1. Jin Huang M.I.T. For Transversity Collaboration Meeting Jan 29, 2010 @ JLab

2. Overview Goals, Focuses Comparison of MLE Application of MLE in Transversity Yield Calculation Asymmetry Estimation Angular Modulation Estimation Discussion Asymmetry Cross Check SSA HRS/BigBite Single DSA HRS Single DSA Overview Summary and TODOs Transversity Collaboration Meeting Jin Huang 2

3. Goals, Focuses Comparison of MLE Transversity Collaboration Meeting Jin Huang 3

4.  Knowing ◦ total charge and DAQ/electronics life time of each spin state ◦ target/beam polarization, density and luminosity ◦ for each event, physics event type, which spin/helicity state it’s from and related kinematics variables  Wanted: angular modulations Transversity Collaboration Meeting Jin Huang 4

5.  Maximum likelihood Estimation (MLE) is a popular statistical method providing estimates for the model’s parameters  At large total event numbers, MEL is ◦ asymptotically unbiased  its bias tends to zero as the sample size increases ◦ asymptotically efficient  no asymptotically unbiased estimator has lower asymptotic mean squared error than the MLE. Transversity Collaboration Meeting Jin Huang 5

6.  Cross check with existing methods  Do not require binning for angular modulation estimation ◦ Use all angular information since do not bin data  bin data = assume all data coming from bin center or loosing angle information O(bin size/2π)  Possible to 1 st order canceling by using weighted center ◦ More stable if statistics is low  Fitting method require statistics is high in each bin, or Poisson Distribution is near Gaussian. Eg. It will fail if average bin count <1 Transversity Collaboration Meeting Jin Huang 6

7.  A trade over in current version of MLE method ◦ Lower statistical uncertainty for risk of higher systematical bias due to yield drift ◦ Size of trade over is related to local charge asymmetry  To be Further discussed  Avoidable if performing local pair MLE (under development) Transversity Collaboration Meeting Jin Huang 7

8. Yield Calculation Asymmetry Estimation Angular Modulation Estimation Discussion Transversity Collaboration Meeting Jin Huang 8

9.  MLE yield estimation expression is simple: ◦ effective charge (life time, target density corrected)  Comparing with weighted sum (Chi2 fit) ◦ Weight sum break down at low-each-bin statistics Transversity Collaboration Meeting Jin Huang 9

10.  weighted sum show bias when statistics of each bin is low (<10)  Similar situation for angular binned fitting Transversity Collaboration Meeting Jin Huang 10

11.  For polarized asymmetry between multiple ±spin states, MLE result is ◦ combination of sums, Easy to calculate  With assumption: Yield do not drift ◦ Causing the stat. for sys. trade over ◦ Avoidable by removing this assumption Transversity Collaboration Meeting Jin Huang 11

12.  Naive example: Consider an experiment with 2 pair of spin states Spin+ - + - Transversity Collaboration Meeting Jin Huang 12 C 1+ C 1- C 2+ C 2-

13.  or local A C = globe A C ◦ MLE result = local pair result  or large local A C ◦ Local Pair match within pair, loosing stat. ◦ MLE match beyond local pair for best stat. uncer. ◦ However, MLE have higher risk of comparing two states far away and more biased by yield drift Transversity Collaboration Meeting Jin Huang 13 C 1+ C 1- C 2+ C 2- C 1+ C 1- C 2+ C 2-

14.  Local Paired MLE ◦ From MLE equation for each pair ◦ And combine as  Under study, hopeful Transversity Collaboration Meeting Jin Huang 14

15.  In Matrix format ◦ Matrix Elements are Event by Event sums + charge asymmetry-acceptance corrections Transversity Collaboration Meeting Jin Huang 15

16.  Similar format as SSA  Very low charge asymmetry -> ◦ MLE As reliable as local pair method in case of yield drift ◦ Dependence on knowledge of acceptance is tiny  Longitudinal terms show up as corrections  Higher precision on modulation since leading twist is only one term Transversity Collaboration Meeting Jin Huang 16

17.  Combinable with Blue team method ◦ Full MLE, good for low stat channels and DSA ◦ MLE for angular modulation on local pair then combine all together. Low systematics, difficult since some state have low counts ◦ Angular bin the data, use MLE to get asymmetry in each bin, then do 2D angular fitting: only useful for cross check ◦ MLE supporting local pairs (under development) Transversity Collaboration Meeting Jin Huang 17

18. SSA HRS/BigBite SingleDSA HRS Single DSA Overview Transversity Collaboration Meeting Jin Huang 18

19.  Comparing MLE asymmetries with existing ones ◦ SSA: Compared with Blue  Blue Team algorithm: local pair sum  Different code after replay  In depth cross check ◦ DSA: Compared with results reported in last collaboration meeting  Last algorithm: fitting over state-by-state asymmetry (similar as blue team old method)  data for each spin state is identical  Demonstrate Difference between algorithm Transversity Collaboration Meeting Jin Huang 19

20. Transversity Collaboration Meeting Jin Huang 20  Consistent within 1 σ 1. No Yield Correction Applied Yet 2. Possible Different Run List (HRS problem only run)

21. Transversity Collaboration Meeting Jin Huang 21

22.  Similar to No-Pol. Case ◦ Bias due to approximation in MLE is small Polarizations will be included since this slide Transversity Collaboration Meeting Jin Huang 22

23.  Trend is consistent  Although some points differs more Transversity Collaboration Meeting Jin Huang 23

24. Transversity Collaboration Meeting Jin Huang 24

25.  Trend is consistent  Also show T1/T6 difference Transversity Collaboration Meeting Jin Huang 25

26. Transversity Collaboration Meeting Jin Huang 26

27.  Consistent to high precision ◦ Because of small charge asymmetry Transversity Collaboration Meeting Jin Huang 27

28.  Believe or Not, we have more than 500 asymmetries (channels, kinematics bins)  Fit method and MLE consist at high statistics  The difference could be significant when statistics is low Transversity Collaboration Meeting Jin Huang 28 Coinc (e’ π) Coinc (e’ K+) Coinc (e’ K-)

29. Transversity Collaboration Meeting Jin Huang 29

30.  MLE ◦ Useful ◦ Could extract Yield/Asymmetry/DSA,SSA Modulations  Cross Check ◦ MLE perform great for DSA ◦ Consist within error bar with blue team SSA (no correction yet) Transversity Collaboration Meeting Jin Huang 30

31.  Test angular modulation with real data/corss check  Local Pair MLE  Background removal Transversity Collaboration Meeting Jin Huang 31