Who: Jens Krog (CP3-Origins)
When: Friday, October 30, 2015
The discovery of a bosonic resonance at the Large Hadron Collider (LHC) has forced the scientific community to take the theory for electroweak symmetry breaking including a Higgs scalar seriously, if not to accept it all together. The Higgs boson is now incorporated in the standard model (SM), and in this work we will mainly focus on the behavior of this or similar theories at small length scales.
Besides from the inherent hierarchy problem in scalar theories, these also may suffer from other complications. The isolated scalar φ prove to be “trivial” due a the positive sign of its beta function, while the incorporation of Yukawa couplings threaten to drive the coupling negative and invoke instability of the electroweak vacuum. One should either make sure that the theory stays consistent at least until the Planck scale, where unknown gravitational effects should appear, or abandon the idea of fundamental scalars. These two possibilities are the motivation for the results presented here.
In this thesis we investigate the ultra violet (UV) behavior for the standard model and a set of extensions with respect to the issues mentioned above. We elucidate on previously unknown relations between the renormalization group (RG) equations of the standard model stemming from the required abelian nature of the Weyl anomaly, and propose a new lowest order calculation that satisfies the consistency conditions. We investigate the issue of instability in certain extensions of the standard model, and find that the electroweak vacuum may be stable in these extension where the parameters for the dark matter sector are constrained. Additionally we find that the extensions, in the same way as the standard model, are consistent with the idea of asymptotic safety, where the quartic scalar coupling vanishes at the Planck scale.
By instead allowing a divergence of the scalar coupling, one may interpret the gauge-Yukawa theory as being the low-energy description of a theory of fermions with a four-fermion interaction. We demonstrate that a large class of gauge-Yukawa theories may be equivalent to a theory of fermions and composite scalars, and determine the allowed parameter space for the gauge-Yukawa theory. We finally show that the Higgs boson may arise from such a theory as composite of neutrinos provided extra scalars are present.
We show that the observed vacuum expectation value (VEV) and mass for the Higgs field arise naturally in specific extensions utilizing the Coleman-Weinberg mechanism while including viable dark matter candidates.