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.