The discovery of a Higgs-like particle at the LHC together with the absence, so far, of any hint of new physics calls for a more profound understanding of the structure and internal consistency of Gauge-Yukawa theories underpinning the standard model of particle interactions. I will start by demonstrating that Gauge-Yukawa theories obey gradient flow relations that constrain and organise the perturbative expansion in the gauge, Yukawa and scalar couplings. As a relevant application I will briefly mention how these relations affect the computation of the standard model vacuum stability. I will then move to prove the existence, at the quantum level, of controllable ultraviolet fixed points (asymptotic safety) for certain four-dimensional Gauge-Yukawa theories structurally similar to the standard model. I will conclude by outlining the relevant phenomenological and theoretical implications of the existence of four dimensional gauge-Yukawa theories displaying complete (in all the couplings) interacting ultraviolet fixed points at the quantum level.
Oct 2014 - Sep 2015
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