I How to find the most likely modes of decay for a particle

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What are the most likely modes of decay for ##\Omega ^{-}## into 2 hadrons?

##BR_{k}=\frac{\Gamma _{k}}{\Gamma}##
##\Gamma=\frac{\hbar}{\tau }##
##\Gamma _{k}=\Gamma _{if}=2\pi \rho|<\Psi _{i}|H_{Int}|\Psi _{f}>|^{2} (E_{f})##

I took a look at the Particle Data Group, and the most likely modes are ##\Omega ^{-}\rightarrow \Lambda K^{-}## (68%) and ##\Omega ^{-}\rightarrow\Xi ^{0}\pi ^{-}## (24%). I have some difficulties to understand which particle i should use to calculate the branching ratios. The exercise only says that it can decay in 2 hadrons, but it doesn't say which. How can i know this without looking at books as i did?

[Moderator's note: Moved from a homework forum with the expectation someone here can help.]
 

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clem

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Those are the only hadrons light enough for Omega to decay to.
 
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##\Omega ^{-}\rightarrow\Xi ^{-}\pi ^{0}## is possible, too. There is enough energy, it is not immediately clear why this decay mode is less common.
 

Vanadium 50

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There is enough energy, it is not immediately clear why this decay mode is less common.
The fact that the width is 1/3 the charged pion mode suggests its an issue with color lines, although I haven't worked it out.
 
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