- #1
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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?
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?