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

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• mPlummers
In summary, the most likely modes of decay for ##\Omega ^{-}## into 2 hadrons are ##\Omega ^{-}\rightarrow \Lambda K^{-}## (68%), ##\Omega ^{-}\rightarrow\Xi ^{0}\pi ^{-}## (24%), and ##\Omega ^{-}\rightarrow\Xi ^{-}\pi ^{0}## (8%). The Particle Data Group lists these as the only possible decay modes for the Omega particle. The exercise does not specify which hadrons should be used in the calculation, but the available options are limited to those mentioned above due to the energy requirements. However, it is not immediately clear why ##\Omega ^{-}\rightarrow\Xi ^{-
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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Those are the only hadrons light enough for Omega to decay to.

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

mfb said:
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

## 1. What is the process for determining the most likely modes of decay for a particle?

The process for determining the most likely modes of decay for a particle involves analyzing the particle's properties, such as its mass, charge, and spin, and using theoretical models and experimental data to predict the possible decay modes. This is often done through advanced calculations and simulations.

## 2. What factors influence the likelihood of a specific decay mode for a particle?

The likelihood of a specific decay mode for a particle is influenced by several factors, including the particle's mass, energy, and quantum numbers, as well as the available decay channels and the laws of conservation of energy and momentum. The strength of the interaction between the decaying particle and its decay products also plays a role.

## 3. Can the most likely modes of decay for a particle change over time?

Yes, the most likely modes of decay for a particle can change over time as new experimental data and theoretical models become available. This is particularly true for unstable particles, which may have multiple possible decay modes with varying probabilities.

## 4. How does the Standard Model of particle physics help in determining the most likely modes of decay for a particle?

The Standard Model of particle physics provides a framework for understanding the fundamental particles and their interactions. This model is used to predict the possible decay modes for a given particle based on its properties and the known interactions between particles. Experimental data is also used to test and refine the predictions of the Standard Model.

## 5. Are there any experimental techniques specifically designed to study the decay modes of particles?

Yes, there are several experimental techniques that are specifically designed to study the decay modes of particles. These include particle colliders, which accelerate particles to high energies and observe their decay products, and particle detectors, which can identify and measure the properties of the decay products. Other techniques, such as scattering experiments and precision measurements, can also provide valuable information about the decay modes of particles.

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