DC Binning Based On Wire Numbers

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DC Binning Based on Wire Numbers

The bin size based on wire number will need to be a uniform width of 1, as in an increment of 1 between the integer values of the wires. This uniformity in bin size based on wire numbers is not uniform when viewed by the angle theta due to the Drift Chamber geometry discussed earlier.

Modifying evio2root.cc

The corresponding theta scale can be superimposed over the bin plot using the minimum and maximum angles

[math]\theta_{n=1}=5.23^{\circ}\ \ \ \theta_{n=112}=41.07^{\circ}[/math]

Since the scale on the axis describing the wire number bins runs from 0 to 113, we will account for these theoretical theta using the polynomial fit for the expression of theta as a function of the wire number.

[math]\theta_{n}=4.93253 +0.297371 n+0.000566298 n^2-3.04016 \times 10^{-6} n^3[/math]

[math]\theta_{n=0}=4.93^{\circ}\ \ \ \theta_{n=113}=41.38^{\circ}[/math]

gStyle->SetStripDecimals(kTRUE);
TF1 *fit_function=new TF1("fit_function","[0]+[1]*x+[2]*x*x+[3]*x*x*x",4.93,41.38);
fit_function->SetParameters(4.93253,0.297371,0.000566298,-.00000304016);
TGaxis *A1 = new TGaxis(0,5000,113,5000,"fit_function",510,"-");
A1->SetTitle("Angle Theta(degrees)");
A1->Draw();

<gallery> File:Layer1bins.png|thumb|center|500px|alt=DC Bin Hits Isotropic Distribution|Figure 5.1.1: An Isotropic CM frame distribution of bin hits in the DC for superlayer 1, layer 1. File:Layer1bins_Isotropic.png|thumb|center|500px|alt=DC Bin Hits Isotropic Distribution|Figure 5.1.2: An Isotropic lab frame distribution of bin hits in the DC for superlayer 1, layer 1. <\gallery>

Using the expression for n in terms of Theta:

[math]n = \frac{-957.412}{\tan{ \theta}+2.14437}+430.626[/math]

This relationship can be used to multiply each Moller Scattering angle theta in the lab frame, with it's differential cross-section weight, to find the Moller differential cross-section as a function of wire number in the lab frame.

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