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Attempts to incorporate in a coherent picture the B-decay anomalies presumably observed in b→c and b→s semi-leptonic decays have to face the absence of signals in other related experiments, both at low and at high energies. By extending and making more precise the content of Barbieri et al. (Eur Phys J C 77(1):8, 2017), we describe one such attempt based on the Pati–Salam SU(4) group, that unifies colour and the B-L charge, in the context of a new strongly interacting sector, equally responsible for producing a pseudo-Goldstone Higgs boson.

A bstract We study the scenario of dark photon Dark Matter where the mass is generated through the Higgs mechanism rather than the constant Stueckelberg mass. In this construction the dark sector contains necessarily extra degrees of freedom and interactions that lead to non-trivial dynamics including thermalization, phase transitions, cosmic string production. As a consequence the predictions of Stueckelberg theories are vastly modified, strongly depending on the couplings to curvature and on the scale of inflation H I compared to the scale f of spontaneous symmetry breaking. We find in particular that only in extreme regions of parameter space the phenomenology of Stueckelberg dark photon is reproduced. These scenarios are strongly constrained by isocurvature perturbations unless the dark sector is approximately Weyl invariant.

A bstract We study vector boson fusion production of new scalar singlets at high energy lepton colliders. We find that CLIC has the potential to test single production cross-sections of a few tens of attobarns in di-Higgs and di-boson final states. In models with a sizeable singlet-Higgs mixing, these values correspond to a precision in Higgs couplings of order 0.1% or better. We compare our sensitivities with those of the LHC and interpret our results in well-motivated models like the Twin Higgs, the NMSSM and axion-like particles. Looking forward to even higher energy machines, we show that the reach of muon colliders like LEMMA or MAP overcomes the one of future hadron machines like FCC-hh. We finally study the pair production of the new scalar singlets via an off-shell Higgs. This process does not vanish for small mixings and will constitute a crucial probe of models generating a first order electro-weak phase transition.

A bstract Dark sectors with purely gravitational couplings to the Standard Model are unavoidably populated from the SM plasma by graviton exchange, and naturally provide dark matter candidates. We examine the production in the relativistic regime where the dark sector is approximately scale invariant, providing general analytical formulas that depend solely on the central charge of the dark sector. We then assess the relevance of interactions that can lead to a variety of phenomena including thermalisation, non-perturbative mass gaps, out-of-equilibrium phase transitions and cannibalism in the dark sector. As an illustrative example we consider the dark glueball scenario in this light and show it to be a viable dark matter candidate due to the suppression of gravitational production. We go on to extend these results to strongly coupled CFTs and their holographic duals at large- N with the dark dilaton as the dark matter candidate.

A bstract We use the framework of relativistic and non-relativistic conformal field theories (CFT) to derive general results relevant for the production of weakly coupled and strongly coupled dark sectors through thermal interactions. Our result reproduce trivially known formulas for 2 → n processes and extend to general m → n processes as well as interacting dark sectors. As concrete examples we consider freeze-in of a relativistic CFT coupled to the SM with contact interactions and derive Sommerfeld enhancement of non-relativistic cross-sections from the theory of fermions at unitarity.

A bstract We study the dynamics of the Peccei-Quinn (PQ) phase transition for the QCD axion. In weakly coupled models the transition is typically second order except in the region of parameters where the PQ symmetry is broken through the Coleman-Weinberg mechanism. In strongly coupled realizations the transition is often first order. We show examples where the phase transition leads to strong supercooling lowering the nucleation temperature and enhancing the stochastic gravitational wave signals. The models predict a frequency peak in the range 100–1000 Hz with an amplitude that is already within the sensitivity of LIGO and can be thoroughly tested with future gravitational wave interferometers.

A bstract We investigate the nightmare scenario of dark sectors that are made of non-abelian gauge theories with fermions, gravitationally coupled to the Standard Model (SM). While testing these scenarios is experimentally challenging, they are strongly motivated by the accidental stability of dark baryons and pions, that explain the cosmological stability of dark matter (DM). We study the production of these sectors which are minimally populated through gravitational freeze-in, leading to a dark sector temperature much lower than the SM, or through inflaton decay, or renormalizable interactions producing warmer DM. Despite having only gravitational couplings with the SM these scenarios turn out to be rather predictive depending roughly on three parameters: the dark sector temperature, the confinement scale and the dark pion mass. In particular, when the initial temperature is comparable to the SM one these scenarios are very constrained by structure formation, ∆ N eff and limits on DM self-interactions. Dark sectors with same temperature or warmer than SM are typically excluded.

A bstract We analyze quantitatively the tuning of composite Higgs models with partial compositeness and its interplay with the predicted Higgs mass. In this respect we identify three classes of models, characterized by different quantum numbers of the fermionic colored resonances associated with the top quark, the so-called top partners. The main result of this classification is that in all models with moderate tuning a light Higgs, of 125 GeV mass, requires the presence of light top partners, around 1 TeV. The minimal tuning is comparable to the one of the most attractive supersymmetric models in particular the ones realizing Natural SUSY. This gives further support to an extensive program of top partners searches at the LHC that can already probe the natural region of composite Higgs models.

A bstract The strong CP problem can be solved if the laws of nature are invariant under a space-time parity exchanging the Standard Model with its mirror copy. We review and extend different realizations of this idea with the aim of discussing Dark Matter, neutrino physics, leptogenesis and collider physics within the same context. In the minimal realization of ref. [ 1 ] the mirror world contains a massless dark photon, which leads to a rather interesting cosmology. Mirror electrons reproduce the dark matter abundance for masses between 500–1000 GeV with traces of strongly interacting dark matter. This scenario also predicts deviations from cold dark matter, sizable ∆ N eff and colored states in the TeV range that will be tested in a variety of upcoming experiments. We also explore scenarios where the mirror photon is massive and the mirror particles are charged under ordinary electromagnetism with very different phenomenology. We also show that, for the measured values of the SM parameters, the Higgs effective potential can give rise to a second minimum at large field value as required to break spontaneously the parity symmetry.

A bstract We study the Higgs mass in composite Higgs models with partial compositeness, extending the results of ref. [ 1 ] to different representations of the composite sector for SO(5)/SO(4) and to the coset SO(6)/SO(5). For a given tuning we find in general a strong correlation between the mass of the top partners and the Higgs mass, akin to the one in supersymmetry. If the theory is natural a Higgs mass of 125 GeV typically requires fermionic partners below TeV which might be within the reach of the present run of LHC. A discussion of CP properties of both cosets is also presented.