Study of correlation between AL(+eta) and AL(-eta), both determined from the same 8 statisticaly independent spin sorted yields.

Method: generate & reco AL 5000 times, produce correlation plot, compute correlation.

Code snipets below show  key parts of both steps.

Simplifications: lumi[spin]=const, ALL=0, P=1

Attached code  allows to run full simu in ~10 seconds.

Table 1 shows how correlation changes depending on assumed asymmetries.

Conclusion:

• in general, correlation is given by formula COR=-1.3*AL(-eta)*AL(+eta)*P1*P2
• for the case of double-sided computation of AL~0.2 (and P=1) the correlation between reco ALs is of -5%. It is negative - meaning both reco ALs tend to move toward or against each other.
• for the case of single-sided computation of AL~0.3 (and P=1) the correlation between reco ALs is of -11%. 

Double-sided reco of AL

Single-sided reco of AL determined from the same 8 statisticaly independent spin sorted yields.

Reminder of the meaning of correlation coefficient (from Wikipedia)