# A Strategies for kinematics of a four-body decay?

1. May 9, 2016

### Hepth

Does anyone have suggestions on the strategies for a four-body decay's kinematics? I'm just wondering what is out there. Last time I had to calculate something I just did it straightforward, but I know there must be other methods. (Like preferring to work in energies over invariants). I usually base it off of

preprint : http://ccdb5fs.kek.jp/cgi-bin/img/allpdf?198311072 [Broken]

But are there new strategies? Say for a four-lepton final state.

Thanks

edit: I should also add, that if you prefer analytic solutions there must be preferred methods. Numerically it probably doesn't matter due to the cuts being easy to implement.

Last edited by a moderator: May 7, 2017
2. May 9, 2016

### Staff: Mentor

Strategies for what?

Experimentally, I think most analyses look at the invariant masses of 2 or sometimes 3 particles, especially if you expect resonances. There are 5 degrees of freedom in the decay, at least if we can ignore or do not know the initial spin of the decaying particle.

3. May 9, 2016

### Hepth

So assume a decaying pseudoscalar to 4 leptons (or neutrinos), and you want to calculate the partial width. I have calculated this before, and basically you get integrable divergences when you try to integrate (due to the denominator's energies) that can be removed by changes of coordinates of the invariants. This is seen in the preprint I posted, but the same paper is here if you have access http://journals.aps.org/prd/abstract/10.1103/PhysRevD.29.2027

On page 29, the replacements (3.6) are needed to be able to easily do the integral, this is because the denominator is divergent at the integration boundaries.

I guess I'm asking if there are any guides like the PDG's Kinematics, on different situations (2 massive, 2 massless; 4 massive; 4 massless; 2 resonances decaying; 0 resonances) etc. Each case has a scheme of invariants that are beneficial for the analytic integration, and problems that occur, mainly due to the boundaries.

When doing loop integrals there are a lot of guides for controlling your infrared and collinear divergences by looking at the matrices of coefficients of the feynman parameters, and doing certain situations differently. I was looking for something similar for kinematics.

Thank you.

4. May 9, 2016

### Staff: Mentor

No idea about the theoretical side, sorry.