Theta Dependent Components

Figure 3: Definition of Moller electron variables in the CM Frame in the x-z plane. Using [math]\displaystyle{ \theta '_2=\arccos \left(\frac{p^'_{2(z)}}{p^'_{2}}\right) }[/math]

[math]\displaystyle{ \Longrightarrow {p^'_{2(z)}=p^'_{2}\cos(\theta '_2)} }[/math]

Checking on the sign resulting from the cosine function, we are limited to:

[math]\displaystyle{ 90^\circ \le \theta '_2 \le 180^\circ \equiv \frac{\pi}{2} \le \theta '_2 \le \pi Radians }[/math]

Since,

[math]\displaystyle{ \frac{p^'_{2(z)}}{p^'_{2}}=cos(\theta '_2) }[/math]

[math]\displaystyle{ \Longrightarrow p^'_{2(z)}\ should\ always\ be\ negative }[/math]