Matrix elemnet of pion decay

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  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
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[tex]\pi^+ \rightarrow \pi^0 + \mu^+ + \nu[/tex]

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.
 
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