Undergrad Understanding Kaon Behavior: Decays and Predictions by Gell-Mann and Pais

[Pedro de la Torre]

Hello, I am startfing to study kaons and I can not understand why (or how) We know that the decay process of k → 2 π is much faster than the K → 3π.

In the Griffits´ book he says that: The reason is the energy released is greater.

But I don´t get it.

Can someone explain me this issue a bit?

And, if possible, how could Gell-Mannand Pais predict the conversion between a K° and its antiparticle?

 

[Vanadium 50]

In the Griffits´ book he says that: The reason is the energy released is greater.

But I don´t get it.

Have you read the whole book? Or only that sentence?

 

[Pedro de la Torre]

I am reading it... I am only in the 5th chapter.

 

[vanhees71]

I think Griffiths's wording is a bit confusing. What he means to say is the following: Take the kaon in the initial state at rest. The energy is given by its rest energy $m_K c^2$. To decay into 2 or three 3 pions you need more the $2 m_{\pi} c^2$ or $3 m_{\pi} c^2$ of energy, respectively. Thus the available phase space (in terms of the pions' three momenta) is much larger for the decay into 2 than 3 pions, and thus the lifetimes of the CP eigenstates $K_s$ and $K_l$ ("K short" and "K long") are quite different: $\tau_s=0.895 \cdot 10^{-10} \text{s}$ and $\tau_l=5.11 \cdot 10^{-8} \text{s}$ as written in Griffiths's book.

 

[Pedro de la Torre]

It´s great! thank you!

And about the conversion between the K° and its antiparticle, how can be predicted such phenomenom?

 

[ChrisVer]

And about the conversion between the K° and its antiparticle, how can be predicted such phenomenom?

the question is unclear. Do you mean how one can measure this? or how it can happen?

 

[vanhees71]

Well, both the $\mathrm{K}^0$ and the $\overline{\mathrm{K}^0}$ can decay to two pions. Now think of this process in terms of Feynman diagrams, it's pretty clear that you can built a loop diagram where a $\mathrm{K}^0$ is converted to a $\overline{\mathrm{K}^0}$. For a very nice treatment within quantum mechanics (applying the famous Wigner-Weisskopf approximation), including the important discovery of CP violation in the neutral-kaons system (Nobel to Cronin and Fitch 1964) see

O. Nachtmann, Elementary Particle Physics - Concepts and Phenomenology, Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1990.

 

[Vanadium 50]

And about the conversion between the K° and its antiparticle, how can be predicted such phenomenom?

See Figure 4.12 in Griffiths. This is why I asked you if you were working through the whole thing. Each chapter builds on the ones before it. You can't jump around and learn the material.

 

[Pedro de la Torre]

Yes, I did not understand when I saw for first time, but now I have completely understood.

Thank you.