Searching for Lepton Flavour (Universality) Violation and Collider Signals from a Singly-Charged Scalar Singlet

In recent years, evidence for lepton flavour universality violation beyond the Standard Model has been accumulated. In this context, a singly charged $SU(2)_L$ singlet scalar ($\phi^\pm$) is very interesting, as it can only have flavour off-diagonal couplings to neutrinos and charged leptons, therefore necessarily violating lepton flavour (universality). In fact, it gives a (necessarily constructive) tree-level effect in $\ell\to\ell^\prime\nu\nu$ processes, while contributing to charged lepton flavour violating only at the loop-level. Therefore, it can provide a common explanation of the hints for new physics in $\tau\to\mu\nu\nu/\tau(\mu)\to e\nu\nu$ and of the Cabibbo Angle Anomaly. Such an explanation predicts ${\rm Br }[\tau\to e\gamma]$ to be of the order of a few times $10^{-11}$ while ${ \rm Br}[\tau\to e\mu\mu]$ can be of the order of $10^{-9}$ for order one couplings and therefore in the reach of forthcoming experiments. Furthermore, we derive a {novel} coupling-independent lower limit on the scalar mass of $\approx 200\,$GeV by recasting LHC slepton searches. In the scenario preferred by low energy precision data, the lower limit is even strengthened to $\approx300\,$GeV, showing the complementary between LHC searches and flavour observables. Furthermore, we point out that this model can be tested by reinterpreting DM mono-photon searches at future $e^+e^-$ colliders.