Event by Event Comparison

Here I compare the 2008 jet code which used a 3x3 jet patch and my 2009 jet code which uses a 5x5 jet patch event by event in the L2VirtualAlgo2009 framework. I have run over 500k events from the file /star/institutions/iucf/balewski/StarTrigSimuEvents/R7140046.eve.bin

The L2jet code scans the entire calorimeter using two 1-dimensional searches.  The calorimeter is divided into 30 phi bins each having 15 eta bins for a total of 450 bins. Each bin is a trigger patch consisting of a 4x4 patch of individual towers. The jet code first scans the phi bins and finds the 3 or 5 bin continuous group having the highest ET, it then finds the group having the second highest ET which is at least 2 phi bins away from the edge of the first group. The scan in phi allows for groups which wrap around in phi, ie 29-0-1-2-3 groups are possible. Then the code looks for the highest grouping in eta. For each of the 15 eta bins, the code adds the ETs in that eta bin from each phi bin in the group found in the last step. The code then scans the 15 eta bins for the 3 or 5 bin group with the highest total ET. Unlike the phi scan, the eta scan does not allow for groups which wrap around, ie the group 13-14-0-1-2 is not possible. The total ET of the eta bin group found is the jet patch ET. Finally the code calculates the ET weighted eta and phi positions of the jet patch.

The jet patches can then pass one of 4 conditions. There is the oneJet condition which is satisfied if the highest jet patch has ET above a certain threshold and there are three dijet conditions, endcap-endcap dijets, endcap-barrel dijets, and barrel-barrel dijets. The endcap-endcap and endcap-barrel conditions each have three requirements that must be passed, that the sum of ET weighted etas from the low and high jet patch be above a threshold, that the ET of the high jet patch be above a threshold, and that the ET of the low jet patch be above a threshold. The barrel-barrel condition only has requirements on the ETs of the high and low jet patches with no requirement on ET weighted eta. In principle, all of these thresholds can be different and the values are initalized in a setup file.
 

Fig 1: Here are the number of events which passed the various selection conditions.

Bins 1-4 are for oneJet events, bins 6-9 are for endcap-endcap dijets, bins 11-14 are for endcap-barrel dijets, bins 16-19 are for barrel-barrel dijets and bins 21-24 are for events which passed any of the previous dijet conditions.

Within each group, the bins are ordered as follows:

• First bin: event passes in 5x5 || event passes in 3x3
• Second bin: event passes in 5x5 && event passes in 3x3
• Third bin: event passes in 5x5 && event does NOT pass in 3x3
• Fourth bin: event does NOT pass in 5x5 && event passes in 3x3

Here are the values for each bin:

I have made plots showing the difference in eta, phi, and ET between jet patches in the 3x3 and 5x5 code. Pages 1-8 show the comparisons for events which satisfy the endcap-endcap condition in both the 3x3 and 5x5 code. Pages 9-16 show the comparisons for events which satisfy the endcap-barrel condition in both the 3x3 and 5x5 code. Pages 17-24 show the comparisons for events which satisfy the barrel-barrel condition in both the 3x3 and 5x5 code. Pages 25-32 show the comparisons for all events, regardless of condition. Pages 33-40 show the comparisons for events which satisfy the one jet condition in both the 3x3 and 5x5 code. Pages 41-48 show the comparisons for events which satisfy one of the dijet conditions in both the 3x3 and 5x5 code.

The comparison plots between the 3x3 and 5x5 code are here.

3x3 to 5x5 Discrepancies

 The plots shown in the pdf above are for events in which the jet patches pass a specific condition in both the 3x3 and 5x5 code. As such, we would expect that the jet patches would be strongly correlated in eta and phi with the ET of the 5x5 JP being slightly larger due to it including more towers. For a given condition we do see that the majority of events are tightly correlated in eta and phi, yet there remain some events for which the 3x3 and 5x5 code give very different results. See for example pages 17 and 18 in the pdf.

To investigate what may be causing these descrepencies, I looked at events which passed the dijet condition in both 3x3 and 5x5 (bin 22) and printed off the eta, phi, and ET of the high and low JP for the 3x3 and 5x5 code for events in which the difference in the high JP eta between the 3x3 and 5x5 code was >= 2. Looking at this information, it became clear that in many of these events the two codes were swapping which JP was the high and low. So the high JP found by the 3x3 code would become the low JP in the 5x5 code and the low JP found by the 3x3 code would become the high JP in the 5x5 code. To test if this swapping was causing the odd events I regenerated the plots on pages 17 and 18 but suppressed all events where the eta difference between the 5x5 low JP and the 3x3 high JP AND the phi difference between the 5x5 low JP and the 3x3 high JP were both <= 0.5. The results are shown below.

Fig 2: Plots showing the effects of suppressing events in which the 3x3 and 5x5 code swap which JPs are high and low. Top plots show eta correlation for the high JP (left) and the low JP (right) for events which pass BB condition in both 3x3 and 5x5. Bottom plots show eta correlatioin for same conditions but with swapped JP events excluded.

Fig 3: Plots showing the effects of suppressing events in which the 3x3 and 5x5 code swap which JPs are high and low. Top plots show phi correlation for the high JP (left) and the low JP (right) for events which pass BB condition in both 3x3 and 5x5. Bottom plots show phi correlatioin for same conditions but with swapped JP events excluded.

 Another discrepancy between the 3x3 and 5x5 code can be seen by looking at bin 24 in the first figure. These are events which passed one dijet condition in the 3x3 code but no dijet conditions in the 5x5 code. One would expect that a larger jet patch would satisfy any condition that a smaller jet patch satisfied. To investigate this, I printed out the ET, eta and phi for each event in bin 24 as well as whether or not the event passed the various parts of each dijet condition. The printout of this information can be found here. In working several events out by hand, it appears that many of these events have ET or eta values which are close to the set threshold values. For example, in going from a 3x3 to 5x5 jet patch the extra ET could be distributed asymmetrically, causing the ET weighted eta to be pulled more in one direction. For an event which passed a condition containing an eta requirement in the 3x3 code, this asymmetric eta shift could be enough to pull the event below threshold in the 5x5 code.

A second cause of events passing a dijet condition in the 3x3 code but not the 5x5 code is that for some events, the 3x3 code finds more ET in a jet patch than the 5x5 code does. This brings up the third major discrepency that I have looked into, namely, how can a jet patch having more towers have less ET than a jet patch having fewer towers when the code is designed to find the jet patch with the highest energy. Examples of these events can be seen on pages 47 and 48 of the pdf given above. To investigate this, I again printed out the ET, eta, and phi as well as the ET in each phi bin and the summed ET in each eta bin for the 3x3 and 5x5 code for all events in which the ET in the high jet patch for the 3x3 code was higher than the ET in the high jet patch for the 5x5 code. The printout of this information can be found here. The reason for the 3x3 code sometimes finding more ET than the 5x5 code rests with the fact that the jet code uses two 1-dimensional searches instead of a true 2-dimensional search. So, while the code will always find the phi group with the highest total ET, regardless of jet patch size, that ET could be distributed in eta differently in different phi bins. For example, assume that the highest 3 phi bin group consists of bins 0, 1, and 2 with the ET of the bins being 3, 4, and 5 respectively. Now the code looks at how that ET is distributed in eta, let all the ET from phi bin 0 rest in eta bin 2 and all the ET from phi bins 1 and 2 rest in eta bin 3. Adding the same numbered eta bins together gives an ET of 3 in eta bin 2 and an ET of 9 in eta bin 3. Therefore the highest eta bin group would consist of bins 2, 3, and 4 and the jet patch would have a total ET of 12. Now we move to the 5x5 case. Assume that the highest 5 phi bin group consists of bins 1, 2, 3, 4, and 5 with the ET of the bins being 4, 5, 0, 0, and 6 respectively. We already know that the ET from bins 1 and 2 rest in eta bin 3, but the ET from phi bin 5 can rest in any eta bin. For arguments sake, assume that the ET from phi bin 5 is split evenly between eta bins 11 and 12. After adding the eta bins together, eta bin 3 has an ET of 9 as before and eta bins 11 and 12 each have an ET of three. So the highest eta bin group would consist of bins 3, 4, 5, 6, and 7 and the jet patch would have a total ET of 9. So although the code found the largest phi bin group, the distribution of ET in eta meant that the 3x3 code actually found a larger ET.

Conclusions

The agreement between the 3x3 and 5x5 code is generally very good. The discrepencies which do occur make up a small fraction of the total number of accepted events and their causes are understood.