# Golden Rule for Decays in Griffiths' Introduction to Elementary Particles ?

1. Mar 18, 2010

### TMFKAN64

Golden Rule for Decays in Griffiths' "Introduction to Elementary Particles"?

Hello, I'm getting a bit bogged down in constant factors while reading Griffiths' "Introduction to Elementary Particles", 1st edition. In particular, I'm having problems with equation 6.15:
$$d\Gamma = |M|^{2}\frac{S}{2\hbar m_{1}}\left[ \left(\frac{c\, d^{3}p_{2}}{(2\pi)^{3}2E_{2}}\right) \left(\frac{c\, d^{3}p_{3}}{(2\pi)^{3}2E_{3}}\right)\cdots \left(\frac{c\, d^{3}p_{n}}{(2\pi)^{3}2E_{n}}\right)\right]\times (2\pi)^{4}\delta^{4}(p_{1}-p_{2}-p_{3}\cdots-p_{n})$$

I've found some slides online at http://www-pnp.physics.ox.ac.uk/~libby/Teaching/Lecture4.pdf that discuss normalizing the wave function and phase space so it is Lorentz invariant, but this only explains part of my problem. What I still don't understand is:
• Where do the $$c$$ in the numerators of the momentum terms come from?
• Where does the $$(2\pi)^{4}$$ term before the delta function come from?
• Where did the $$\hbar^{3n}$$ in the density of states go? (The $$\frac{1}{(2\pi\hbar)^{3n}}$$ is responsible for the $$2\pi$$ factors in the momentum terms, right?)
• Why doesn't the first fraction have $$m_{1}c^{2}$$ in the denominator?

Any assistance would be greatly appreciated.