MODERN COSMOLOGY

188 Dark matter and particle physics

sparticle are ‘canonical’ examples of the hot and cold DM, respectively. This

choice does not mean that these are the only interesting particle physics

candidates for DM. For instance axions are still of great interest as CDM

candidates and the experimental search for them is proceeding at full steam.

• The possibility of warm dark matter which has recently attracted much
  attention in relation to the possibility of light gravitinos (as WDM
  candidates) in a particular class of SUSY models known as gauge-mediated
  SUSY breaking schemes.


• Finally the problem of the cosmological constantin relation to the
  structure formation in the universe as in theCDM or QCDM models.

5.2 The SM of particle physics

In particle physics the fundamental interactions are described by the Glashow–
Weinberg–Salam standard theory (GSW) for the electroweak interactions [1–3]
(for a recent review see [4]) and QCD for the strong one. GWS and QCD are
gauge theories based, respectively, on the gauge groupsSU( 2 )L×U( 1 )Yand
SU( 3 )cwhereLrefers to left,Yto hypercharge andcto colour. We recall that
a gauge theory is invariant under a local symmetry and requires the existence of
vector gauge fields living in the adjoint representation of the group. Therefore in
our case we have:

(i) three gauge fieldsWμ^1 ,Wμ^2 ,Wμ^3 forSU( 2 )L;

(ii) one gauge fieldBμforU( 1 )Y;and

(iii) eight gauge bosonsλaμforSU( 3 )c.

The SM fermions live in the irreducible representations of the gauge group
and are reported in table 5.1: the indicesLandRindicate, respectively, the left
and right fields,b= 1 , 2 ,3 the generation, the colour is not shown.
The Lagrangian of the SM is dictated by the invariance under the Lorentz
group and the gauge group and the request of renormalizability. It is given
by the sum of the kinetic fermionic partLKmatand the gauge oneLK gauge:
L=LKmat+LK gauge. The fermionic part reads for one generation:

LKmat=iQLγμ

(

∂μ+igWμaTa+i

g′

6

Bμ

)

QL+idRγμ

(

∂μ−i

g′

3

Bμ

)

dR

+iuRγμ

(

∂μ+i

2 g′

3

Bμ

)

uR+iELγμ

(

∂μ+igWμaTa−i

g′

2

Bμ

)

EL

+ieRγμ

(

∂μ−ig′Bμ

)

eR (5.1)

where the matricesTa=σa/2,σaare the Pauli matrices,gandg′are the coupling
constants of the groupsSU( 2 )LandU( 1 )Y respectively. The Dirac matrices
γμare defined as usual. The colour and generation indeces are not specified.
This LagrangianLKmatis invariant under two global accidental symmetries, the