# Reconstruction and Trigger Efficiency Correction Factor

Now that I have my raw pion spectrum (see here) I need to proceed in transforming those raw counts into a cross section measurement. The first step in this process is calculating a correction factor that accounts for inefficiencies in the trigger and reconstruction algorithm. I will calculate this correction factor using the filtered, full-pythia MC sample. To first order the correction factor C = N_{reco}(Pt)/N_{true}(Pt) where N_{reco} = the number of pions found with our reconstruction algorithm and trigger, binned in Pt, after all cuts have been applied, and N_{true} is the true number of pions in the pythia record within the usable detector volume that should have fired the trigger. Note that C is not strictly a reconstruction efficiency. It represents a convolution of efficiencies in the reconstruction algorithm, trigger, acceptance, finite detector resolution, bin migration, merging and splitting effects.

Goal:

Calculate generalized correction factor.

Data Sets Used:

T2 Platinum MC (see here.) Previous studies (here and here) show that this MC sample very reasonably mimics the real data, especially within the pion mass peak.

Cuts:

- filtered pythia MC events pass L2gamma software trigger
- Reco/True Pt > 5.5 GeV
- Charged Track Veto.
- At least one good strip in each SMD plane
- Reco Z Vertex found and |vtx| < 60 cm.
- Reco Zgg < 0.7
- Reco/True |particle eta| < 0.7 (*)

Bins:

9 pt bins, with boundries {5.5, 6., 6.5, 7., 7.75., 9., 11.5, 13.5, 16., 21.}

Plots:

1)

The above plot shows the generalized correction factor N_{reco}(Pt)/N_{true}(Pt). N_{reco} is the number of reconstructed pions, where pions are found and reconstructed using the exact same procedure as is done for real data. The events in the MC sample are properly weighted.

We would like to check the applicability of a correction factor calculated similarly to the one above. To do this I split the filtered MC sample into two separate samples. One of these (MCd) I treat as data and the other (MCt) I treat as MC. I run the MCd sample through normal pion reconstruction and extract a raw yield spectrum. Then from the MCd sample I calculate a correction factor similar to the one above. I then apply the correction factor to the MCd raw yield distribution. The results are below.

The black squares are the raw yields of the 'data' set as a function of Pt. The red squares are the true pt distribution of pythia pions. The blue squares are the fully corrected yields obtained by applying the correction factor to the black points. As you can see, after applying the correction factor to the reconstructed 'data' the true distribution is obtained.

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