## Non–perturbative aspects of physics beyond the Standard Model

##### Abstract

The Large Hadron Collider (LHC) and the four major experiments set up along
its 27 kilometers of circumference (ATLAS, CMS, ALICE and LHCb), have
recently started to explore the high–energy frontier at √s = 8 TeV, and will
move to even higher energy in just about 2 years. The aim of physics searches
at LHC experiments was to complete the picture of the Standard Model (SM) of
elementary particles with the discovery of the Higgs boson and to look for specific
signatures of models extending the current understanding of particle interactions,
at zero and non–zero temperature. In 2012, the official discovery of the Higgs
boson, the only missing particle of the StandardModel, was announced by ATLAS
and CMS. Other important results include the measurement of rare decay modes
in heavy quarks systems, and indications of CP violation in charm decays by
LHCb. Signatures of beyond the Standard Model (BSM) physics are currently
being looked for in the experimental data, and this often requires the knowledge
of quantities that can be computed only with non–perturbative methods.
This thesis focuses on some possible extensions of the SM and the analysis of
interesting physical observables, like masses or decay rates, calculated using non–
perturbative lattice methods. The approach followed for the main part of this
work is to model BSM theories as effective field theories defined on a lattice.
This lattice approach has a twofold advantage: it allows us to explore non–
renormalizable gauge theories by imposing an explicit gauge–invariant cutoff and
it allows us to go beyond perturbative results in the study of strongly interacting
systems. Some of the issues of the SM that we will try to address include,
for example, the hierarchy problem and the origin of dynamical electroweak
symmetry breaking (DEWSB).
We investigate non–perturbatively the possibility that the lightness of the mass
for an elementary scalar field in a four–dimensional quantum field theory might
be due to a higher–dimensional gauge symmetry principle. This idea fits in the
Gauge–Higgs unification approach to the hierarchy problem and the results we
present extend what is known from perturbative expectations. Extra dimensional
models are also often used to approach DEWSB.
Another approach to DEWSB implies a new strongly interacting gauge sector
that extends the SM at high energies and it is usually referred to as Technicolor.
The phenomenological consequences of Technicolor can only be studied by non–
perturbative methods at low energy since the theory is strongly coupled at large
distances. We perform a comprehensive lattice study of fermionic and gluonic
scalar bound states in one of the candidate theories for Technicolor BSM physics.
We relate our findings to the nature of the newly discovered Higgs boson.
New physics is also commonly believed to be hidden in the flavour sector of the
SM. In this sector, lattice calculations of non–perturbative input parameters are
needed in order to make precise predictions and extract signals of possible new
physics. In particular, heavy quark physics on the lattice is still in development
and it is important to understand the relevant discretisation errors. We describe
a preliminary study of the mixing parameter of heavy–light mesons oscillations in
a partially–quenched scenario, using staggered dynamical fermions and domain
wall valence fermions.