Abstract: The linear seesaw mechanism provides a simple way to generate neutrino masses. In addition to Standard Model particles, it includes quasi-Dirac leptons as neutrino mass mediators, and a leptophilic scalar doublet seeding small neutrino masses. Here we review its associated physics, including restrictions from theory and phenomenology. The model yields potentially detectable μ-> e gamma rates as well as distinctive signatures in the production and decay of heavy neutrinos ( N-i) and the charged Higgs boson (H-+/-) arising from the second scalar doublet. We have found that production processes such as e(+) e(-) -> NN, e- gamma -> NH- and e(+) e(-) -> H (+) H- followed by the decay chain H-+/--> l(+/-) (i) N, N -> l`(+/-) (j) W (-/+) leads to striking lepton number violation signatures at high energies which may probe the Majorana nature of neutrinos.

Abstract: We consider the phenomenological signatures of Simplified Models of Flavourful Leptoquarks, whose Beyond-the-Standard Model (SM) couplings to fermion generations occur via textures that are well motivated from a broad class of ultraviolet flavour models (which we briefly review). We place particular emphasis on the study of the vector leptoquark Delta(mu) with assignments (3, 1, 2/3) under the SM's gauge symmetry, SU(3)(C) x SU(2)(L) x U(1)(Y), which has the tantalising possibility of explaining both R-K(*) and R-D(*) anomalies. Upon performing global likelihood scans of the leptoquark's coupling parameter space, focusing in particular on models with tree-level couplings to a single charged lepton species, we then provide confidence intervals and benchmark points preferred by low(er)-energy flavour data. Finally, we use these constraints to further evaluate the (promising) Large Hadron Collider (LHC) detection prospects of pairs of tau-flavoured Delta(mu), through their distinct (a)symmetric decay channels. Namely, we consider direct third-generation leptoquark and jets plus missing-energy searches at the LHC, which we find to be complementary. Depending on the simplified model under consideration, the direct searches constrain the Delta(mu), mass up to 1500-1770 GeV when the branching fraction of Delta(mu), is entirely to third-generation quarks (but are significantly reduced with decreased branching ratios to the third generation), whereas the missing-energy searches constrain the mass up to 1150-1700 GeV while being largely insensitive to the third-generation branching fraction.

Abstract: We develop the Tree-Loop Duality Relation for two- and three-loop integrals with multiple identical propagators (multiple poles). This is the extension of the Duality Relation for single poles and multi-loop integrals derived in previous publications. We prove a generalization of the formula for single poles to multiple poles and we develop a strategy for dealing with higher-order pole integrals by reducing them to single pole integrals using Integration By Parts.