# Quick question on Fermi Golden Rule

Adopted from my lecture notes, found it a little fishy:

Shouldn't ##\frac{dp}{dE} = \frac{E}{p}## given that ##p = \sqrt{E^2 - m^2}##. Then the relation should be instead:

$$\frac{dp}{dE} = \frac{E}{p} = \frac{E}{\sqrt{E^2 - m^2}}$$

## Answers and Replies

Yes, you are right but the problem tells you that B and C are massless. This means that the magnitude of their momenta is equal to their energies. In particular, conservation of energy tells you that ##E_B=E_C=E_A/2## and so ##p_B=p_C=E_A/2##, giving ##dp_B/dE=1/2##.

Yes, you are right but the problem tells you that B and C are massless. This means that the magnitude of their momenta is equal to their energies. In particular, conservation of energy tells you that ##E_B=E_C=E_A/2## and so ##p_B=p_C=E_A/2##, giving ##dp_B/dE=1/2##.
And I suppose ##c=1##?

Exactly.

unscientific