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

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

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

 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

 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

 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

 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

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

 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

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

 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

 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-

 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-

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

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

 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

 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

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

 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

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)

Transversity Collaboration Meeting Jin Huang 21

 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

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

Transversity Collaboration Meeting Jin Huang 24

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

Transversity Collaboration Meeting Jin Huang 26

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

 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-)

Transversity Collaboration Meeting Jin Huang 29

 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

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