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 $elltoell^prime u u$ 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 $tautomu u u/tau(mu)to e u u$ and of the Cabibbo Angle Anomaly. Such an explanation predicts ${rm Br }[tauto egamma]$ to be of the order of a few times $10^{-11}$ while ${ rm Br}[tauto emumu]$ 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.