# How do we know the group property of a new particle?

Suppose I have a particle $$W'$$ which can decay into $$\mu$$ and $$\nu_{\mu}$$ and $$e$$ and $$\nu_{e}$$.

Suppose we know such new gauge bosons come from some additional gauge group added to the Standard Model. If such particle is discovered, and these two decays had been confirmed, what could be the first conclusion about their gauge group one can draw from this? I am wondering what one could infer about the new symmetry group from these two facts and why?

I have no clue how this is related to symmetry.

PS: My question comes from this:

The above figures from the ATLAS experiment (ATLAS-CONF-2017-016) show results from a search for new heavy gauge bosons decaying to eν (left) and µν (right).

My professor asked me the following question:

Such new gauge bosons come from some additional gauge group added to the Standard Model. If the analysis considered here would have discovered the $$W'$$bosons that were searched for, what would be the first thing you would conclude about the new gauge group?

But I have no idea how this question should be answered.

• This seems a bit confused. A gauge group is a property of a theory. You mean what representation of the gauge group $W'$ transforms in? – knzhou May 24 at 18:00
• Yes, I re-edited the problem. Hope that make my question clearer. – Universe Maintainer May 24 at 18:04
• You mean μ and $\bar{\nu}_\mu$ etc like the decay of the W, or are you going for lepton number violation? Are you stuck on gauge groups, or are simple old fashioned (50s, 60s) global conservation laws that are troubling you? Have you mastered the history of particle physics and the emergence of quantum numbers such as strangeness, and the violations of such by some interactions but not others? – Cosmas Zachos May 24 at 20:54
• @CosmasZachos Thank you for your reply! please see the PS part. – Universe Maintainer May 24 at 21:08
• Homework and "no idea"? oh... – Cosmas Zachos May 24 at 21:19

I do not think this is a good question, except for the trivial answer: it fits the model with which we calculated the curves that fitted the $$W'$$ seen, and thus the assumed group properties.