1. Jin Huang M.I.T. For Transversity Collaboration Meeting Mar 26, 2010 @ JLab

2. Overview Why MLE General Progress Yield DistributionA_UT Comparison with Blue Team Helicity Convention Møller Assumption He3 Elastic Check Delta Production Check Photo-pion production Check TODO A_LT A_LL Contamination A_LU Model dependency Parameter Bin Centering N2 dilution Transversity Collaboration Meeting Jin Huang 2

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

4.  Knowing ◦ A pool of SIDIS events ◦ Run condition data  Wanted: ◦ Extract Parameter with a specific model ◦ Ex. Angular modulation 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.  Finalized MLE Tech Note with Yi and Xin ◦ http://www.jlab.org/~jinhuang/Transversity/MLE.pdf  MLE have been used to analyze ◦ Yield Distribution ◦ Asymmetries (Discussed in last collaboration meeting) ◦ A_UT Angular Distribution ◦ A_LT Angular Distribution ◦ A_LU Angular Distribution  There are topics of following chapters Transversity Collaboration Meeting Jin Huang 8

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10.  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 10

11.  Transversity Q^2 Distribution ◦ y axis: Yield Density (uC -1 GeV -2 ) Transversity Collaboration Meeting Jin Huang 11

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14.  Consistent for most points Transversity Collaboration Meeting Jin Huang 14

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17. Transversity Collaboration Meeting Jin Huang 17  Mostly Consistent  Similar Fluctuation as Asymmetries  Not Local Pair MLE yet Very Preliminary

18. Transversity Collaboration Meeting Jin Huang 18

19.  Beam helicity flip fast at 30Hz  Helicity signal flag each state  Relative phase (sign) between signal and helicity is unknown  Møller could tell the sign. However we miss the calibration between HRS signal sign and Møller sign  In alternative using physics asymmetry to calibrate the phase (Møller Sign Convention) Transversity Collaboration Meeting Jin Huang 19

20.  Møller People: Sign Convention haven’t changed for last 10 years. Last calibration 6 moth before transversity show inverse sign (Møller & HRS)  Elastics He3 Asymmetry: Compare to both theory calculation and A1n data-> same sign (Møller & HRS)?  However, also compare to A1n, ◦ 1 pass Delta production (HRS Single) ◦ 5 pass photo-production of pion (HRS Single) Suggest inverse sign (Møller & HRS)? Transversity Collaboration Meeting Jin Huang 20

21.  Cross Check is welcome ◦ I have detailed analysis record  Looking for other experiment data  From other He3 series experiment  Test in PREX running (difficult) Transversity Collaboration Meeting Jin Huang 21

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23.  Raw A_LT modulation ◦ Two section: IHWP IN and OUT Sign difference already applied Transversity Collaboration Meeting Jin Huang 23 Very Preliminary

24.  All information are used  Not possible to get reliable A_LL correction Transversity Collaboration Meeting Jin Huang 24

25.  At Transverse state ◦ A_LT get max sensitivity ◦ But A_LL shadow A_LT in sign as spin flip  At Vertical Spin State ◦ Sensitivity are small to both A_LT and A_LL  As if solving equation ◦ 1*A_LT+0.1*A_LL=DSA_T + ◦ -1*A_LT-0.1*A_LL=DSA_T - =-DSA_T + ◦ Small*A_LT+Small*A_LL=DSA_V Transversity Collaboration Meeting Jin Huang 25 Direction of Separation=0 Direction that A_LL be cancelled

26. Transversity Collaboration Meeting Jin Huang 26  Xiaodong posted ELOG 320 for NLO theory predictions for 3He and neutron A_1h SIDIS  A1_he3 is smaller than 5% in our kinematics region Solution: Use A_LL from others

27.  With A_1n from HERMES data, the total LL correction is small Transversity Collaboration Meeting Jin Huang 27 Very Very Preliminary, Assuming Møller Sign Convention 10% N2 Dilution Assumed

28.  Naive model from He3 -> Neutron Transversity Collaboration Meeting Jin Huang 28 Very Very Preliminary He3 Asym Assumptions+ Assuming 86.5% Neutron Pol. No Proton A_LT No Nuclear Effect No FSI

29.  Sensitivity drop fast as higher order terms are included Transversity Collaboration Meeting Jin Huang 29 Very Preliminary

30.  Two theorist willing to work on prediction of A_LT for our kinematics ◦ Peter Schweitzer of Univ Connecticut  light-cone constituent quark models  By End of April ◦ Alexei Prokudin of Jlab theory group  Wandzura-Wilczek approximation  Very soon  Looking forward to hear from them Transversity Collaboration Meeting Jin Huang 30

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33.  Most Data around Sin(phi_h)=0  Tail Stretch to +- 90  Biased to small angle at low x Transversity Collaboration Meeting Jin Huang 33

34. Transversity Collaboration Meeting Jin Huang 34 Blue: IHWP IN Red: IHWP OUT magenta: Sum two to sign of IHWP IN magenta Line: FIt of Magenta points with sin(phi_h) curve Very Preliminary Sign: Assume Old Møller Sign Convention

35.  Black Points are from fitting of last slides ◦ Consistent with MLE results Transversity Collaboration Meeting Jin Huang 35 Very Preliminary

36. Transversity Collaboration Meeting Jin Huang 36 Transverse Only Vertical Only Very Preliminary

37.  Kinematics Factor Sqrt(2ε(1- ε)) scale is applied Transversity Collaboration Meeting Jin Huang 37 Very Preliminary

38.  Consistent with 0 in our sensitivity Transversity Collaboration Meeting Jin Huang 38 Very Preliminary

39. Transversity Collaboration Meeting Jin Huang 39 Very Preliminary

40.  Most kinematics variable is not correlated with phi_h  However p_t is correlated ◦ “sensitivity” weighted bin average ◦ Sensitivity(p T,n )= sum(sin(phi_h)^2)@p T,n Transversity Collaboration Meeting Jin Huang 40

41.  Hall B and HERMES data suggest higher dependency on z.  We can also bin in z ◦ nevertheless, most kinematics variables are correlated Transversity Collaboration Meeting Jin Huang 41 Very Preliminary

42. The END Transversity Collaboration Meeting Jin Huang 42