The Deep Underground Neutrino Experiment (DUNE) will be a world-class neutrino observatory and nucleon decay detector designed to answer fundamental questions about the nature of elementary particles and their role in the universe.

Lepton flavor violating Higgs decays can arise in flavor symmetry models where the Higgs sector is responsible for both the electroweak and the flavor symmetry breaking. Here we advocate an S4 three-Higgs-doublet model where tightly constrained flavor changing neutral currents are suppressed by a remnant Z3 symmetry. A small breaking of this Z3 symmetry can explain the 2.4 σ excess of Higgs decay final states with a µτ topology reported recently by CMS if the new neutral scalars are light. The model also predicts sizable rates for lepton flavor violating Higgs decays in the eτ and eµ channels because of the unifying S4 flavor symmetry.

An unspecified strong dynamics may give rise to composite vectors sufficiently light that their interactions, among themselves or with the electroweak gauge bosons, be approximately described by an effective Lagrangian invariant under SU (2) L ×SU (2) R /SU (2) L+R . We study the production at the LHC of two such states by vector boson fusion or by the Drell-Yan process in this general framework and we compare it with the case of gauge vectors from a SU (2) L × SU (2) R × SU (2) N gauge model spontaneously broken to the diagonal SU (2) subgroup by a generic σ-model. Special attention is payed to the asymptotic behaviour of the different amplitudes in both cases. The expected rates of multi-lepton events from the decay of the composite vectors are also given. A thorough phenomenological analysis and the evaluation of the backgrounds to such signals, aiming at assessing the visibility of composite-vector pairs at the LHC, is instead deferred to future work.