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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 avor puzzle. In this work we will tackle the hierarchy problem with
scale symmetry and the avor puzzle with discrete avor 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 avor 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 avor symmetry.
