# Pion decay into electron and anti-neutrino

In Peskin and Schroeder Books Chapter 5 subsubection Bound State equation (5.43)

$\mathcal{M}(\uparrow \uparrow \rightarrow B)=\sqrt{2M}\int \frac{d^3k}{(2\pi)^3}\tilde{\psi^\ast}(\mathbf{k})\frac{1}{\sqrt{2m}}\frac{1}{\sqrt{2m}}\mathcal{M}(\uparrow \uparrow \rightarrow \mathbf{k} \uparrow, - \mathbf{k}\uparrow)$

My question : If i would like to calculate the decay width of pion decay, can anybody tell me how to use that equation.

You mixed up eq43 with eq44, you should replace $\left|B\right\rangle$ with $\mathcal{M}(\uparrow\uparrow\rightarrow B)$
• @Panuluh regarding p 264, you can see there that in the paradigm of effective field theory we write down the pion muon neutrino vertex based on known symmetries, combining all our (analytic) ignorance about the microscopic theory description of pion decay in one constant $f_\pi$. Then this is totally unknown, except you can estimate it using dimensional analysis (or precisely using the lattice as Melquiades noted). Then he goes on to calculate ratios which is the only thing you can predict, by canceling $f_\pi$ – Ali Moh Mar 8 '15 at 4:35