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HISKP-LQCD / hadron

R package implementing analysis tools for lattice QCD
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matrixfit amplitude convention #172

Open kostrzewa opened 5 years ago

kostrzewa commented 5 years ago

This is something that I've wanted to discuss for a while now but never really got around to.

The conventional physical normalisation of a PS correlator is:

A^2 * ( exp(-E_pst) + exp(-E_ps(T-t)) = G_ps^2 / (2 E_ps) * ( exp(-E_pst) + exp(-E_ps(T-t))

such that

G_ps = sqrt( 2 * E_ps ) * A

where G_ps is the bare matrix element of the PS current between a pion state and the vacuum.

This comes from the fact that for infinite T, we would simply have

G_ps^2 / (2 E_ps) *  exp(-E_pst)

and the same relationship between A and the matrix element. However, in matrixfit (and in hadron in general) a factor of 0.5 is added to the model, such that

0.5 * A^2 * ( exp(-E_pst) + exp(-E_ps(T-t)) = G_ps^2 / (2 E_ps) * ( exp(-E_pst) + exp(-E_ps(T-t))

and then

G_ps = sqrt( E_ps ) * A

Of course there's nothing wrong with this as long as one keeps track of that factor of 0.5, but I was wondering what the reason was for having it around in the first place.

kostrzewa commented 5 years ago

For the shifted and pc models, instead, no such factor is carried around.