Phenomenology of Scalar Leptoquarks at the LHC in Explaining the Radiative Neutrino Mass, Muon $g-2$ and Lepton Flavour Violating Observables

We study the phenomenology of a particular leptoquark extension of the Standard Model (SM), namely the doublet-singlet scalar leptoquark extension of the SM (DSL-SM). Besides generating Majorana mass for neutrinos, these leptoquarks contribute to muon and electron $(g-2)$ and various lepton flavour violating processes. Collider signatures of the benchmark points (BPs), consistent with the neutrino oscillation data, anomalous muon/electron magnetic moments, experimental bounds on the charged lepton flavour violation observables, etc., are studied at the LHC/FCC with centre-of-mass energies of 14, 27 and 100 TeV. While the two $-1/3$ charged colored scalars from singlet and doublet leptoquark mix with each other, the charge $2/3$ colored scalar from the doublet leptoquark remains pure. With a near-degenerate mass spectrum, the pure and mixed leptoquark states are shown to be distinguishable from multiple finalstates, while discerning between the two mixed states remain very challenging.