New Aspects Of Scale And Discrete Flavor Symmetry Breaking

Abstract

The Standard Model (SM) of particle physics is complete with the discovery of the Higgs particle. However the SM cannot be a complete theory of nature as it does not explain the origin of neutrino mass, dark matter (DM), dark energy, matter-antimatter asymmetry and smallness of the strong CP parameter. From theoretical point of view we do not understand the origin of the scale separation between the electroweak (EW) and the Planck scale, and also the flavor puzzle. In this work we will tackle the hierarchy problem with scale symmetry and the flavor puzzle with discrete flavor symmetries, charting new symmetry groups and their breaking, while investigating their implied phenomenologies along the way. In the first part we provide two novel mechanisms to explain the origin of the EW scale generated by quantum effects from an anomalous breaking of a classical scale invariant extension of the SM. For the first model we utilize a direct scale transmission from condensation of a scalar, charged under a high representation of QCD, to trigger EW symmetry breaking (EWSB) dynamically. In the second model, we will use the indirect scale transmission approach to generate the EW scale transmitted by a singlet scalar mediator which couples to the SM and a strongly coupled hidden sector. Chiral symmetry in the dark fermion sector is broken spontaneously due to nonperturbative effects of the running coupling in the hidden sector, triggering indirectly EWSB due to dimensional transmutation and providing stable DM candidates in the form of dark pions. In the last part of this work we focus on charting new discrete flavor symmetry groups to obtain experimentally acceptable leptonic and quark mixing patterns. The interesting new discrete groups that we have found are classified mathematically and provide a new starting point for model building in discrete flavor symmetry