# I 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.]

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#### clem

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

#### mfb

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

Staff Emeritus
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.

• mfb

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