Decay rates
Definition: decay rate
The decay rate $\Sigma$ gives the probability of a particle decaying in a given time frame $$d\Sigma = \frac{1}{T}dP$$
Note: for $t\to -\infty$ the state is not an asymptotic state otherwise it would be an eigenstate to the hamiltonian and would not decay after some time. We assume the interaction happens over a finite timespan ?
Decay rate formula
For an $1 \to n$ decay process we have $$d\Gamma = \frac{(2\pi)^4 |\mathcal{M}|^2}{2M}d\Phi$$ with the lorentz invariant phase space $\Phi$