Solving Three Body Decay: Colin's Challenge

[colin.mcenroe]

Hello all,

I have been racking my brain trying to figure out how to analyze a three body decay (lambda_c ---> kaon, pion proton). What I have done is taken the kaon on an arbitary axis and set the decay in a plane. Now I found out that the angles assumed by the pion and proton can be anything from collinear to wide open on a nearly uniform distribution. My problem is that I have three equations, 2 for p-conservation and one for e-conservation, but the only way I have been able to eliminate my variables has inevitably led to the problem of radicals I cannot simplify because of the energy relationship E = sqrt(m^2 + |p|^2). I don't know if anything I just said makes any sense, but I am lost.

My ultimate goal is to attain the 4-vector for each of the three particles and create a Dalitz plot based on the invariant masses of the pion-kaon and the proton-kaon. Please help if you can!

Colin

 

[CarlB]

Try looking here:
http://www.answers.com/topic/dalitz-plot?cat=technology

 

[mormonator_rm]

Hello all,

I have been racking my brain trying to figure out how to analyze a three body decay (lambda_c ---> kaon, pion proton). What I have done is taken the kaon on an arbitary axis and set the decay in a plane. Now I found out that the angles assumed by the pion and proton can be anything from collinear to wide open on a nearly uniform distribution. My problem is that I have three equations, 2 for p-conservation and one for e-conservation, but the only way I have been able to eliminate my variables has inevitably led to the problem of radicals I cannot simplify because of the energy relationship E = sqrt(m^2 + |p|^2). I don't know if anything I just said makes any sense, but I am lost.

My ultimate goal is to attain the 4-vector for each of the three particles and create a Dalitz plot based on the invariant masses of the pion-kaon and the proton-kaon. Please help if you can!

Colin

Hello,

I did work on a similar problem once upon a time as part of a research project involving montecarlo simulation of proton-antiproton annihilation into the three-pi0 background. This also had to be treated as a three-body decay in the center-of-mass, and if you search for my article "Mass and Width of f2(1270) from E760 Neutral Data" in the NCUR 2003 "Proceedings" you will find my treatment of the problem. Decay isotropy was a critical component of the treatment, as well as conservation of both energy and momentum. I wrote a program in FORTRAN that produced simulated three-body events within this framework in the process. I also found a very good book in doing this work that gives a good treatment of the problem from the ground up, but the title is not on the tip of my tongue; I'll have to look it up. But it is cited in my references. Send me a PM if you need anything. Good luck!