# What is the phase space for outgoing photons?

For a scattering process for which $n$ fermions are scattered, (by some conventions) the cross section acquires a phase space factor of: $$d\sigma \sim \prod_{i=1}^n\frac{d^3p_i}{(2\pi)^3 2E_i}$$

1. In this convention, what is the equivalent phase space factor for an outgoing photon?

2. How is it that different conventions differ by arbitrary factors of $2$ and $\pi$? isn't the cross section a measurable which has to "stay put" irrespective of the convention used?

• 1. it's the same expression for the photon as for any other particle (just remember that you are overcounting the phase space if the particles are identical, and need to include a factorial factor to get it right) 2. the cross-section is notation independent, but you have written just the phase space, not the full cross-section. The independent quantity is phase-space times |scattering amplitude|^2. If your convention for the phase-space differs by a factor of 2 then the convention for the scattering amplitude differs too, and by a factor of $1/\sqrt{2}$ Commented Jul 11, 2014 at 12:05
• @TwoBs - I'll accept that as answer :) Could you show where in the amplitude these factors come into play? I assume they come into play inside the normalization $u(p,s)\bar{u}(p,s)=$? Commented Jul 11, 2014 at 16:32