Particle momenta and cross section

[Schwarzschild90]

Will someone explain this step to me?

 

[DrDu]

Some more background would be helpful. I suppose this is for massless particles where p^2=0?

 

[Schwarzschild90]

Yes. It's for electron muon scattering

 

[DrDu]

But neither electrons nor myons are massless. Or is this some approximation?

 

[Schwarzschild90]

The event is viewed in a CM frame.

 

[ChrisVer]

it has nothing to do with CM frame ($p^2= m^2$ in any frame -frame independent minkowski product).
Probably they consider electron/muon with high enough momenta/Energy so that they can be considered massless (i.e. the last $=$ in 2nd line should be $\approx$ instead)

 

[mfb]

They neglect the particle masses, right.

 

[Schwarzschild90]

I was in a rush. CM has nothing to do with it.

Indeed, the particles considered are massless.

I figured it out.

 

[Schwarzschild90]

Why can we set E/c = p?

 

[mfb]

It is the same approximation of massless particles.

 

[ChrisVer]

$E = \sqrt{p^2 + m^2} \Rightarrow E = p + \mathcal{O}\big(\frac{m^2}{2p}\big)$
(taylor expanding the square root for m<<p)