We construct a four-dimensional SU(5) grand unified theory in which the proton is stable. The standard model leptons reside in the 5 and 10 irreps of SU(5), whereas the quarks live in the 40 and 50 irreps. The SU(5) gauge symmetry is broken by the vacuum expectation values of the scalar 24 and 75 irreps. All fields that are not part of the standard model are heavy. Stability of the proton requires three relations between the parameters of the model to hold. However, abandoning the requirement of absolute proton stability, the model fulfills current experimental constraints without fine-tuning.

There is a long-standing discrepancy between the neutron lifetime measured in beam and bottle experiments. We propose to explain this anomaly by a dark decay channel for the neutron, involving one or more dark sector particles in the final state. If any of these particles are stable, they can be the dark matter. We construct representative particle physics models consistent with all experimental constraints.

We demonstrate that a phenomenologically viable four-dimensional grand unified theory with no proton decay can be constructed. This is done in the framework of the minimal nonsupersymmetric SU(5) GUT by introducing new representations and separating the physical quark and lepton fields into different multiplets. In such a theory all beyond Standard Model particles are naturally heavy, but one can tune the parameters of the model such that gauge coupling unification is achieved and some of the new particles are at the TeV scale and accessible at the LHC.

The manuscript by Berezhiani (arXiv:1812.11089) proposes a model that has the neutron decaying into a mirror neutron with a branching fraction of 1%, alleviating the tension between neutron lifetime measurements in beam vs bottle experiments. We show that the model as proposed is inconsistent with experiment. Variations of the model may work at the expense of extreme breaking of the $Z_2$ symmetry between the Standard Model and its mirror copy.

We discuss our recently proposed interpretation of the discrepancy between the bottle and beam neutron lifetime experiments as a sign of a dark sector. The difference between the outcomes of the two types of measurements is explained by the existence of a neutron dark decay channel with a branching fraction 1%. Phenomenologically consistent particle physics models for the neutron dark decay can be constructed and they involve a strongly self-interacting dark sector. We elaborate on the theoretical developments around this idea and describe the efforts undertaken to verify it experimentally.

We summarize our recent proposal of explaining the discrepancy between the bottle and beam measurements of the neutron lifetime through the existence of a dark sector, which the neutron can decay to with a branching fraction 1%. We show that viable particle physics models for such neutron dark decays can be constructed and we briefly comment on recent developments in this area.

We analyze a recently proposed extension of the Standard Model based on the SU(4)×SU(2)L×U(1)X gauge group, in which baryon number is interpreted as the fourth color and dark matter emerges as a neutral partner of the ordinary quarks under SU(4). We show that under well-motivated minimal flavor-violating assumptions the particle spectrum contains a heavy dark matter candidate which is dominantly the partner of the right-handed top quark. Assuming a standard cosmology, the correct thermal relic density through freeze-out is obtained for dark matter masses around 2-3 TeV. We examine the constraints and future prospects for direct and indirect searches for dark matter. We also briefly discuss the LHC phenomenology, which is rich in top quark signatures, and investigate the prospects for discovery at a 100 TeV hadron collider.

We propose an extension of the Standard Model in which baryon number is promoted to be part of a non-Abelian gauge symmetry at high energies. Specifically, we consider the gauge group SU(4)×SU(2)L×U(1)X, where the SU(4) unifies baryon number and color. This symmetry is spontaneously broken down to the Standard Model gauge group at a scale which can be as low as a few TeV. The SU(4) structure implies that each SM quark comes along with an uncolored quark partner, the lightest of which is stabilized by the generalized baryon number symmetry and can play the role of dark matter. We explore circumstances under which one can realize a model of asymmetric dark matter whose relic abundance is connected to the observed baryon asymmetry, and discuss unique signatures that can be searched for at the LHC.

We perform a systematic study of models involving leptoquarks and diquarks with masses well below the grand unification scale and demonstrate that a large class of them is excluded due to rapid proton decay. After singling out the few phenomenologically viable color triplet and sextet scenarios, we show that there exist only two leptoquark models which do not suffer from tree-level proton decay and which have the potential for explaining the recently discovered anomalies in B meson decays. Both of those models, however, contain dimension five operators contributing to proton decay and require a new symmetry forbidding them to emerge at a higher scale. This has a particularly nice realization for the model with the vector leptoquark $(3,1)_{2/3}$, which points to a specific extension of the Standard Model, namely the Pati-Salam unification model, where this leptoquark naturally arises as the new gauge boson. We explore this possibility in light of recent B physics measurements. Finally, we analyze also a vector diquark model, discussing its LHC phenomenology and showing that it has nontrivial predictions for neutron-antineutron oscillation experiments.

Building on our recent proposal to explain the experimental hints of new physics in $B$ meson decays within the framework of Pati-Salam quark-lepton unification, through the interactions of the $(3,1)_{2/3}$ vector leptoquark, we construct a realistic model of this type based on the gauge group ${\rm SU}(4)_L \times {\rm SU}(4)_R \times {\rm SU}(2)_L \times {\rm U}(1)'$ and consistent with all experimental constraints. The key feature of the model is that ${\rm SU}(4)_R$ is broken at a high scale, which suppresses right-handed lepton flavor changing currents at the low scale and evades the stringent bounds from searches for lepton flavor violation. The mass of the leptoquark can be as low as $10 \ {\rm TeV}$ without the need to introduce mixing of quarks or leptons with new vector-like fermions. We provide a comprehensive list of model-independent bounds from low energy processes on the couplings in the effective Hamiltonian that arises from generic leptoquark interactions, and then apply these to the model presented here. We discuss various meson decay channels that can be used to probe the model and we investigate the prospects for discovering the new gauge boson at future colliders.