FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

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FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++ Jackie Glister Dalhousie University, Saint Mary’s University Halifax, NS Canada Hall A E05-103 Meeting Dec. 8, 2005

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FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++. Jackie Glister Dalhousie University, Saint Mary’s University Halifax, NS Canada Hall A E05-103 Meeting Dec. 8, 2005. Maximum Likelihood. - PowerPoint PPT Presentation

Transcript of FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Page 1: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

FPP Software: PALM++Polarization Analysis using Likelihood Method in C++

Jackie GlisterDalhousie University, Saint Mary’s University

Halifax, NS Canada

Hall A E05-103 Meeting Dec. 8, 2005

Page 2: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Maximum Likelihood• The Likelihood function is defined as the

product of the probabilities for all protons to scatter at angles θfpp and Φfpp:

where εα = Ac(θfpp)ΣβSαβ·Tβ

• A set of 6 linear equations is solved and matrix inversion is done to extract the 6 polarization components at the target.

L x fppi

y fppi

i

N

1

21

1 sin co s

Polarization of proton at target in cm

Page 3: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Current Input Variables (as developed for E91-011):these were from ESPACE

• θfpp

• z_close: scattering vertex in carbon• z_diff• coincidence time• p_miss• E_miss• Target: θe, θp, Φe, Φp, yp

• δp

• βp

• GM• SpecThetaE, SpecThetaP

These variables all had cutsimposed in E91-011 analysisfor ensuring clean eventsand acceptance definition.

Page 4: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Other INPUT Variables(as used in E91-011)

Variables used for rotations and calculation of polarization• helicity sign of beam

• Φfpp

• focal plane: Φp, θp

• Φxq, θxq, W, Q2

• pe, pp corrected for energy loss in target

• Ebeam

• ε (for response functions)

Other input variables (not used in E91-011 analysis)• M_miss• focal plane: xp, yp

• Asum (not sure what this variable even is)• SClose (not sure what this variable even is)

Page 5: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Spin-Transport Matrix

F = S·T

S = RfppCRspecRhallRw

1) Rw : Wigner rotation from cm to lab

2) Rhall : rotation from lab to hall

3) Rspec : rotation from hall to spectrometer4) C : spin transport through magnetic field of

spectrometer. 3 options in PALM++: a) Dipole approximation b) Pentchev approximation c) COSY model

5) Rfpp : transformation to fpp coordinate system

Page 6: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

• 5° ≤ θfpp ≤ 20° to eliminate reactions due to Coulomb scattering and ensure the track is entirely within rear wire chamber.

• False asymmetry expressed as expansion of sine and cosine of Φfpp and 2Φfpp with coefficients (a, b, c and d) calculated by R. Roche. Factor added to angular distribution in FPP.

• Analyzing power calculated using McNaughton fit (with parameters re-evaluated for E91-011 by R. Roche in p momentum range 0.703 – 1.378 GeV/c).

• Polarization (and Response Functions) calculated with and without out-of-time background subtraction.

Page 7: FPP Software: PALM++ Polarization Analysis using Likelihood Method in C++

Other things in PALM++ Specific to E91-011 (and will need to be skipped for future uses)

• Measured p(e,e’p)0 XS Legendre coefficients read in from file and used to calculate cross sections needed for response function likelihood fits

• Bin centering of XS done using MAID

• Offset to beam energy applied• Corrections to some kinematic variables (W, Q2, θxq, Φxq)

through call to ESPACE subroutine

• Elastic polarization components calculated and added to false asymmetry (method of handling contamination/dilution of polarization by elastic-tail)

• Maid acceptance averaged polarizations and response functions calculated with a call to Jim Kelly’s epiprod program

This just because initial ESPACE kinematicsdone with wrong Eo