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.
+ 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.
- ~pp~A<sub>raw</sub> = (N<sub>+</sub> - N<sub>-</sub>)/(N<sub>+</sub> + N<sub>-</sub>)
N<sub>+</sub> = �<sub>+</sub> L<sub>+</sub> �<sub>+</sub> + Bck
~/pp~ and likewise for -=N<sub>-</sub>.
+ ::-+A{SUB()}phys{SUB} = (sigma{SUB()}+{SUB} - sigma{SUB()}-{SUB}) / (sigma{SUB()}+{SUB} + sigma{SUB()}-{SUB})+-::
while<br />::-+A{SUB()}raw{SUB} = (N{SUB()}+{SUB} - N{SUB()}-{SUB})/(N{SUB()}+{SUB} + N{SUB()}-{SUB})+-::<br />and
::-+N{SUB()}+{SUB} = sigma{SUB()}+{SUB} L{SUB()}+{SUB} eta{SUB()}+{SUB} + Bck+-;::
/>likewise for -+N{SUB()}-{SUB}+-.<br />
What one finds, to first order in the false and true asymmetries, is:<br />::-+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.
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