We believe we should have new physics at higher energies because treating the SM as an effective field theory introduces additional terms in the Lagrangian whic

We believe we should have new physics at higher energies because treating the SM as an effective field theory introduces additional terms in the Lagrangian which are suppressed (~ divided) by some energy scale. These additional terms are the ones allowing lepton flavor violation (so a muon decaying to an electron and a photon, for example) but we know from experiments that these events are incredibly rare. This tells us that the energy scale of new physics is very high. However, we could also have new physics at lower energy scales, as is the case with axions.