Theta Dependent Components

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

$\Longrightarrow {p^'_{2(z)}=p^'_{2}\cos(\theta '_2)}$

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

$90^\circ \le \theta '_2 \le 180^\circ \equiv \frac{\pi}{2} \le \theta '_2 \le \pi Radians$

Since,

$\frac{p^'_{2(z)}}{p^'_{2}}=cos(\theta '_2)$

$\Longrightarrow p^'_{2(z)}\ should\ always\ be\ negative$

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