Tri-bimaximal-Cabibbo Mixing: Flavour violations in the charged lepton sector

Mathew Thomas Arun, Anirudhan A. Madathil

Published 2023-01-17Version 1

The well understood structure of $U_{pmns}$ matrix mandates a Cabibbo mixing matrix in the first two generations of the charged lepton sector if we assume Tri-bimaximal mixing in the neutrino sector. This ansatz, called Tri-bimaximal-Cabibbo mixing, on the other hand, is ruled out immediately by charged lepton flavour violating decays of mesons. In this article, we aim to show that the resurrection of the theoretically well motivated tri-bimaximal mixing scenario comes naturally within Minimal Flavour Violation hypothesis in the lepton sector. We analyse the flavour violating currents $\mu\rightarrow e e e$, $\mu Ti \to e Ti$, $\pi^0\rightarrow e^+ \mu^{-}$ and $K_L \rightarrow \mu^+ e^-$ in this scenario and show that the New Physics that generates mixing among the charged lepton could lie within the reach of hadron colliders. Though the most stringent constrain on New Physics is $\gtrsim \mathcal{O}(26$ TeV) for maximal coupling, more natural coupling relaxes it to $\gtrsim \mathcal{O}(4$ TeV).