Abstract:The clockwork mechanism is a novel method for generating a large separation between the dynamical scale and interaction scale of a theory. We demonstrate how the mechanism can arise from a sequence of strongly-coupled sectors. This framework avoids elementary scalar fields as well as ad hoc continuous global symmetries, both of which are subject to serious stability issues. The clockwork factor, q, is determined by the consistency of the strong dynamics. The preserved global U(1) of the clockwork appears as an accidental symmetry, resulting from discrete or U(1) gauge symmetries, and it is spontaneously broken by the chiral condensates. We apply such a dynamical clockwork to construct models with an effectively invisible QCD axion from TeV-scale strong dynamics. The axion couplings are determined by the localisation of the Standard Model interactions along the clockwork sequence. The TeV spectrum includes either coloured hadrons or vector-like quarks. Dark matter can be accounted for by the axion or the lightest neutral baryons, which are accidentally stable.

In the absence of direct evidence of new physics, any ultraviolet theory can be reduced to its specific set of low-energy effective operators. As a case study, we derive the effective field theory for the seesaw extension of the Standard Model, with sterile neutrinos of mass M > m W . We systematically compute all Wilson coefficients generated at one loop. Hence, it becomes straightforward to (i) identify the seesaw parameters compatible with the smallness of neutrino masses; (ii) compute precision lepton observables, which may be sensitive to scales as large as M ∼ 10 3 TeV; and (iii) establish sharp correlations among those observables. We find that the flavour-conserving Wilson coefficients set an upper bound on the flavour-violating ones. The low-energy limits on µ → e and τ → e, µ transitions suppress flavour violation in Z and Higgs decays, as well as electric dipole moments, far beyond the experimental reach. The precision measurements of G F , m W , and Z partial decay widths set more stringent bounds than present and future limits on τ → e, µ transitions. We also present a general spurion analysis, to compare the seesaw with different models, thus assessing the discriminating potential of the effective approach.