How large can lepton mixing be?

Abstract

We show that, contrary to common expectations, the observed charged leptons can have a substantial mixing with new heavier fermions, at the level of 20$\%$. This can happen, in the language of effective theories, when the effect of mixing with heavier fermions vanishes at tree level in operators of mass-dimension 6 (or it is suppressed by the small charged lepton masses), a cancellation that can be naturally ensured by symmetries. Using a model that realizes this scenario we consider all current direct and indirect constraints and show that experimental constraints on the mixing are so mild that, given the current direct limit on the mass of the heavy fermions, theoretical considerations become the leading current constraints on the mixing. We also estimate the sensitivity to the mixing at future experiments, including the high-luminosity phase of the LHC and, most notably, the FCC-ee, and FCC-hh. We find a pattern in which the reach of direct searches in hadron machines makes theoretical considerations lead the limits while the precision of lepton machines can beat these theoretical considerations. We find that the FCC can finally reach per mille precision in the mixing squared of the charged leptons