Stars as Laboratories for Fundamental Physics - MPP Theory Group

254 Chapter 7
interactions dominate. For example, even otherwise sterile neutrinos
should be thermally emitted from black holes which are thought to
emit blackbody radiation of all physical fields. Equally, they would have
been produced in the very early universe when quantum gravitational
effects dominate. However, their present-day cosmic density, like that
of primordial gravitons, would be very dilute relative to microwave
background photons.
If neutrinos were Majorana particles they could still have a mass
even though it could not arise from the usual Higgs field which induces
Dirac masses. However, a Majorana mass could arise from the
interaction with a second Higgs field which also develops a vacuum expectation
value. Then the smallness of the neutrino masses could be
due to a small vacuum value of the new Higgs field while the Yukawa
couplings would not need to be anomalously small.
It is also possible that the r.h. components of the neutrinos do exist,
but are themselves (sterile) Majorana fermions with large masses.
It should be noted that any Dirac fermion (four components) can be
viewed as a combination of two Majorana fermions (two components
each) with degenerate masses. Certain variations of such models (“seesaw
mass models”) predict for the light, interacting neutrinos
m 1 : m 2 : m 3 = m 2 e : m 2 µ : m 2 τ or m 2 u : m 2 c : m 2 t . (7.1)
The smallness of the neutrino masses is then a suppression effect by
the large mass scale of the heavy sterile state whose mass would arise,
for example, at the grand unification scale of 10 15 −10 16 GeV.
For an elementary introduction to the most common models for neutrino
masses see, for example, Mohapatra and Pal (1991). The dizzying
variety of such models alone attests to the fact that even very basic
questions about the nature of neutrinos remain unanswered. While
some mass schemes like the see-saw relationship Eq. (7.1) are intriguing,
they have no predictive power because there are many other possibilities.
Therefore, it is best to remain open to all possibilities which are
not excluded by experimental or astrophysical arguments.
7.1.3 Kinematical Mass Bounds
Unsurprisingly, much experimental effort goes into attempts to measure
or narrow down the range of possible neutrino masses, an area where
astrophysics and cosmology have made their most renowned contributions
to particle physics. Direct laboratory experiments rely on the