# Run 9 Simulation Fudge Factors Investigation

Updated on Wed, 2015-04-15 13:45. Originally created by pagebs on 2015-04-08 00:30.

A new look at the weights and fudge factors for the Run 9 simulation ...

The Run 9 embedding was run in 10 partonic pT bins: 2-3, 3-4, 4-5, 5-7, 7-9, 9-11, 11-15, 15-25, 25-35, and 35-inf. To make a smooth spectrum, the events from each pT bin need to be weighted by a factor of (sigma/nevents) where sigma is the cross section for that partonic pt bin and nevents are the number of generated events from that bin. It was also found that 'fudge factors' were needed to fine tune the agreement between bins, primarially for the low pT bins where it is known that pythia gets the cross section wrong. The fudge factors were found by fitting Exp(A+BX+CX^2) to each partonic pt bin spectrum and taking the ratio of those functions evaluated at the bin edges. Working on the 500 GeV simulation, Zilong found that the chi2 fitting procedure was biasing the fits low at the high end of the partonic pt bins where statistics are low and devised a scheme to compensate.

Below, I apply Zilong's technique for finding the fudge factors and their errors to the Run 9 200 GeV simulation. I bin in increments of 0.02 GeV and I itterate the fitting procedure at both the high and low ends of the spetra 4 times, each time assigning the error as the value of the fit function at that point.

Figure 1: Comparison of the RFF, FF, and combined fudge factors

Figure 2: The partonic pT spectra normalized using the raw weights (sigma/nevents) and the raw weights modified by the fudge factors. Also shown are the zoomed in views of three different regions of the full spectrum.

To see what effect the fudge factors had on my results, I looked at the data/simu comparisons as well as the full dijet cross section using several different weighting schemes:

Original: These are the weights I have used up to this point. They were taken directly from Pibero's analysis note and did not account for the fact that we use slightly different sets of runs.

MWF: These are the weights I calculated above from the pythia.root files I use in my analysis and which include the fudge factor corrections

MWNF: These are the same as MWF except I do not apply the fudge factors except for the 2-3 pt bin

Figure 3: The data/simu comparisons for the L2JetHigh (left) and JP1 (right) samples. The comparison with the orginal simulation is shown in red, the MWF sample in blue and the MWNF sample in green.

To see how these effects propagated through to the cross section, I produced the full unfolded cross section using the three weighting schemes:

Figure 4: The ratio (New-Old)/Old for the cross section where Old is the cross section calculated using the original weighting scheme and New is the cross section unfolded using either the MWF (red) or MWNF (blue) weights.

Because the theory is corrected for UEH effects which are estimated in a data-driven way, ie by looking at the difference between the particle and parton level unfolded cross sections, the weights could affect the theory.

Figure 5: The ratio (New-Old)/Old for the UEH corrected theoretical cross sections where Old and New are the same as in figure 4

Figure 6: The (Data-Theory)/Theory ratio for all three weighting schemes

Figure 7: Comparison of the cross sections for each partonic pt bin as listed in Pibero's analysis note to the cross sections calculated as the average of the returned cross sections from all simulation jobs as recorded in the log files. Note that Pibero's analysis note has one cross section for the RFF and FF parts of the simulation and here the cross sections calculated from the log files are done for RFF and FF seperately.

Figure 8: Comparison of the fudge factors calculated using the full simulation sample and the combined cross section. The points in red were found using Pibero's analysis note cross sections and the points in blue were found using the log file average cross sections. Note that these are the independent fudge factors meaning that the fudge factors from other bins are not taken into account. So fudge(bin i) = weight(bin i+1)*fit(bin i+1)/weight(bin i)*fit(bin i).

Figure 9: The cross sections for the 35-inf partonic pt bin returned from each of the 408 jobs which ran for the RFF part of the simulation. The black line is the average, the green lines show the +/- 1 sigma range, and the blue line is the cross section cited in Pibero's analysis note.

The Run 9 embedding was run in 10 partonic pT bins: 2-3, 3-4, 4-5, 5-7, 7-9, 9-11, 11-15, 15-25, 25-35, and 35-inf. To make a smooth spectrum, the events from each pT bin need to be weighted by a factor of (sigma/nevents) where sigma is the cross section for that partonic pt bin and nevents are the number of generated events from that bin. It was also found that 'fudge factors' were needed to fine tune the agreement between bins, primarially for the low pT bins where it is known that pythia gets the cross section wrong. The fudge factors were found by fitting Exp(A+BX+CX^2) to each partonic pt bin spectrum and taking the ratio of those functions evaluated at the bin edges. Working on the 500 GeV simulation, Zilong found that the chi2 fitting procedure was biasing the fits low at the high end of the partonic pt bins where statistics are low and devised a scheme to compensate.

Below, I apply Zilong's technique for finding the fudge factors and their errors to the Run 9 200 GeV simulation. I bin in increments of 0.02 GeV and I itterate the fitting procedure at both the high and low ends of the spetra 4 times, each time assigning the error as the value of the fit function at that point.

Figure 1: Comparison of the RFF, FF, and combined fudge factors

Figure 2: The partonic pT spectra normalized using the raw weights (sigma/nevents) and the raw weights modified by the fudge factors. Also shown are the zoomed in views of three different regions of the full spectrum.

To see what effect the fudge factors had on my results, I looked at the data/simu comparisons as well as the full dijet cross section using several different weighting schemes:

Original: These are the weights I have used up to this point. They were taken directly from Pibero's analysis note and did not account for the fact that we use slightly different sets of runs.

MWF: These are the weights I calculated above from the pythia.root files I use in my analysis and which include the fudge factor corrections

MWNF: These are the same as MWF except I do not apply the fudge factors except for the 2-3 pt bin

Figure 3: The data/simu comparisons for the L2JetHigh (left) and JP1 (right) samples. The comparison with the orginal simulation is shown in red, the MWF sample in blue and the MWNF sample in green.

To see how these effects propagated through to the cross section, I produced the full unfolded cross section using the three weighting schemes:

Figure 4: The ratio (New-Old)/Old for the cross section where Old is the cross section calculated using the original weighting scheme and New is the cross section unfolded using either the MWF (red) or MWNF (blue) weights.

Because the theory is corrected for UEH effects which are estimated in a data-driven way, ie by looking at the difference between the particle and parton level unfolded cross sections, the weights could affect the theory.

Figure 5: The ratio (New-Old)/Old for the UEH corrected theoretical cross sections where Old and New are the same as in figure 4

Figure 6: The (Data-Theory)/Theory ratio for all three weighting schemes

Figure 7: Comparison of the cross sections for each partonic pt bin as listed in Pibero's analysis note to the cross sections calculated as the average of the returned cross sections from all simulation jobs as recorded in the log files. Note that Pibero's analysis note has one cross section for the RFF and FF parts of the simulation and here the cross sections calculated from the log files are done for RFF and FF seperately.

Figure 8: Comparison of the fudge factors calculated using the full simulation sample and the combined cross section. The points in red were found using Pibero's analysis note cross sections and the points in blue were found using the log file average cross sections. Note that these are the independent fudge factors meaning that the fudge factors from other bins are not taken into account. So fudge(bin i) = weight(bin i+1)*fit(bin i+1)/weight(bin i)*fit(bin i).

Figure 9: The cross sections for the 35-inf partonic pt bin returned from each of the 408 jobs which ran for the RFF part of the simulation. The black line is the average, the green lines show the +/- 1 sigma range, and the blue line is the cross section cited in Pibero's analysis note.

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