This page details the second iteration of my jet pt correction trials ...

I have made modifications to the correction schemes described in this blog post, I have also added another correction scheme. I describe the new methods below:

Method 1: This correction method is essentially the same as the first correction method described in the post linked above, I fit the means of the detector / particle jet pt plots and then plot the fit parameters as a function of pt (see fig 2) so I can get a correction factor for any given jet pt and det eta. In the previous incarnation, I used 6 pt bins and the lack of statistics in the highest pt bins was causing the fit function to have very sharp transitions. To combat this, I have combined the last three pt bins so the bins are now [5,10), [10,15), [15,20), and [20+]. I have also put a cut on the detector / particle jet pt ratio to eliminate highly weighted statistical fluctuations which were distorting the mean values bin to bin. Finally, when I plot the fit parameters in figure 2 I now put the points at the left edge of the pt bin, not the middle. I apply this correction for jets with det eta >= 0.5 and all pt, but for jets with pt greater than 20GeV the fit parameters used for the 20+ pt bin are used. So above 20, the correction factor will be the same for a given eta value.

Figure 1: This figure shows the detector jet pt / particle jet pt ratio vs det eta for 4 jet pt bins. The points are the means of each bin and the fit is of the form A+(1-A)*(1/(exp[(x-B)/C]+1)). A figure showing what the final bin looks like before and after the Y cut can be seen here.

Figure 2: This plot shows the three fit parameters for the 4 different pt bins for the curves shown in figure 1. The points in the top pannels are fit with quadratics and the points in the bottom pannel are fit with a pol1.

Figure 3: This figure shows a summary of the first correction method. The top two pannels show the size of the correction factor for a given pt and eta. The bottom two pannels show the difference between the original jet pt and the corrected jet pt for a given jet pt and eta.

Method 2: This method is very similar to the second method described in the blog page linked above. I fit the means along X of the particle jet Vs detector jet pt scatter plot with a quadratic for 6 eta bins and then plot the parameters of the quadratic fits as a function of eta. The only change from the last incarnation is that I now plot the points at the left edge of the eta bin instead of the middle (see fig 5). I also now apply the correction to jets with pt <= 30GeV and det eta > 0.5.

Figure 4: This figure shows the particle jet pt vs detector jet pt for 6 different eta bins. The points are the means of each x bin and the fit is a 2nd order polynomial.

Figure 5: This figure shows the three parameters of the quadratic fits in figure 4 as a function of eta bin. The points now are plotted at the left edge of each eta bin. Note that I have omitted the point for bin [1.3,1.5) because it was an outlier.

Figure 6: This figure shows a summary of the second correction method. The top two pannels show the corrected jet pt for a given original jet pt and det eta. The bottom two pannels show the difference between the original jet pt and the corrected jet pt for a given value of the original pt and det eta. As noted above, I only apply this correction for pt <= 30GeV.

Method 3: This method is the correlary to method 2 described above. For this correction, I look at the detector pt vs particle jet pt scatter plot. I again find the mean value of each X bin and now fit those means with a third order polynomial in each of 6 eta bins. The fit is valid for particle jet pt between 3 and 30 GeV. As in Method 2, I plot the fit parameters as a function of eta (see figure 8). The fit parameters as a function of eta are not as well behaved as in Method 2 and it is hard to find a clear trend. Because the detected pt is on the Y axis and the corrected pt is on the X, I need to solve a qubic equation for X. I do this numerically. If, for a given Y value I cannot find an X value which solves the qubic between x=3 and x=30, I apply no correction.

Figure 7: This figure shows the detector vs particle jet pt scatter plots for 6 different eta ranges. The points are the means of each X bin and the fit is a third order polynomial.

Figure 8: This figure shows the 4 parameters of the qubic fits for each eta bin seen in figure 7. The top two pannels are fit with constants and the bottom two pannels are fit with lines. The points are plotted at the left edges of the bins. Note that the point from bin [0.9,1.1) was an outlier and is not shown.

Figure 9: This figure shows a summary of the third correction method. The layout is the same as figure 6 above.

Method 4: The last correction method is a modification of the third correction method described in the blog post linked above. It involves correcting the pt of a jet in the endcap based on the pt of a jet in the barrel. In the previous incarnation, I simply replaced the endcap jet pt with the barrel jet pt for the correction. Now, I base the correction on plots of the endcap particle jet pt vs the barrel detector jet pt. I find the mean of each X bin and fit the means with a quadratic. I do this for 3 seperate endcap det eta bins: [1.0,1.2), [1.2,1.4), and [1.4, 1.7]. Currently, I do not try to plot the fit parameters as functions of eta, I simply apply the same correction to all jets which fall into one of the three eta bins.

Figure 10: This figure shows the endcap particle jet pt vs the barrel detector jet pt for all eta (top left), and the three endcap jet eta bins mentioned above. The points are the means of each X bin and the fit line is a quadratic.

Now that the four correction schemes used in this study have been described we can see how well each one does in correcting the measured jet pt back to the true jet pt. Please see the linked pdfs as well because some of the correction methods have pathologies which do not show up in the 'all bins' plots shown in figures 11 and 12.

Figure 11: This figure shows the detector / particle jet pt ratio for the uncorrected jets (upper left) and the ratio after each correction method is applied. This plot shows all jet pt.

A pdf with the correction plots for the different pt bins can be found here.

Figure 12: This figure shows the particle jet vs detector jet pt for the uncorrected jets (upper left) and after each correction. This plot shows jets with any det eta.

A pdf with the correction plots for the different eta bins can be found here.