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

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.

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

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  1. 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

  2. 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. Polarization of proton at target in cm

  3. 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.

  4. 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)

  5. 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 spectrometer 4) 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

  6. 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.

  7. 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

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