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I Kaons behavior

  1. Nov 11, 2017 #1
    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?
     
  2. jcsd
  3. Nov 11, 2017 #2

    Vanadium 50

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    Have you read the whole book? Or only that sentence?
     
  4. Nov 11, 2017 #3
    I am reading it... I am only in the 5th chapter.
     
  5. Nov 11, 2017 #4

    vanhees71

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    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.
     
  6. Nov 11, 2017 #5
    It´s great! thank you!

    And about the conversion between the K° and its antiparticle, how can be predicted such phenomenom?
     
  7. Nov 11, 2017 #6

    ChrisVer

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    the question is unclear. Do you mean how one can measure this? or how it can happen?
     
  8. Nov 12, 2017 #7

    vanhees71

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    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.
     
  9. Nov 12, 2017 #8

    Vanadium 50

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    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.
     
  10. Nov 12, 2017 #9
    Yes, I did not understand when I saw for first time, but now I have completely understood.

    Thank you.
     
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