Phenomenology of SU(5) low-energy realizations: the diphoton excess and Higgs flavor violation

We discuss different $\rm SU(5)$ low-energy realizations and illustrate their use with the diphoton excess and Higgs flavor violation, which require new physics at the TeV scale. In particular, we study two scenarios for a $750$ GeV resonance: in the first one the resonance belongs to the adjoint of $\rm SU(5)$, being either an $\rm SU(2)_L$ singlet or a triplet, while in the second case the signal is due to the CP-even and CP-odd states of a new $\rm SU(2)_L$ Higgs doublet belonging to a ${\bf 45}_H$ or a ${\bf 70}_H$ representations, giving rise to a two-Higgs doublet model at low energies. We study the fine-tuning needed for the desired members of the multiplets to be light enough, while having the rest at the GUT scale. In these scenarios, the production and decay into photons of the new resonance are mediated by the leptoquarks (LQ) present in these large $\rm SU(5)$ representations. We analyse the phenomenology of such scenarios, focusing on the most relevant predictions that can help to disentangle the different models, like decays into gauge bosons, Standard Model (SM) fermions and LQs pair production. In the case of the ${\bf 45}_H$ (the Georgi-Jarlskog model), we also study the possibility to have Higgs flavor violation. We find that $B_s$ mixing limits (in addition to $\tau\rightarrow \mu \gamma$) always imply that $\rm{BR}(h\rightarrow \tau\mu,\,bs)\lesssim 10^{-5}$.