MODERN COSMOLOGY

Lepton number violation and neutrinos as HDM candidates 195

looking for missingνμinνμ→ντoscillations, MINOS (in US) and OPERA
(with neutrino beam from CERN to Gran Sasso) are long-baseline experiments
devoted to this aim, which are under construction.
The tritium beta-decay experiments are searching directly for the effective
electron neutrino massmβand the present Troitzk [15] and Mainz [16] limits
givemβ≤ 2 .5–2.9 eV; there are perspectives to increase the sensitivity down to
1eV.
Theββ 0 νdecay predicted if neutrinos are Majorana particles will indicate
the value of the effective mass|〈m〉|, the present Heidelberg–Moscow bound is
(see, for example, [17]):

|〈m〉| ≡

∣

∣

∣

∣

∑

i

Uei^2 mi

∣

∣

∣

∣≤0.2–1 eV (5.26)

but in the near future there are perpectives to reach|〈m〉| ∼ 0 .01 eV.
Finally the direct search formνat accelerators has so far given negative
results leading to upper bounds [18]:

mνμ< 0 .19 MeV, mντ< 18 .2 MeV (5.27)

from LEP at 90% C.L. and 95% C.L. respectively.
From all these experiments we can conclude that neutrinos have masses and
that their values must be much lower than the other mass scales in the SM.

5.4.2 Neutrino masses in the SM and beyond

The SM cannot account for neutrino masses: we cannot construct either a Dirac
mass term as there is only a left-handed neutrino and no right-handed component,
or a Majorana mass term because such a mass would violate the lepton number
and the gauge symmetry.
To overcome this problem, many possibilities have been suggested:
(1) Within the SM spectrum we can form anSU( 2 )Lsinglet withνLusing
a triplet formed by two Higgs fieldHasνLνLHH. When the Higgs fieldH
develops a vev, this term gives rise to a Majorana mass term. However, this
term is not renormalizable, breaks the leptonic symmetry and does not give an
explanation of the smallness of the neutrino masses.
(2) We can introduce a new Higgs tripletand produce a Majorana mass
term as in the previous case whenacquires a vev.
(3) However, the most economical way to extend the SM is to introduce
a right-handed componentNR, a singlet under the gauge group, which couples
with the left-handed neutrinos. The lepton numberLcan be either conserved
or violated. In the former option neutrinos acquire a ‘regular’ Dirac mass like
all other charged fermions of the SM. The left- and right-handed components of
the neutrino combine together to give rise to a massive four-component Dirac
fermion. The problem is that the extreme lightness of the neutrinos (in particular