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Neutral pion 2 gamma decay question

  1. Apr 4, 2013 #1
    I've been reading some books on how neutral pion decay proceeds through chiral anomaly recently. What I found wired is people always use the matrix element of the axial current between vacuum and a pion as granted, saying the matrix element should be a vector and the pion momentum is the only vector one can use so we have <vac|[itex]J_{\mu5a}[/itex]|[itex]\pi^b(p)[/itex]> = [itex]-i p_\mu \delta_{ab} f_\pi[/itex]. But if you take the divergence of this, you get the [itex] {m_\pi}^2 f_\pi[/itex] which equals zero in chiral limit. This is not true in the case of pion 2 photon decay since when the current is coupled to electromagnetic fields the divergence of the axial current is non-zero and proportional to [itex] E \bullet B[/itex]. Another question I have is why the pion decay constant from charged pion decay can be used to calculate neutral pion decay width and get the correct result. Someone help here?
  2. jcsd
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