. From studies with the old embedding 55 GeV/c seemed a sensible limit. The lower limit will likely depend upon our ability to understand low matching probabilities in VPDMB from 5-7.1 GeV/c.

Current Status of Transverse Momentum Comparison

Figure 1

JP0	JP1
JP2	AJP

Figure 1 shows the most up-to-date comparison of the jet-patch-triggered p_T distributions. These have been run with new embedding trees that exclude the same hot towers I exclude by hand in the data trees. There are possibly a handful from hot trigger patches which remain in embedding but not in data, but the effect should be quite minimal. For JP0, I have relaxed the low-p_T cut-off all the way to 5 GeV/c, simply to see if there is any sign of the trigger threshold. The samples are normalized against the number of data counts within a (fairly) arbitrary range of p_T:

• JP0: 9.9 - 55 GeV/c
• JP1: 9.9 - 55 GeV/c
• JP2: 16.3 - 65 GeV/c
• AJP: 16.3 - 65 GeV/c

On can see that the distributions for JP1 and JP2 are not entirely unlike those we have seen previously in the 2009 inclusive jet studies at 200 GeV. For AJP, the distributions are quite different. As we will see in a moment, this is not the case when I simply take all events which satisfy the conditions for AJP. So, this may have to do with interplay between AJP and other triggers at high p_T. For JP0, the comparison above 9.9 GeV/c (perhaps even above 8.4 GeV/c) seems basically in line with the others. However, there appears to be no sign of a "turning on" of the trigger.

Comparing to the "Total" Embedding Distribution

A first check was to compare the data distribution to the distribution of "matched" and "unmatched" embedding jets, i.e. both those reconstructed jets which match to a parton or particle jet and those that fail to match to a parton or particle jet. The thinking was that, in principle, the data distribution does contain "unmatched" jets; thus, for purposes of comparing to embedding the current procedure was a bit of apples-to-oranges. However, the comparison of data to the "total" embedding distribution is actually worse for JP0. The 7.1-8.4 GeV/c bin disagrees more with the "total" embedding distribution.

ADC Distributions

One of the first places to check is the ADC distribution. If the proper trigger threshold is not applied in the simulator the spectrum should not appear to match what is in the data, requiring both a software and hardware trigger. To get an idea of how this compares between data and simulation, I binned the stored ADC values for JP0, JP1, JP2, and AJP jet patches as a function of jet p_T, provided the hardware (data only) trigger, software trigger, geometric trigger, and p_T requirements were met. For this study, I filled the histograms for every trigger where the hardware, software, and geometric triggers were satisfied. Thus, the samples are not orthogonal in contrast to the distributions in Fig. 1.

Figure 2

JP0	JP1
JP2	AJP

In Fig. 2, I show the distributions for data and embedding for the various jet-patch triggers. Again, the distributions are normalized to the number of counts in the data. In general, the comparisons are sensible, in particular, at high-p_T. The appropriate ADC thresholds appear to be applied in all cases. However, one notices that near the p_T cut-offs, there seems to be some inconsistent behavior in the embedding. For clarity I post the comparisons for JP0 including a zoom-in, below, in Fig. 4.

Figure 3

JP0	JP1
JP2	AJP

In Fig. 3, I show the pT comparisons integrating over the full range of ADC, as shown in Fig. 2. The data distributions are slightly different than those in Fig. 1, as they do not attempt to maintain orthogonal sets of events. One can see, there is very little difference, except in the case of AJP. Here, the comparison between data and embedding is quite similar to that in JP2. This may have to do with interplay between AJP and the other triggers. AJP is dependent upon adjacent JP0 (or higher) patches. Since, in the data, I check for all other JP triggers before checking for AJP, it may be that I am robbing the data AJP distribution of events at a non-negligible rate at high p_T. Since the embedding distribution is filled for every event satisfying the trigger, I may not be comparing apples to apples in Fig. 1. Perhaps, since the comparisons are reasonable when filling for every event, it is good enough, at this point, to treat AJP and JP2 as a singular event class.

Figure 4

It appears that particularly near the threshold, the embedding distribution is not nearly as smooth as the data distribution.

Figure 5

In Fig. 5, I show the ADC distributions for four bins of JP0 jets. The distributions are normalized to the number of counts in the corresponding data distribution. The 6-7.1 GeV/c bin is simply for reference and is not intended to be used for the analysis. From Fig. 1 one notes that the top two distributions correspond to two bins which appear to be out of line in comparison with the data, while the bottom two appear to be well-behaved (note, again, that the p_T normalization is somewhat arbitrary; so one should not over-interpret). However, it seems as though the top two distributions undershoot the data distributions above ~50 counts by more than the lower two distributions.

Figure 6

In Fig. 6 I show the same distributions as in Fig. 5, but rebinning by a factor of 4. It seems that certainly by the 9.9-11.7 GeV/c bin, the distributions agree much better above 50 counts. With the rebinning, it is not so clear to me that the 7.1-8.4 GeV/c bin is any worse than the 8.4-9.9 GeV/c bin.

Removing Partonic Transverse Momentum Bins

One feature from 200 GeV analyses has been that the comparisons are better when one drops the lowest partonic p_T bins. So, far I have not done so. Here, I present the results of dropping, in particular, the 2-5 GeV/c partonic p_T bins.

Figure 7

With 2 < pT, parton < 5 GeV/c	Without 2 < pT, parton < 5 GeV/c

In Fig. 7, I show the comparison of the p_T spectra for all events passing the JP0 conditions, as in Fig. 3. Again, the data, are very slightly different from the sample in Fig. 1. which does not include those events which satisfy the requirements for VPDMB. If I drop partonic p_T bins 2-5, I see the distribution generally turn over much like the data. However, jet p_T bin 7.1-8.4 GeV/c is still slightly higher than the data (Data/M.C. from ~0.59 with 2-5 GeV/c bins to ~0.82 without). Dropping partonic p_T bins from 2-4 GeV/c but keeping the 4-5 GeV/c bin also seems to cause some improvement but not nearly as dramatic as dropping the 4-5 GeV/c bin. Dropping the 5-7 GeV/c bin has a significantly negative effect on the spectrum.

Figure 8

With 2 < pT, parton < 5 GeV/c	Without 2 < pT, parton < 5 GeV/c

In Fig. 8 I show the ADC spectra as a function of jet p_T with (left) and without (right) the 2-5 GeV/c partonic p_T bins. Just by looking at the z-scales, one can see there is improvement in the agreement between data and embedding. The general shape near the thresholds also appears to have improved. There still appears to exist some fluctuations which may account for the remaining difference in the near-threshold Data/M.C. comparisons.

Figure 9

With 2 < pT, parton < 5 GeV/c	Without 2 < pT, parton < 5 GeV/c

From Fig. 9, it does not appear that anywhere close to all of the disagreement has disappeared, though, it does seem to have improved, somewhat.

Figure 10: No Partonic p_T from 2 to 5 GeV/c

In Fig. 10, I show the data-embedding comparisons for jet p_T between 6 and 11.7 GeV/c excluding partonic p_T between 2 and 5 GeV/c rebinning by a factor of 4. This is comparable to Fig. 6. One can see significant improvement in the 6-7.1 GeV/c bin. Otherwise, there is improvement; but it seems only subtle. This perhaps makes sense given the modest improvements seen in most of the bins in Fig. 7.

A Sanity Check: Enforcing Thresholds by Hand

A useful sanity check is to enforce the various jet-patch-trigger thresholds "by hand." In this study, I compare p_T distributions for JP0 jets integrating only over the range of ADC's relevant for JP1 and JP2. If things are sensible, I should observe the trigger turn-on for the various other jet-patch triggers. For this study, I keep the 2-5 GeV/c partonic p_T bins.

Figure 11

JP0 with JP1 Threshold	JP1 with JP1 Threshold

Integrating over a range of ADC > 44, I should recover something close to the JP1 spectrum. What I observe (Fig. 11) seems not so vastly different. The bins below the JP1 p_T threshold appear a bit high. The trigger turn-on for JP1 is clearly evident.

Figure 12

JP0 with JP2 Threshold	JP2 with JP2 Threshold

In Fig. 12 I show the result of enforcing the JP2 threshold on the JP0 distribution. Note: the JP0 comparison is normalized over a different range than the JP2 comparison, as outlined above. The trigger turn-on is quite evident, as in the comparisons with JP1 thresholds. Subthreshold, there are some disagreements, but the effects are qualitatively similar. Note, also, that the embedding do not have the L2 filter that should not make much difference at high-p_T but may at low-p_T, in particular, subthreshold.

Checking the Geometric Trigger

Another piece of the analysis I have not checked with the new embedding is the geometric trigger, i.e. the associations between jets and trigger patches. Currently, the associates require both |Δη| < 0.6 and |Δφ| < 0.6. It may be informative to evaluate how data and simulation compare with the new embedding sample, in particular as it relates to the aforementioned JP0 peculiarity.

For the following study, I required a hardware (data only) trigger, software trigger, and p_T cut. I, then, found the most closely associated jet-patch (of the relevant trigger) to the jet in question . This should allow us to assess the sensibility of the embedding and the standard geometric trigger cut.

Figure 13

JP0	JP1
JP2	AJP

In Fig. 13, I show the distance, ΔR, between jets and the most closely associated jet patch of the proper trigger as a function of p_T bin. One can see fairly decent agreement in nearly all cases. Again, at low p_T in JP0, there appear to be some fluctuations in embedding which are not reflected in the data. One can also see that the shapes of the AJP correlations are a bit different than the other triggers; and that the AJP embedding and data distributions agree quite well.

Figure 14

6.0 < pT < 7.1 GeV/c	7.1 < pT < 8.4 GeV/c
8.4 < pT < 9.9 GeV/c	9.9 < pT < 11.7 GeV/c

In Fig. 14 I show the Δη-Δφ correlation between JP0 jets and the nearest JP0 jet patch for four bins of jet p_T. With black lines I show the boundaries of the standard geometric trigger cut. One can see that the cut appears fairly sensible for these jets. One check is to compare the percentages of embedding jets and data jets that fall within the geometry cut. I find for the above bins

Table 1

Jet pT [GeV/c]	Percent Within Cut (data)	Percent Within Cut (Embedding)
6.0 < pT < 7.1	55.7%	65.6%
7.1 < pT < 8.4	72.3%	74.7%
8.4 < pT < 9.9	80.9%	70.5%
9.9 < pT < 11.7	85.5%	83.4%

Of course, I don't cite an uncertainty, so it is difficult to know how different are the above percentages. Naïvely, I would assume that the embedding jets (which require a match to a parton jet and particle jet) would exhibit a higher percentage within the cut. Indeed, in the 6-7.1 GeV/c bin, that appears to be the case. However, 7.1-8.4 GeV/c bin appears quite close, and the 8.4-9.9 GeV/c bin is the opposite of what I would expect.

If I compare to the "total" embedding distribution, including "matched" and "unmatched" jets, I find the following percentages:

Table 2: Comparison to "Total" Embedding

Jet pT [GeV/c]	Percent Within Cut (data)	Percent Within Cut (Embedding)
6.0 < pT < 7.1	55.7%	64.3%
7.1 < pT < 8.4	72.3%	73.0%
8.4 < pT < 9.9	80.9%	75.8%
9.9 < pT < 11.7	85.5%	86.1%

So, the 6-7.1 GeV/c bin remains largely unchanged, while there is better agreement in the 8.4-9.9 GeV/c bin. I admit, I find this confusing. The 7.1-8.4 GeV/c bin is "improved," though, at the end of the day, I do not know how statistically significant it is.

A final check is to compare the data percentage to the embedding percentage when I exclude partonic p_T bins 2-5 GeV/c. I find the following:

Table 3: Comparison to Embedding Without the 2-5 GeV/c Partonic p_T Bins

Jet pT [GeV/c]	Percent Within Cut (data)	Percent Within Cut (Embedding)
6.0 < pT < 7.1	55.7%	51.1%
7.1 < pT < 8.4	72.3%	71.2%
8.4 < pT < 9.9	80.9%	70.7%
9.9 < pT < 11.7	85.5%	82.6%

So, in this case, the percentages are quite similar to Table 1, except, the 6-7.1 GeV/c bin is quite improved. The 7.1-8.4 GeV/c bin is, again, "improved," relative to Table 1, though it is difficult to say if the "improvement" is real or statistics.

AJP Geometric Trigger

A final study for this very lengthy entry is to examine the AJP associations. As one can see in Fig. 13, the shape of the AJP associations is quite different from JP0-JP2. It is good to verify if the current cut is sensible for AJP.

Figure 15

16.3 < pT < 19.2 GeV/c	19.2 < pT < 22.7 GeV/c
22.7 < pT < 26.8 GeV/c	26.8 < pT < 31.6 GeV/c

In Fig. 15, one can quite readily see that AJP embedding statistics are quite limited when binned so fine. However, the general features are consistent, as also in Fig. 13. However, the shape of the AJP Δη-Δφ associations, as with the ΔR associations, are quite different from JP0-JP2. There appears to be a very strong correlation in the very center, however, a good 30-35% of jets appear to fall outside the geometry cut. This is in contrast to JP0-JP2 where, for a similar range of pT, JP0-JP2 show percentages closer to 15-20% outside the cut. This makes me wonder if a wider cut in Δφ makes sense for AJP.