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[tex]J_{\alpha}=\bar{\psi_{e}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{e}} +\bar{\psi_{\mu}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{\mu}}[/tex]?

And will this factor complicate calculations of decay rate of muon very much? I've seen that the standard form of current in the most popular books contains just [tex]1-\gamma^{5}[/tex].