We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the potential necessarily contains a flat direction in the classical limit. This flat direction is lifted by small quantum corrections and inflation is realised without need for an unnatural fine-tuning. In the conformal limit, the effective potential becomes linear in the inflaton field, yielding to specific predictions for the spectral index and the tensor-to-scalar ratio, being respectively: n s −1 ≈ −0.025 N⋆ 60 −1 and r ≈ 0.0667 N⋆ 60 −1 , where N ⋆ ≈ 30−65 is a number of efolds during observable inflation. This predictions are in reasonable agreement with cosmological measurements. Further improvement of the accuracy of these measurements may turn out to be critical in falsifying our scenario.

A model of monopolium is constructed based on an electromagnetic dual formulation of Zwanziger and lattice gauge theory.To cope with the strong coupling nature of the magnetic charge, for which the monopole is confined, U (1) lattice gauge theory is applied. The monopole is assumed to have a finite-sized inner structure based on a 't Hooft-Polyakov like solution in which the magnetic charge is uniformly distributed on the surface of a sphere. The monopole and antimonopole potential becomes linear plus Coulomb outside the sphere and is constant inside.Numerical estimation gives two kinds of solutions: One which has a small binding energy, and hence the para-(J = 0) and ortho-(J = 1) monopoliums have degenerate masses. For the parameter choices considered, they both have O(1 − 10) TeV masses and are very shortlived. The other solution has a small monopole mass and large binding energy, with an illustrative example of parameter choices giving a 750 GeV para-monopolium and 1.4 TeV ortho-monopolium. The production rate of the former is one order of magnitude smaller than the announced enhancement, but they may be the target of future LHC searches and the 100 TeV colliders.

Heavy long-lived multi-charged leptons (MCLs) are predicted by various new physics models. These hypothetical MCLs can form bound states, due to their high electric charges and long life times. In this work, we propose a novel strategy of searching for MCLs through their bound state productions and decays. By utilizing LHC-8 TeV data in searching for resonances in the diphoton channel, we exclude the masses of isospin singlet heavy leptons with electric charge |q| ≥ 6 (in units of electron charge) lower than ∼1.2 TeV, which are much stronger than the corresponding 8 TeV LHC bounds from analysing the high ionisation and the long time-of-flight of MCLs. By utilising the current 13 TeV LHC diphoton channel measurements the bound can further exclude MCL masses up to ∼1.6 TeV for |q| ≥ 6. Also, we demonstrate that the conventional LHC limits from searching for MCLs produced via Drell-Yan processes can be enhanced by including the contribution of photon fusion processes.