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

[mPlummers]

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.]

 

[Meir Achuz]

Those are the only hadrons light enough for Omega to decay to.

 

[mfb]

$\Omega ^{-}\rightarrow\Xi ^{-}\pi ^{0}$ is possible, too. There is enough energy, it is not immediately clear why this decay mode is less common.

 

[Vanadium 50]

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.