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  How can you actually measure decay constants?

+ 3 like - 0 dislike

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 $ ?
asked May 21, 2014 in Theoretical Physics by JeffDror (650 points) [ revision history ]
edited May 29, 2014 by JeffDror

As far as I understand, we measure this constant experimentally, with help of calculations of the track properties.

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