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