History: AsymmetryCorrections

To extract GEn/GMn, the true "physics" asymmetry must be determined. Since the "raw" asymmetry immediately measured from the data must be corrected for false asymmetry contributions, dilution, and finite acceptance effects.

I recommend that you work through the algebra to understand the correction factors for the asymmetry. Here, I will start with the number of events ~~red:N~~ in the positive (+) and negative (-) helicity state and state the final expression.

::-+A{SUB()}phys{SUB} = (sigma{SUB()}+{SUB} - sigma{SUB()}-{SUB}) / (sigma{SUB()}+{SUB} + sigma{SUB()}-{SUB})+-::
while
::-+A{SUB()}raw{SUB} = (N{SUB()}+{SUB} - N{SUB()}-{SUB})/(N{SUB()}+{SUB} + N{SUB()}-{SUB})+-::
and
::-+N{SUB()}+{SUB} = sigma{SUB()}+{SUB} L{SUB()}+{SUB} eta{SUB()}+{SUB} + Bck+-;::
likewise for -+N{SUB()}-{SUB}+-.

What one finds, to first order in the false and true asymmetries, is:
::-+A{SUB()}phys{SUB} = 1/D ( A{SUB()}raw{SUB} - (1 - Q{SUB()}-{SUB}/Q{SUB()}+{SUB} eta{SUB()}-{SUB}/eta{SUB()}+{SUB}) )+-::
where -+~~red:eta~~+- is the overall efficiency, and -+~~red:Q~~+- is the accumulated charge for each helicity state.

-=False Asymmetries=-
The sources for false asymmetries for GEn are:
# Beam charge asymmetry (more accumulated charge in one helicity state than the other)
# DAQ Livetime asymmetry
# Electronic Livetime asymmetry
# Tracking efficiecy asymmetry

The last three are due generally to the asymmetry in the background pion-production cross-section, which is ~1% for the Kine4 dataset.