PYTHIA simulation of J/Psi polarization

The purpose of this analysis is to check if different input J/Psi polarization changes acceptance corrections. If our analysis doesn't generate longitudinal polarization we see from the data analysis.

In our data analysis we use acceptance corrections from embedding with no input J/Psi polarizaton.

First a J/Psi PYTHIA simulation with no input J/Psi polarization was done. Then from obtained J/Psi collection we chose only those which could give a full transverse polarization (polarization parameter = 1) or full longitudinal polarization (polarization parameter = -1).  For those three cases, in order to check if the input J/Psi polarization is important for this analysis, acceptance corrections were calculated and compared.

For a crosscheck an acceptance correction obtained from the PYTHIA simulation with no input J/Psi polarization was applied to cos(theta*) distribution after cuts for a simulation with transverse/longitudinal input J/Psi polarization. This should give the "original" transverse/longitudinal input J/Psi polarization distribution.

All distributions are for |y(J/Psi)| < 1.

Cos(theta*) distributions after cuts are with following cuts:

|eta| < 1 for both electrons

pT > 0.8 GeV/c for both electrons

Acceptance is: (cos(theta*) after cuts) / cos(theta*)

To cos(theta*) distributions function: norm(1+lambda*(cos²(theta*))) is fited. Where lambda is a polarization parameter.

lambda = 0 - no polarization

lambda = 1 - full transverse polarization

lambda = -1 - full longitudinal polarization

All calculation are done in HX frame.

• no input J/Psi polarization

Fig. 1. input cos(theta*)	Fig. 2. cos(theta*) after cuts

Fig. 3. acceptance

Fig. 1a. input cos(theta*) - 10 bins	Fig. 2a. cos(theta*) after cuts -10 bins

Fig. 3a. acceptance - 10 bins

• transverse input J/Psi polarization

Fig. 4. input cos(theta*) lambda = 0.9982 +/- 0.0067	Fig. 5. cos(theta*) after cuts

Fig. 6. acceptance

Fig. 6a. acceptance - 10 bins

• longitudinal input J/Psi polarization

Fig. 7. input cos(theta*) lambda = -1 +/- 0	Fig. 8. cos(theta*) after cuts

Fig. 9. acceptance

Fig. 7a. input cos(theta*) - 10 bins lambda = -1.003 +/- 0.001	Fig. 8a. cos(theta*) after cuts - 10 bins

Fig. 9a. acceptance - 10 bins

• comparison of acceptance distributions

Fig. 10. comparison of acceptance distributions

Above plot shows that acceptance distribution doesn't depend on input J/Psi polarization.

Fig. 10a. comparison of acceptance distributions - 10 bins

Distributions are very similar in the range -0.8 - 0.8.

A difference in acceptance in a first and last bin for longitudinal polarization is due to very steep shape of cos(theta*) at extreme values for longitudinal polarization.

For a crosscheck input cos(theta*) distributions for transvers/longitudinal polarized sample are obtained, using the acceptance correction from simulation with no input J/Psi polarization.  Distributions are shown below on the left hand side. On the right hand side are "original" input cos(theta*) distributions (obtained from the simulation, and shown also above).

Input cos(theta*) distirbution for transverse/longitudinal polarized sample was obtained in followin steps:

• acceptance distribution was taken from the simulation w/ no input J/Psi polarization
• cos(theta*) distribution after cuts  for the simulation w/ transverse/longitudinal input J/Psi polarization was obtained
• cos(theta*) distribution after cuts was corrected using the acceptance distirbution in order to get the input J/Psi cos(theta*) distribution
• to the input J/Psi cos(theta*) distribution obtained in that way function norm(1+lambda*(cos²(theta*)))  was fitted in order to get the lambda value

• Input cos(theta*) distribution for transverse polarizarion obtained using acceptance from simulation with no input J/Psi polarization

Fig. 11. after applying  acceptance correction lambda = 0.9905 +/- 0.0105	Fig. 12. from simulation lambda = 0.9982 +/- 0.0067

Fig. 11a. after applying  acceptance correction - 10 bins lambda = 0.9703 +/- 0.0105	Fig. 12a. from simulation - 10 bins lambda = 0.9928 +/- 0.0068

• Input cos(theta*) distribution for longitudinal polarizarion with acceptance from simulation with no input J/Psi polarization

Fig. 13. after applying  acceptance correction lambda = -0.9995 +/- 0.0010	Fig. 14. from simulation lambda = -1 +/- 0

Fig. 13a. after applying  acceptance correction - 10 bins lambda = -0.9886 +/- 0.0017	Fig. 14a. from simulation - 10 bins lambda = -1.003 +/- 0.001