“Part I : Lepton flavor violating processes are highly suppressed in the Standard Model. Therefore, if observed, lepton flavor violation would be a clear indication of new physics beyond the Standard Model. We study the process $e^+e^-\to\tau\mu$ at tree-level in the Standard Model Effective Field Theory allowing for arbitrary $e^+e^-$ beam polarizations. The estimated sensitivities derived from the future circular $e^+e^-$ colliders FCC-ee and CEPC, are complementary to those obtained from low-energy tau decays at BaBar and Belle, as well as projections from Belle-II. For the linear collider CLIC, our projected sensitivities not only complement but in certain scenarios surpass those achievable with low-energy tau decay measurements at Belle-II.

Part II : If time permits, I will discuss recent work on spin dependent dark matter electron scattering. The number of material response functions that need to be computed simplify greatly in the presence of symmetries. Further simplifications can be achieved when the electron’s initial and final states are eigenstates of the same Hamiltonian. I will additionally discuss the response coefficients generated by some generic models, and how they provide insight into the dark sector.”