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3 body relativistic phase space

  1. Sep 16, 2009 #1
    Hi,
    Do you know if there is an explicit formula for the integrated 3 body relativistic phase space of 3 particle with the same mass? I.e. M->3m
    Or an approximate one?
    Thank you!
     
  2. jcsd
  3. Sep 17, 2009 #2
  4. Sep 17, 2009 #3
    There is only the differential cross section... I need the total cross section i.e. the integral of your formula. In the case of 3 massive body I think I can't integrate it. I did only the numerical integration...
     
  5. Sep 17, 2009 #4
    In the case of a K+ --> pi+ pi+ pi-, I think the total probability of the decay is the probability of decaying between point 1 and point 2, times the branching ratio for this decay mode (~21.5%).
     
  6. Sep 21, 2009 #5
    I didn't understand what is point 1 and point 2...
    Anyhow I found the formula for the integrated 3 body phase space:
    [tex] \Phi= \frac{1}{\pi^3 2^7 M^2} \int_{s_2}^{s_3}{\frac{d s}{s} \sqrt{(s-s_1)(s-s_2)(s_3-s)(s_4-s)}},
    [/tex]
    Where M is the mass of the initial state and [tex] s_1=(m_1-m_2)^2, \quad s_2=(m_1+m_2)^2, \quad s_3=(M-m_3)^2, \quad s_1=(M+m_3)^2
    [/tex].
    I think you can do this integral only numerical...
     
  7. Sep 24, 2009 #6

    sri

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    http://www.google.com" [Broken]
     
    Last edited by a moderator: May 4, 2017
  8. Sep 25, 2009 #7
    thanks a lot! ...
     
  9. Feb 2, 2012 #8
    Help! Four body relativistic phase space

    Hello everybody!

    I urgently need the value of the integrated four body phase space, whereby the four outgoing particles all have equal mass m.
    So I need the analogon of the formula for Phi which "Final" posted, but this time for four outgoing particles...

    Thanks a lot,

    Basti
     
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