Fractionary Charged Particles Confronting Lepton Flavor Violation and the Muon's Anomalous Magnetic Moment

In light of the result published by the Fermilab Muon $(g-2)$ experiment, we investigate a simple model that includes particles of fractional electric charges: a colour-singlet fermion and a scalar with charges $2/3e$ and $1/3e$, respectively. The impact of these particles on the muon anomalous magnetic moment are examined, particularly the restrictions on their Yukawa couplings with the light leptons. Given that lepton flavor violation processes impose stringent constraints on certain scenarios beyond the Standard Model, we asses the one-loop contribution of the new particles to $(g-2)$ in order to identify regions in the parameter space consistent with the Fermilab results and compatible with the current and projected limits on the branching ratio $Br(\mu \rightarrow e \gamma)$. Taking into account the current lower bound for the masses of fractionary charged particles, which is around 634 GeV, we show that the mass of the scalar particle with fractional charge must exceed 1 TeV and may be discovered in future collider experiments. Finally, we also study the validity of our model in light of the QCD lattice results on the muon $(g-2)$.Comment: 14 pages, 5 figure