Experimental probes to tell the kind of electroweak realisation apart

Abstract

The discovery of the Higgs boson was the latest piece of the puzzle to be added to the electroweak sector of the Standard Model (SM), which, via the Higgs mecha- nism, provides fermions with masses and ensures unitarity in the SM. This is further backed up experimentally, with results thus far in agreement with the SM. However, the SM is incomplete and some attempts to fill in the blanks with new physics inter- fere with the mechanism of electroweak symmetry breaking, yet are still compatible with experiment. Definitively determining the true nature of electroweak symmetry breaking is key to understanding the electroweak sector, but is nonetheless an am- bitious goal as a result of the high energy scales involved. We can, however, begin to uncover the next puzzle pieces at the lower energy scales of current colliders. Effective Field Theories (EFTs) are the rediscovered tool in a particle physicist’s belt which will allow us to do this. They are a model-independent framework that can be used to classify the low-energy effects of heavy, new physics on experimental results which deviate from the Standard Model prediction.
The Standard Model Effective Field Theory (SMEFT), where the Higgs dou- blet transforms linearly under electroweak symmetry, is the most studied approach. However, the SMEFT is not as general an EFT as the Higgs EFT (HEFT), where electroweak symmetry transforms non-linearly. The question we attempt to address in this thesis is, is it SMEFT or HEFT? Or, equivalently, if electroweak symmetry is linearly or non-linearly realised. So far, nature has not been forth- coming. As such, we are interested in experimental probes which may answer this question.
We begin by considering collider phenomenology: how scattering amplitudes may differ between the two theories. In particular, we find partial evidence for a ‘minimum distance’ between the SM value for such amplitudes and HEFT theories, such that SMEFT becomes the sole theory whose amplitudes approach the SM. It is possible that, if non-decoupling new physics is lurking in the electroweak sector, we may be able to confirm a non-linear realisation by future collider programs.
Yet our question is a non-local one, with the decisive physics lying a distance ∼ v away in field-space, with particle colliders only probing near the vacuum. We turn instead to non-perturbative physics. Firstly, to sphaleron solutions in HEFT, which we find are less phenomenologically significant. Secondly, to first order phase transitions, where detectable gravitational wave remnants, do- main wall formation, and vacuum decay in the far distant future could take place, and single out HEFT theories. We find that results from cosmology are complimentary to those from particle colliders and the combination of both such measurements could help to pin down whether it is HEFT or SMEFT.