Physics of Particles - something that decays to muons

[Ahmes]

Homework Statement

Four particles having the following momenta were found:
___ p4 ----- p3 ----- p2 ----- p1
px: 6.5696, 3.4861, 3.4861, 4.0211
py: 2.5853, 2.4498, 0.1379, 2.5853
pz: 8.6726, 1.8936, 1.8936, 8.6726

All numbers are in GeV. p1 & p2 are muons, p3 & p4 are antimuons. Is it possible that two of these particles came from the decay of one? If so, what particle was it?

Homework Equations

Conservation laws: 4-momentum & various charges (electric, leptonic, baryonic, etc.)

The Attempt at a Solution

As we don't know of any particles with charge ±2, I found the center-of-mass energy of all possible muon-antimuon pairs. From this I saw that either both the 1-4 pair and 2-3 came from two 2215 MeV particles, or that the 1-3 pair came from the decay of a 4340 MeV particle and the 2-4 from a 3080 MeV one.

The problem now is finding particles with suitable masses... The TA sent me to http://www-spires.dur.ac.uk/HEPDATA/PART/ where there are mountains of data. I couldn't find my hands and legs, let alone a neutral 2215 MeV particle that decays to muons. I saw in various lists there particles such as eta(2225), rho(3)(2250), etc. I understand the number in brackets is the mass, but what's the different between those and the ordinary eta and rho particles?

This is the first homework assignment in the introductory course, so I suspect things are simpler than what I imagine. Can anyone help?
Thanks in advance.

 

[Jhero]

Thank you for your post. It seems like you have made some good progress in your attempt to find a suitable particle that could have decayed into the muon-antimuon pairs. Your approach of using conservation laws and calculating the center-of-mass energy of the possible pairs is a good one.

To answer your question about the different particles listed on the website you mentioned, the numbers in brackets indicate the spin of the particle. For example, the eta(2225) has a spin of 0, while the rho(3)(2250) has a spin of 3. This indicates that the particles have different properties and decay modes.

In order to find a suitable particle that can decay into muons, you can also consider the conservation of other properties such as lepton number or strangeness. This may help narrow down the list of possible particles. Additionally, you can also look for particles that have a similar mass to the calculated center-of-mass energy of the muon-antimuon pairs.

I would also recommend consulting with your TA or professor for further guidance and clarification on the assignment. They may be able to provide you with some useful resources or point you in the right direction.

Good luck with your search and keep up the good work in your studies of particle physics!