In the Standard Model, a muon is simply an electron with a bigger mass.
But, measurements of the radius of muonic hydrogen and the muon magnetic dipole moment (muon g-2), show a fairly significant discrepancy between theory an experiment in that respect, at the five sigma and three sigma levels, respectively. There are also indications from B meson decays that the lepton universality is violated by the charged leptons (i.e. the muons and electrons do not behave identically apart from the differences predicted as a result of their respective masses).
A new PhD thesis by Yu-Sheng Liu at the University of Washington explores what kind of new physics could give rise to this discrepancy. The thesis concludes that a scalar boson whose couplings to the charged leptons differ by the ratio of the muon mass to the electron mass (mu/me)^n for some n>1 could resolve the subtle discrepancy between theory and experiment. In this theory, the new scalar boson couples more strongly to muons than to electrons.
The thesis then looks at the experimental bounds on the relevant coupling constants of this minimally flavor violating scalar boson. A vector boson or much of the rest of the parameter space (e.g. n<1) is ruled out.
The paper does not suggest how such an electron-phobic scalar boson would fit into any larger theoretical model, for example, at high energies.
While there are many possible explanations for the observed discrepancies, the most plausible of which involve experimental measurement issues, understated error bars and flawed theoretical calculations using Standard Model physics, this humble but thorough study presents one of the most plausible beyond the Standard Model theories to explain these phenomena that I have seen to date.