# Clarification neutral Kaon decay (Griffith, Elem. Particles)

• Dr.AbeNikIanEdL
In summary, the conversation discusses the construction of CP eigenstates in Kaon decays and the possible decay modes under the assumption of CP conservation. It also addresses a footnote mentioning the potential for a Kaon to decay into three pions, which raises a question about angular momentum conservation. The questioner is confused about how a state with nonzero angular momentum could be produced in a Kaon decay, given that both Kaons and pions have spin 0.
Dr.AbeNikIanEdL
Gold Member
I was reading in Griffit's "Introduction to Elementary Particles" when I stumbled over the following Remark in chapter 4.4.3.1. CP eigenstates are constructed by

$|K_1> = \frac{1}{\sqrt{2}}(|K^0> - |\bar{K^0})$
$|K_2> = \frac{1}{\sqrt{2}}(|K^0> + |\bar{K^0})$

and, assuming CP conservation, the only possible decay modes should be

$K_1 \rightarrow 2\pi$
$K_2 \rightarrow 3\pi$

In the footnote at the end of the page (146) it is mentioned that "with the right combination of orbital angular momentum, it is possible to construct a ## CP=+1## state of the [##3\pi##] system, [...] this might allow ##K_1## to decay (rarely) into ##3\pi## [...]".
Now my question is, as Kaons as well as pions have spin 0, wouldn't angular momentum conservation forbid any orbital angular momentum in the final state? Do I miss something or is ##K_1 \rightarrow 3\pi## then rigorously forbidden (under the assumption of strikt CP conservation)?

Dr.AbeNikIanEdL said:
I was reading in Griffit's "Introduction to Elementary Particles" when I stumbled over the following Remark in chapter 4.4.3.1. CP eigenstates are constructed by

$|K_1> = \frac{1}{\sqrt{2}}(|K^0> - |\bar{K^0})$
$|K_2> = \frac{1}{\sqrt{2}}(|K^0> + |\bar{K^0})$

and, assuming CP conservation, the only possible decay modes should be

$K_1 \rightarrow 2\pi$
$K_2 \rightarrow 3\pi$

In the footnote at the end of the page (146) it is mentioned that "with the right combination of orbital angular momentum, it is possible to construct a ## CP=+1## state of the [##3\pi##] system, [...] this might allow ##K_1## to decay (rarely) into ##3\pi## [...]".
Now my question is, as Kaons as well as pions have spin 0, wouldn't angular momentum conservation forbid any orbital angular momentum in the final state? Do I miss something or is ##K_1 \rightarrow 3\pi## then rigorously forbidden (under the assumption of strikt CP conservation)?
Why do you think that orbital angular momentum would be forbidden in the final state? This is unrelated to the particles being spin 0 or not. You can in principle imagine a bound state of two spin 0 particles and this bound state could have excited states with nonzero angular momentum. Can you clarify your question?

My reasoning was as follows:
Total angular momentum should be conserved in this decay, so ##J = l + s## should not change. The Kaon has ##l = 0## and ##s = 0##, so ##J = 0##. Therefore the final state must have ##J = 0## as well. Pions are spin 0 particles, so there are no spins to add up, ##s = 0## in the overall final state. So any nonzero angular momentum ##l## would make the total angular momentum ##J## being some nonzero value, violating total angular momentum conservation.
I am clear that three pions could form a state with nonzero angular momentum, I just don't understand how this state could be produced in a Kaon decay, sorry for not being clear about that.

## 1. What is clarification neutral Kaon decay?

Clarification neutral Kaon decay, also known as K0 decay, is a type of particle decay that involves the neutral Kaon particle transforming into other particles. This process is governed by the weak interaction, one of the four fundamental forces of nature.

## 2. What is the significance of studying clarification neutral Kaon decay?

Studying clarification neutral Kaon decay allows scientists to better understand the fundamental laws of nature, such as the weak interaction and the Standard Model of particle physics. It also provides insights into the behavior of matter and antimatter, as the neutral Kaon can decay into both particles and antiparticles.

## 3. How is clarification neutral Kaon decay observed?

Clarification neutral Kaon decay is observed through experiments using particle accelerators and detectors. These experiments involve colliding particles at high energies and recording the resulting decay products. By analyzing the data, scientists can determine the properties and behavior of the neutral Kaon particle.

## 4. What is the role of the Griffith, Elem. Particles book in understanding clarification neutral Kaon decay?

The Griffith, Elem. Particles book is a comprehensive resource that covers various topics in particle physics, including clarification neutral Kaon decay. It provides a detailed explanation of the underlying principles and equations involved in this type of particle decay, making it a valuable reference for scientists studying this phenomenon.

## 5. How does clarification neutral Kaon decay impact our understanding of the universe?

Clarification neutral Kaon decay is an important process that occurs in the natural world and is crucial for understanding the structure and behavior of matter. By studying this phenomenon, scientists can gain a deeper understanding of the fundamental laws of physics and the origins of the universe.

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