Stars as Laboratories for Fundamental Physics - MPP Theory Group

Miscellaneous Exotica 559
mass, and in supernovae. Another motivation to consider majoron
models is the possibility to account for fast neutrino decays in order to
avoid cosmological neutrino mass bounds. In the laboratory, majorons
could show up in experiments searching for neutrinoless 2β decays.
The main motivation for the introduction of majorons is the puzzling
smallness of neutrino masses (if they have nonvanishing masses at
all) relative to other fermions. As outlined in Sect. 7.1, in the particlephysics
standard model it is thought that all Dirac fermions acquire a
mass by their interaction with a background Higgs field which takes on
a classical value (vacuum expectation value) Φ 0 everywhere; neutrino
masses could well arise in the same fashion, except that the Yukawa
couplings to the Higgs field would have to be extremely small. Alternatively,
one may speculate that neutrino masses are so small because
they arise in a different fashion. Notably, the known sequential neutrinos
ν e , ν µ , and ν τ could well be Majorana fermions, i.e. their own
antiparticles so that the ν e is really equivalent to a helicity-plus ν e . As
long as neutrinos are massless this picture is equivalent to an interpretation
where the standard left-handed neutrinos are the two active
components of a four-component Dirac spinor while the two remaining
sterile components would never have been observed because they
do not interact. With a nonvanishing mass these interpretations are
vastly different because helicity flips in collisions would allow one to
produce the (almost) sterile “wrong-helicity” Dirac components. This
possibility was exploited in Sect. 13.8.1 to set bounds on a neutrino
Dirac mass from the SN 187A neutrino signal. For Majorana neutrinos,
a helicity-flipping collision takes an active ν e into an active ν e ,
thus violating lepton number by two units. Therefore, Majorana masses
could not arise from the coupling to the standard Higgs field which is
lepton-number conserving.
Majorana masses could arise, however, by interacting with a different
Higgs field which would develop a vacuum expectation value by
virtue of the usual spontaneous breakdown of a global symmetry. The
resulting Nambu-Goldstone boson is the majoron. (Recall that the
Nambu-Goldstone boson of the standard Higgs field shows up as the
third polarization degree of the massive Z ◦ gauge boson so that there
is no massless Nambu-Goldstone degree of freedom in the standard
model.) In the original model of Chicashige, Mohapatra, and Peccei
(1981), the “singlet majoron model,” the new vacuum expectation value
was considered to be much larger than the standard Φ 0 ≈ 250 GeV.
Large masses would be given primarily to sterile neutrinos postulated
to exist; the standard sequential neutrinos would obtain their small