# Meson decay

1. May 6, 2013

### sunrah

1. The problem statement, all variables and given/known data
$\frac{\Gamma\left( D^{*+} \rightarrow D^{0}\pi^{+}\right)}{\Gamma\left( D^{*+} \rightarrow D^{+}\pi^{0}\right)} = ?$

2. Relevant equations
$D^{*+} = |c\bar{d}\rangle$
$D^{*0} = |c\bar{u}\rangle$

see also Clebsch-Gordon coefficients

3. The attempt at a solution
I know that these are meson decay reactions and those look like gamma functions, but what exactly is the input parameter here? What number does the decay process deliver?

anyway

$D^{*+} \rightarrow D^{0}\pi^{+} = |c\bar{d}\rangle \rightarrow |c\bar{u}\rangle|u\bar{d}\rangle$
$= |\frac{1}{2}, \frac{1}{2}\rangle \rightarrow |\frac{1}{2}, \frac{-1}{2}\rangle|1,1\rangle$, where the numbers are isospin and its z-axis projection, e.g. $|I,I_{3}\rangle$.

now clebstch-gordon:

$|1,1\rangle |\frac{1}{2}, \frac{-1}{2}\rangle = \sum_{J =1/2} ^{3/2}|J,1/2\rangle C^{J,1/2} = \sqrt{\frac{2}{3}}\left( |1/2,1/2\rangle + |3/2,1/2\rangle\right)$

this is where i get stuck. are the CB-factors alone the input parameters of the gamma functions? thanks

Last edited: May 6, 2013
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