Here I compare the dijet invariant mass spectra and error bars on the ALL measurement when using the full invariant mass formula and an approximate formula in which the individual jet masses are ignored.

In the results shown here, I have used this dijet mass formula:

However, the above formula is an approximation in which we assume the transverse momenta of the jets is much larger than the mass of the jets and we can neglect the individual jet masses. The full formula is:

I want to see what effect using the full formula will have on my dijet mass distributions and on the error bars on my ALL measurement.

Figure 1: This figure compares the dijet invariant mass spectrum obtained with the two different invariant mass formulas for the 5 topologies. The red curve is for the massless approximation formula and the blue curve is for the full formula.

Figure 2: This figure compares the dijet invariant mass yield in each bin obtained with the two different invariant mass formulas for the 5 topologies. The red curve is for the massless approximation formula and the blue curve is for the full formula.

Figure 3: This figure compares the statistical errors on the ALL measurement obtained with the two invariant mass formulas for the 5 topologies. The red error bar is for the massless approximation formula and the blue bar is for the full formula.

Figure 4: This figure plots the size of the errors shown in figure 3 for each bin. Again the red points are from the massless approximation and the blue points are from the full formula. The top pane is a linear scale and the bottom pane is a log scale.

Conclusion: The full mass formula tends to shift dijets to a slightly higher invariant mass as would be expected. One issue that will need to be explored further (probably with simulation) is how well the jet mass can be reconstructed, especially in the endcap where tracking information is falling off. This will probably determine which formula most faithfully reflects the true mass.