3 body relativistic phase space

In summary, the conversation involves a request for an explicit formula for the integrated three body relativistic phase space with equal masses, as well as a question about an approximate formula. The conversation then delves into the specifics of K+ decay to pi+ pi+ pi- and the total cross section, with a mention of numerical integration. Finally, the conversation shifts to a request for the integrated four body phase space with equal masses.
  • #1
Final
25
0
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!
 
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  • #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...
 
  • #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%).
 
  • #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...
 
  • #6
http://www.google.com" [Broken]
 
Last edited by a moderator:
  • #7
thanks a lot! ...
 
  • #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
 

1. What is 3 body relativistic phase space?

3 body relativistic phase space is a concept in physics that describes the possible states and movements of three interacting particles in a relativistic system. It takes into account the effects of special relativity, which describes the relationship between space and time.

2. How is 3 body relativistic phase space different from classical phase space?

Classical phase space only considers the positions and momenta of particles, while 3 body relativistic phase space also takes into account the particles' energies and how they change in relation to one another due to relativistic effects.

3. What is the significance of studying 3 body relativistic phase space?

Studying 3 body relativistic phase space allows us to better understand the behavior of particles in relativistic systems, such as high energy collisions or the movement of objects near the speed of light. This knowledge is essential for advancements in fields such as particle physics and astrophysics.

4. Can 3 body relativistic phase space be applied to systems with more than three particles?

Yes, while the term "3 body" is used in the name, the concept of relativistic phase space can be applied to systems with any number of interacting particles. However, as the number of particles increases, the complexity of the calculations also increases significantly.

5. How is 3 body relativistic phase space used in practical applications?

3 body relativistic phase space is used in various practical applications, such as predicting the behavior of particles in particle accelerators, understanding the dynamics of black holes, and developing new technologies in areas such as nuclear energy and space travel.

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