Dark pions through the Z portal: dark Z' mediation

The naturalness problem of the Higgs mass has been a major driver of particle physics for the past decades. However, the absence of signals from the TeV scale at the LHC Runs 1 and 2 has prompted the field to reconsider its viewpoint. This thesis is inspired by the framework of Neutral Naturalness (NN), where the hierarchy problem is still solved by symmetry – as in “traditional” approaches – but the new particles appearing at the TeV scale are rendered neutral under SM QCD, through clever implementation of discrete symmetries. A phenomenologically important and generic prediction of NN scenarios is the existence of a QCD-like dark sector that confines around the GeV scale. In this thesis, we study a dark sector model that features dark pions at the bottom of the hadron spectrum, coupled to the SM via the Z and Higgs portals. A ultraviolet (UV) completion of this model containing heavy vector-like fermions has been studied in previous literature. Here we construct and analyze for the first time a different UV completion of the model, which includes a dark Z' vector mixed with the Standard Model (SM) gauge bosons. In chapter 1 we review the hierarchy problem, its symmetry-based solutions, and the essential features of NN models. In chapter 2 we introduce two theoretical tools, chiral perturbation theory (ChPT) and the electroweak precision tests (EWPT) of the SM, which prove indispensable in the later discussion. In chapter 3 we outline the properties of confining dark sectors inspired by NN, first starting with the well-known Fraternal Twin Higgs model, then moving on to the Z portal model that is the main focus of this thesis. We review the UV completion involving heavy fermions, and illustrate the application of ChPT to the calculation of dark pion decay rates. Our original results are presented in chapter 4 and chapter 5. After writing down the Lagrangian of the Z' completion, we derive important bounds from EWPT and Z invisible decays. Then we calculate the effective decay constant of the CP-odd dark pions in terms of the underlying model parameters, comparing the results with those found previously in the completion containing heavy fermions. In addition, we discuss the decays of CP-even dark pions. These results will, hopefully, provide a basis for future phenomenological studies of the Z' model. In chapter 6 we offer our conclusions.