Interpretation of a before $\gamma^{5}$ in J$_{\alpha}$

[LupusLupus]

Could you explain what's the interpretation of $$a$$ before $$\gamma^{5}$$ in this current:

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

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 $$1-\gamma^{5}$$.

 

[Vanadium 50]

It is the relative strength of the axial current. It's unity for leptons. But where did you get this? It's a poor way to write this, since it's the vector current that changes.

 

[LupusLupus]

But where did you get this? It's a poor way to write this, since it's the vector current that changes.

It's a task from my studies. I have to calculate the decay rate for muon starting from hamiltonian with current in this form. I've started and ran into troubles.