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We perform a systematic study of models involving leptoquarks and diquarkswith masses well below the grand unification scale and demonstrate that a largeclass of them is excluded due to rapid proton decay. After singling out the fewphenomenologically viable color triplet and sextet scenarios, we show thatthere exist only two leptoquark models which do not suffer from tree-levelproton decay and which have the potential for explaining the recentlydiscovered anomalies in B meson decays. Both of those models, however, containdimension five operators contributing to proton decay and require a newsymmetry forbidding them to emerge at a higher scale. This has a particularlynice realization for the model with the vector leptoquark $(3,1)_{2/3}$, whichpoints to a specific extension of the Standard Model, namely the Pati-Salamunification model, where this leptoquark naturally arises as the new gaugeboson. We explore this possibility in light of recent B physics measurements.Finally, we analyze also a vector diquark model, discussing its LHCphenomenology and showing that it has nontrivial predictions forneutron-antineutron oscillation experiments.

Baryon Number and Lepton Universality Violation in Leptoquark and Diquark Models