Leptoquarks with Exactly Stable Protons

We explore a novel mechanism to restrict TeV-scale leptoquark interactions and render the proton exactly stable to all orders in the effective field theory expansion. A scalar condensate breaks a lepton-flavoured $\mathrm{U}(1)_X$ gauge symmetry in the ultraviolet and generates neutrino masses, leaving a discrete $\mathbb{Z}_9$ or $\mathbb{Z}_{18}$ gauge symmetry in the infrared, forbidding $\Delta B = 1$ processes. This provides an elegant framework to address the flavour anomalies and can be adapted to many other new-physics models. The $\mathrm{U}(1)_X$ can emerge from a gauge-flavour unified $\mathrm{SU}(12) \times \mathrm{SU}(2) \times \mathrm{SU}(2)$ theory at even higher energies.