Consider the standard formula for beta decay $n\rightarrow W^{*-}\rightarrow p+e^-+\nu_e$ a standard question that I have seen come up is why can this be treated as a four-point decay. Now intuitively I would answer the question by saying that since $\tilde q^2\lt \lt M_W^2$ the propagator becomes essentially independent of $\tilde q^2$ thus allowing us to treat it as four point. However my I have seen it said (no source available sorry) that it is because: $$\tau=\frac{\hbar}{\Delta E}$$ is so small where $\Delta E$ is a measure of how far off mass-shell the system is. But considering the answer to my previous question about the lifetime of such particles - they don't have one. Thus I am wondering the origin of this last expression and why this allows us to write: $$M=\int \psi_e^* \psi_\nu^* \psi^*_p V\psi_ndV$$ which (correct me if I am wrong) only works for a four point interaction?
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