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

Figures (14)

• Figure 1: Leading branching ratios of the heaviest state, $E_2$, as a function of the mixing squared $\sin^2{\theta_e}$, at $M=1350$ GeV. The decay channels into a heavy state $F=E_1, N, Y$ and a gauge boson $V=Z, W^-,W^+$, all with the same branching fraction, are merged into the channel $E_2\to FV$.
• Figure 2: Ratio of the cross section in our model over the one in the $\mathrm{VLL^D}$ model, for the different decay channels, as a function of the coupling $\lambda^\prime_e$. We are considering the contribution of the heavy lepton pair production with decays in the relevant channels, for $M=1.35$ TeV.
• Figure 3: $eee$ and $ee\mu$ channels via singly produced VLL. Diagram \ref{['fig:zchannel']} is only present in the HNL model, diagram \ref{['fig:wchannel']} is present (with different branching ratios) in both models and diagram \ref{['fig:ychannel']} is only present in our model.
• Figure 4: Ratio of the $3e$+missing energy production via heavy leptons in our model over the one in the HNL case, as a function of the corresponding coupling (recall the identification $V_{eN} \to m^\prime/M$) for different values of $M$.
• Figure 5: 95% C.L. exclusion limits on $\sin^2{\theta}$ as a function of $M$ from direct searches in our model for the case of mixing with $e$ (left), $\mu$ (center) and $\tau$ (right). The excluded region from single production is shown as a colored shaded area, while the one from pair production is shown in grey. Only the white area is allowed by direct searches.