View source for Altering Phi Angles

Using the fact that

<center><math>\cos{\phi} \equiv \frac{p_x}{\sqrt{p^2-p_z^2}}</math></center>


<center><math>\Longrightarrow \sqrt{p^2-p_z^2}=\frac{p_x}{\cos{\phi}}=constant</math></center>


We can simply use the expression

<center><math>\frac{p_x}{\cos{\phi}}=\frac{p_x'}{cos{\left(\phi+\delta \phi\right)}}</math></center>



<center><math>\Longrightarrow p_x'=\frac{p_x \times \cos{\left(\phi+\delta \phi\right)}}{\cos{\phi}}</math></center>


Then, using

<center><math>\sqrt{p^2-p_z^2}=\sqrt{p_x^2+p_y^2}</math></center>


<center><math>\Longrightarrow p_y'=\sqrt{p^2-p_z^2-p_x^{'2}}</math></center>

Starting with a data file of momentum components constructed using awk as described above

<center>[[File:Screen_Shot_2016-02-07_at_3.52.37_PM.png | Starting point]]</center>

A program was written to rotate the phi angle as described above.  The changing x and y components for this distribution can be seen with

<center>[[File:xy.png]]</center>