Documentation of a couple minor errors in the calculation of the cross section and asymmetries ...

The first minor error I found was with my definition for the invariant mass. There is a term which goes as Cosh(delta_rapidity) but instead of using the actual jet rapidity I was using jet pseudorapidity.

Figure 1: The difference between jet psuedorapidity and jet rapidity as a function of the jet pseudorapidity.

Figure 2: The difference between the dijet mass calculated using pseudorapidity and the dijet mass calculated using rapidity vs dijet mass (calculated using pseudorapidity).

Figure 3: The dijet mass spectra when the mass is calculated using pseudorapidity (Red) and rapidity (Blue).

The second error had to do with the corrections made to parton level. Basically, I actually reused the particle level to detector level comparisons when I thought I was using the parton to detector level comparison. This error affected both the cross section and the asymmetry. The cross section was extracted to particle level, and this was done correctly, but the extraction to the parton level was used to calculate the hadronization and underlying event correction applied to the theory calculation. The parton level correction was done incorrectly.

Figure 4: Comparison of the original data / theory ratio (Red) with the parton level error and the corrected data / theory ratio (Blue). The direct comparison between the original and fixed UEH corrected theory is shown in green. Note that this cross section ratio was done with the pseudorapidity mass definition.

The parton level error shows up in the asymmetry via the mass shift. Previously, I showed the mass shifts were virtually identical for the particle level and parton level.

Figure 5: The original mass shifts for the L2 and JP triggers with the parton level error.

Figure 6: The new mass shifts for the L2 and JP triggers with the correct parton level shifts.