Weak force and axial vector coupling

[a dull boy]

Hi physics forum,

I have been reading David Griffith's book "intro to elementary particles" and he
describes the decay of the pi-meson as "pure axial vector"

Can someone tell me what this means, in terms of the weak force vertex consisting of
this factor

γ^u(1-γ⁵)

Thanks, Mark

 

[Vanadium 50]

Only the term with the gamma_5 in it contributes.

 

[a dull boy]

Thanks for the reply. I'll follow up 1) what does that mean physically, for example, do only certain particle types engage in pure axial coupling? 2) can you say a little as how
the math would work (how can the vector part of V-A not contribute, since the axial
part is multiplied by the vector (γ^uγ⁵

I am a novice in this, so it may not be a good question! -Mark

 

[Bill_K]

db, The weak interaction is an interaction between weak currents, J^μJ_μ. For the lepton pair the particles are free, and J_μ is of the V-A form.

However the quarks that make up the pion are not free, they are in a bound pseudoscalar state. You can combine their wavefunction with the 4-momentum k_μ to construct an axial vector current, but there is no way to make a vector current.