MODERN COSMOLOGY

192 Dark matter and particle physics

(i) lacking of the right component they cannot have a Dirac mass term; and

(ii) belonging to aSU( 2 )Ldoublet, they cannot have a Majorana mass term.

However, from experimental data we can infer that neutrinos are massive and
that their mass is very small compared to the other mass scales in the SM. The SM
cannot provide such a mass to neutrinos and hence this consitutes a proof of the
existence of a physics beyond the SM. The problem ofνmasses will be addressed
in more detail in section 5.4.2.

5.2.3 Successes and difficulties of the SM

The SM has been tested widely at accelerators receiving strong confirmations of
its validity. Up to now there are no appreciable deviations from its expectations
even if some observables have been tested at the per mille level. In the future
LHC will reach higher energies and will have the possibility to discover new
physics beyond the SM if this one lies at the TeV scale. Another promising class
of experiments to detect deviations from the SM predictions are rare processes
which are very suppressed or forbidden in the SM such as flavour-changing
neutral currents phenomena orCP-violation ones. All these tests up to now are
compatible with SM expectations.
However, we see good reasons to expect the existence of physics beyond
the SM. From a theoretical point of view the SM cannot give an explanation of
the existence of three families, of the hierarchy present among their masses, of
the fine tuning of some of its parameters, of the lack of unification of the three
fundamental interactions (considering the behaviour of the coupling constants,
we see that they unify at a scaleMX∼ 1015 GeV where a unified simple group
might arise), of the hierarchy problem of the scalar masses which tend to become
as large as the highest mass scale in the theory. From an experimental point of
view, the measured neutrino masses are a proof of a physics beyond SM even if
what the type of physics is still an open question to be addressed. Cosmology also
gives strong hints in favour of a physics beyond the SM: in particular baryogenesis
cannot find a satisfactory explanation in the SM, inflation is not predicted by SM
and finally we have the dark matter problem.

5.3 The dark matter problem: experimental evidence

Let us define
(for a review see [5] and [6]) as the ratio between the densityρ
and the critical density

ρcr=

3 H 02

8 πG

= 1. 88 h^20 × 10 −^29 gcm−^3

whereH 0 is the Hubble constant,Gthe gravitational constant:

=

ρ

ρcr

. (5.17)