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## Homework Statement

Explain what the term "four-momentum transfer ##q##" is

Show that for a high energy muon scattering at an angle ##\theta##, the value of ##q^2## is given approximately by;

##q^2=2E_iE_f(1-cos(\theta))##

where ##E_i## and ##E_f## are the initial and final values of the muon's energy. State when this approximation is justified.

## Homework Equations

##\vec{p}=(p_1,p_2,p_3,iE)##

## The Attempt at a Solution

The first part, four momentum transfer is just the momentum and energy lost/gained in a scattering process by the scattered particle?

And the second part, i know the approximation should be that ##E>>m## but i can't seem to work with 4-momentum.

What i tried to do was;

##q^2=(p_i-p_f)^2=|p_i|^2+|p_f|^2-2p_i\cdot p_f=|p_i|^2+|p_f|^2-E_iE_fcos(\theta)##

and i assume somehow i need to get ##|p_i|^2+|p_f|^2=2E_iE_f## but I am not sure how.

Would it be because the ##E>>m## then the ##p \approx E## but then that would just mean ##q^2=E_i^2+E_f^2-E_iE_fcos(\theta)##