Logic of trigger bias calculation for D_TT analysis

In the estimation of the systematic uncertainty contributed by the trigger bias, the information from the MC sample and model calculation are used.
The logic and steps are noted here.

1, Generate the modeling sample with PYTHIA. Here we would obtain the histograms containing the Lambda counts corresponding to different sources.
2, In a simple way, the implement of the model is actually to combine the polarization from sources with some coefficients and then divide the sum of the counts in order to obtain the spin transfer dependent on fz, eta and so on.

3, In order to obtain the uncertainty from fz shift with each trigger condition, we combine the different sources with their own coefficients and the original relative ratio produced in the Pythia. The the spin transfer dependent fz could be obtained.

From the MC sample used to do the comparison with data (the detector effect is in MC sample) we could extract the fz values for trigger conditions( ZeroBias, JP0,1,2 and AJP ). On the distribution of spin transfer vs. fz, the points corresponding to trigger conditions could be found and the difference between the spin transfer value of JP triggers and the value of ZeroBias are used as the uncertainty contributed by fz shift.

4, The uncertainty contributed by subprocess and fragmenting parton flavor.
The trigger condition can affect the relative ratio of different subprocesses and fragmenting parton flavors in Lambda production. Considering the strong relationship between the relative ratio of different subprocesses and fragmenting parton flavors, so the final effect shows up in the relative ratio of the fragmenting parton flavors.
First combine the different sources sorted by fragmenting parton flavors with their own coefficients and the original relative ratio produced in the Pythia and the spin transfer value is used as the value of ZeroBias.
Second combine the different sources sorted by fragmenting parton flavors with their own coefficients and the relative ratio extracted from the MC sample and the spin transfer value is used as the value of JP triggers.
The difference of the spin transfer values are used as the uncertainties.

5, The uncertainty contributed by decay sources.
The process are similar with the parton flavor part. Here the different sources are sorted by directly produced and produced in some other particle decay.