# How can you actually measure decay constants?

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I'm trying to understand how people actually measure decay constants that are discussed in meson decays. As a concrete example lets consider the pion decay constant. The amplitude for $\pi ^-$ decay is given by,

\big\langle 0 | T  \exp \left[  i \int \,d^4x {\cal H} \right] | \pi ^- (  p _\pi )  \big\rangle

To lowest order this is given by,

i \int \,d^4x  \left\langle 0 | T W _\mu       J ^\mu  | \pi ^- (  p _\pi )  \right\rangle

If we square this quantity and integrate over phase space then we will get the decay rate.

On the other hand, the pion decay constant is defined through,

\left\langle 0 | J ^\mu | \pi ^- \right\rangle = - i f _\pi p _\pi ^\mu

This is clearly related to the above, but it seems to me there are a couple of subtleties.

1. How do we get rid of the time-ordering symbol?
2. Since we don't have a value for $W _\mu$ how can we go ahead and extract $f _\pi$ ?
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