D* -> D + gamma BR calculation

[Hepth]

Can anyone walk me through this calculation? I'm not completely sure how to do it (merely a student).

So is this considered a 1 body radiative decay? So the factorized amplitude would be something like
$$M \propto <D^0|\bar{u}\gamma_\mu\left(1-\gamma_5\right)c|0>[A_1 <\gamma|\bar{u}\gamma_\mu\left(1-\gamma_5\right)c|D^{*0}>+A_2<\gamma|\bar{u}i \sigma_{\mu \nu} p_\nu \left(1+\gamma_5\right)c|D^{*0}>$$

And each matrix can be decomposed into some constants/vectors/polarizations etc.

$$<D^0|\bar{u}\gamma_\mu\left(1-\gamma_5\right)c|0> = i f_{D^0} P_{D^{0}\mu}$$

and the second and third terms can be similarly decomposed into linear combinations of terms depending only on:
Photon Polarization $$\epsilon^{*}_{\gamma \alpha}$$
$$D^{*0}$$ Polarization $$\epsilon^{*}_{D^{*0} \beta}$$
Momentums of the photon and D* (q and p respectively)
And the constants can depend on p^2.

So any sort of combination of these such that the end result yields one remaining index.

Now my first question, for those that do these sort of things, am I handling the D* matrices correctly? Am I missing any effective terms/form factors?

 

[Vanadium 50]

This is over my head, because I am an experimenter, but what are all the gamma_5's doing there? This is an electromagnetic decay, so why are you projecting out the left handed state?