Matrix elemnet of pion decay

[plasmon]

I have studied that the hadronic matrix element of pion decay
(Pi+->mu+ anti muon neutrino) is given as
<0|ubar gamma[mu](1-gamma[5])d|pion>.
The vector current does not seem to contribute, because it cannot connect a state of unnatural parity to hadronic vacuum. Only the axial and pseudoscalar current seems to conribute.
Similarly for pion decay
(Pi+>Pi0 mu+ anti muon neutrino) is given as
<0|ubar gamma[mu](1-gamma[5])d|pion>.
Now The vector current does contribute. The axial current contribution seems to vanish now because a state of unnatural parity is going to unnatural parity!

I do not understand this abstract kind of reasoning.

 

[Norman]

$$\pi^+ \rightarrow \pi^0 + \mu^+ + \nu$$

is not an allowed decay, check conservation of energy.

Correction: it should be a muon neutrino- not anti-neutrino. Negatively charged leptons are considered particles, positively charged leptons are anti-particles. Merely convention. Ah yes... latex does not update with the correction.