jin huang m.i.t. for transversity collaboration meeting mar 26, 2010 @ jlab

Transversity Analysis with Maximum Likelihood

Method

Jin HuangM.I.T.

For Transversity Collaboration MeetingMar 26, 2010 @ JLab

Jin Huang <[email protected]> 2

Overview

•Why MLE•General Progress

Yield Distribution

A_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

Content


OverviewGoals, FocusesComparison of MLE



Knowing ◦ A pool of SIDIS events◦ Run condition data

Wanted:◦ Extract Parameter with a specific model◦ Ex. Angular modulation


Goal


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.


Why MLE


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 1st 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


Benefits


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)


A trade over


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


Progress


Yield Distribution Extraction



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


Yield Estimation


Transversity Q^2 Distribution◦ y axis:

Yield Density (uC-1GeV-2)


Example of 1D Distribution

Jin Huang <[email protected]> 12Transversity Collaboration Meeting

Example of 2D Distribution

Lower side of BB acceptance is favored at low x (low momentum)


A_UT and comparison with Blue Team®



Consistent for most points


Compare Single Arm SSA: Bigbite Pion


Comparing Coinc SSA: e’pi

consistent for most points


Angular Coverage

Correlated and Limited Coverage -> High Convolution between Modulations


Comparison Angular Modulation Mostly

Consistent Similar

Fluctuation as Asymmetries

Not Local Pair MLE yet

Very Preliminary


Sign of Helicity



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)


Origin of the problem


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)?


Preliminary analysis


Cross Check is welcome◦ I have detailed analysis record

Looking for other experiment data From other He3 series experiment Test in PREX running (difficult)


TODO


A_LT and A_LL Contamination



Raw A_LT modulation◦ Two section: IHWP IN and OUT

Sign difference already applied


A_LT

Very Preliminary


All information are used

Not possible to get reliable A_LL correction


A_LT + A_LL with Our Data Only


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


Why we can not?

Direction of Separation=0 Direction that A_LL be cancelled


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


With A_1n from HERMES data, the total LL correction is small


Apply the correction

Very Very Preliminary, Assuming•Møller Sign Convention•10% N2 Dilution Assumed


Naive model from He3 -> Neutron


Neutron A_LT

Very Very Preliminary•He3 Asym Assumptions+•Assuming 86.5% Neutron Pol.•No Proton A_LT•No Nuclear Effect•No FSI


Sensitivity drop fast as higher order terms are included


Higher twist terms

phi_h informationare over used Very Preliminary


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


Theory Supports


A_LU, the first clearly non-zero modulation



Phi_h coverage: 2D


Most Data around Sin(phi_h)=0

Tail Stretch to +- 90 Biased to small

angle at low x


Phi_h coverage: 1D


A_LU by bins •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 PreliminarySign: Assume Old Møller Sign Convention


Black Points are from fitting of last slides◦ Consistent with MLE results


A_LU Full MLE

Very Preliminary


A_LU by spin states: Consistent

Transverse Only

Vertical Only

Very Preliminary

Very Preliminary


Kinematics Factor Sqrt(2ε(1- ε)) scale is applied


A_LU With Kinematics Factor Corr.

Very Preliminary


Consistent with 0 in our sensitivity


A_LU on other hadrons

Very Preliminary


High Model dependencyEx. 2 Term Fit

Very Preliminary


Most kinematics variable is not correlated with phi_h

However p_t is correlated ◦ “sensitivity” weighted

bin average◦ Sensitivity(pT,n)=

sum(sin(phi_h)^2)@pT,n


Kinematics Correlations of A_LU


Hall B and HERMES data suggest higher dependency on z. We can also bin in z

◦ nevertheless, most kinematics variables are correlated


z binning

Very Preliminary


The END


jin huang m.i.t. for transversity collaboration meeting mar 26, 2010 @ jlab

Documents

lt small

hrs signal sign

transversity analysis

staterelative phase

lt modulationtwo section

ll shadow

sign convention havent

angular information