Lattice simulations and analytical computations of five-dimensional gauge theories to study the Higgs boson as an extra-dimensional gauge field
Final Report Abstract
The discovery in 2012 of a scalar particle around 125 GeV has all but confirmed the existence of the Higgs mechanism, which renders the Standard Model of particle physics complete. However, the origin of the potential responsible for Spontaneous Symmetry Breaking (SSB), which leads to the Brout-Englert-Higgs mechanism is, as of yet, unknown, and the arbitrary nature of the required fine tuning of parameters, the so-called hierarchy problem, suggests that a more fundamental process is at work. A class of extensions to the Standard Model aimed at addressing these puzzles by the use of extra dimensions come under the heading of Gauge-Higgs Unification. In these models, the Higgs field originates from the extra-dimensional components of the gauge field and gives rise to massive gauge bosons in the regular four dimensions. In this project, we consider the simplest case of one extra dimension where, due to the higher dimensional gauge invariance, the Higgs potential remains zero at tree level and is generated only through quantum effects. Furthermore, the use of an orbifold geometry can break the gauge group at the fixed points, allowing for a Standard Model-like Higgs field in the fundamental representation. In perturbation theory, where the extra dimension is compactified and the five-dimensional fields are expanded as a series of four-dimensional Kaluza-Klein modes, the Higgs mass is independent of the cut-off (at one-loop). However, we consider a pure gauge theory where it is known that the one-loop effective Higgs potential does not develop a symmetry breaking minimum. Although the Higgs mass typically tends to be light, one way to circumvent this problem is to include fermionic degrees of freedom which induce SSB via the Hosotani mechanism. In this project we followed a different strategy. We simulated a pure gauge theory on a fivedimensional lattice by Monte Carlo methods and found that it exhibits SSB with a massive gauge boson. Moreover on the orbifold boundaries we observed dimensional reduction from five to four dimensions, which suggests that there is a localization mechanism for the gauge field. In five dimensions one worries about the (perturbative) non-renormalizability of the theory and the size of the effects originating from the finite cut-off (the inverse lattice spacing). Although we did not find a second order phase transition, where the cut-off could be removed, our recent data show that there exist a range of cut-off values where cut-off effects are small. We emphasize that the mechanism of SSB which we studied in this project is purely bosonic. As such it represents a novelty in the context of Gauge-Higgs Unification models and might also be useful to describe other systems.
Publications
- Lines of Constant Physics in a Five-Dimensional Gauge-Higgs Unification Scenario
M. Alberti, N. Irges, F. Knechtli and G. Moir
- Higgs mechanism near the 5d bulk phase transition, Phys.Lett. B722 (2013) 378–383
N. Irges, F. Knechtli, and K. Yoneyama
(See online at https://doi.org/10.1016/j.physletb.2013.04.032) - Non-perturbative Gauge-Higgs Unification: Symmetries and Order Parameters, JHEP 1406 (2014) 070
N. Irges and F. Knechtli
- Progress in Gauge-Higgs Unification on the Lattice, PoS LATTICE 2013 (2014) 061
F. Knechtli, K. Yoneyama, P. Dziennik and N. Irges
- Five-Dimensional Gauge- Higgs Unification: A Standard Model-Like Spectrum, JHEP 09 (2015) 159
M. Alberti, N. Irges, F. Knechtli, and G. Moir
- Gauge and Higgs Boson Masses from an Extra Dimension, PoS LATTICE 2014 (2015) 248
G. Moir, P. Dziennik, F. Knechtli, K. Yoneyama and N. Irges
- Extra-dimensional models on the lattice, International Journal of Modern Physics A 31 (2016) 1643002 (23 pages)
F. Knechtli and E. Rinaldi
- Non-Perturbative Gauge-Higgs Unification in Five Dimensions, PoS LATTICE 2015 (2016) 231
G. Moir, M. Alberti, F. Knechtli and N. Irges
