• Higgs boson
• dark matter
• unification

An important discovery of the last century was that the physical
nature of most of the gravitating mass in the universe is completely
unknown. This matter neither emits nor absorbs electromagnetic
radiation at any known wavelength (for this reason it got the name
"dark matter"), and it has been observed until now only indirectly
through its gravitational effects. It dominates the gravitational
potential on all the scales, from dwarf galaxies, to spiral galaxies
(like our Galaxy, the "Milky Way") and to large clusters of
galaxies. The measurements of the light element abundances and of
the fluctuations in the Cosmic Microwave Background show that a
significant part of the dark matter must be non baryonic. These
observations, however, do not tell us anything about the particle
nature of dark matter. Then the question is about the nature, the
origin and the composition of this important component of our
universe, since dark matter does not find an explanation in the
framework of the Standard Model of particle physics. Particle
physics provides us with a large number of dark matter candidates,
which appear naturally in various frameworks for reasons completely
independent from the dark matter problem, and certainly not invented
for the sole purpose of explaining the presence of dark matter in
our universe. Another missing opportunity for the Standard Model is
that gauge couplings do not quite unify at high energy; a possible
solution is to add weakly interacting particles to change the
running, in order to make unification working better.

In this thesis we present a model that has both a cold dark matter
candidate and can improve considerably over the Standard Model in
the direction of successful gauge coupling unification. We introduce
new matter with respect to the Standard Model alone, and we restrict
ourselves to the case in which the added particles are fermions.
Adding just a vector doublet allows remarkable improvements for
unification; this model, furthermore, is highly constrained since it
contains only one new parameter, the Dirac mass for the degenerate
doublets, whose neutral components are the dark matter candidates.
Such model, however, is ruled out by direct detection experiments:
the vector-like vertex with the Z boson for the neutral particles
remains unsuppressed, giving a spin-independent cross section that
is 2-3 orders of magnitude above current limits. This drawback
can be solved including a fermion singlet, with Yukawa couplings
with the doublets and the Higgs boson. Doing this we generate a
mixing between doublets and singlet, so that the neutral particles
become Majorana fermions which have suppressed vector-like couplings
with the Z boson. We impose a parity symmetry so that the new
particles do not couple to ordinary matter. The lightest particle is
stable as a consequence of the symmetry, and we suppose it to be
neutral. We call it lightest neutral particle (LNP).

This model has been already considered for high values of the relic
particle mass. It has also been shown how the gauge coupling
unification at high energy can be achieved and a rate for the proton
decay has been predicted that could be tested in the future. In this
work we focus on the region of parameter space where the mass of the
LNP is smaller than the W boson mass. The
analysis for higher mass was already done, as said above, but the
main reason for doing so is that well above the WW production
threshold, in order to account for the entire dark matter abundance
observed, the mass of charged components of the doublets is quite
high. An important fact is that, for such values of parameters, the
effects on Higgs boson physics are significant, both direct and
indirect. On the one hand there are new available decay channels for
the Higgs boson, and decays into neutral particles may dominate the
total width. On the other hand the new particles contribute to
electroweak observables, so that they may change the indirect upper
limit on the Higgs mass and improve the naturalness of the Higgs
potential. There are thus reasons to give special attention to this
region of parameter space.

We consider for the complete analysis two limiting cases: almost
equal Yukawa couplings (symmetric) and one of them vanishingly small
(asymmetric). In both cases all the observed dark matter abundance
could be explained by the LNP. The spectra of the model are
consistent with negative searches from LEP2 for all the cases. The
spin-independent direct detection cross section is around the
current limits only for the symmetric case. In the asymmetric case
it is well below these limits, as the spin-dependent cross sections
for both cases. However they are all within the sensitivity of
experiments currently under study. The effects on the Higgs physics
are very different in the two cases. In the first case the indirect
upper limit on the Higgs mass is unchanged relative to the Standard
Model. At the same time the Higgs width into a pair of LNP
dominates. As a net result the Higgs boson might be hidden at the
Large Hadron Collider. In the second case, instead, corrections to
the ElectroWeak precision observable T are not negligible and so
the upper limit on the Higgs mass is raised. The width into LNP
pairs can still be of some significance, depending on how much we
raise the mass of the Higgs. Finally we consider a CP violating
phase for the Dirac mass of the charge particle, giving rise to an
electron electric dipole moment. If we keep the LNP mass below
75 GeV the induced electric dipole moment is always below the
current experimental limit, but accessible at the next generation
experiments.