Stars as Laboratories for Fundamental Physics - MPP Theory Group

Nonstandard Neutrinos 253
(“spontaneous symmetry breaking”). Fermion fields ψ interact with the
Higgs field by virtue of a Lagrangian gΦψψ where g is a dimensionless
(Yukawa) coupling constant. In vacuum, this coupling leads to an interaction
term gΦ 0 ψψ which has the form of a standard Dirac mass
term mψψ. Different fermion masses thus arise from different Yukawa
couplings. Φ 0 does not depend on the Lorentz frame because of the
scalar nature of the Higgs field and so gΦ 0 ψψ is the same in all frames,
unlike a refractive photon “mass” in a medium.
It is not known whether the Higgs mechanism is the true source
for the masses of the fundamental fermions. Experimentally, the Higgs
particle (excitations of the Higgs field) has not yet been discovered,
while theoretically the fermion masses are the least appealing aspect
of the standard model because they require a host of ad hoc coupling
constants which must be experimentally determined.
7.1.2 Dirac and Majorana Masses
Neutrinos break the pattern of Fig. 7.1 in that they are much lighter
than the other members of a given family, a discrepancy which is most
severe for the third family where cosmologically m < ντ ∼ 30 eV, eight and
ten orders of magnitude less than m τ and m t , respectively! Moreover,
neutrinos are different in that their r.h. chirality states are sterile because
of the handedness of the weak interaction. The r.h. states interact
with the rest of the world only by gravity and by a possible Yukawa
coupling to the Higgs field.
It is frequently assumed that neutrinos do not couple to the Higgs
field, and that the r.h. components do not even exist, assumptions which
are part of the particle-physics standard model. In this case there are
only two neutrino states for a given family as opposed to four states for
the charged leptons. Actually, one may interpret the two components
of such a neutrino as the spin states of a Majorana fermion which is defined
to be its own antiparticle. Fermions with four distinct states are
known as Dirac fermions. Naturally, a Majorana fermion cannot carry
a charge as that would allow one to distinguish it from its antiparticle.
A magnetic or electric dipole moment is equally forbidden: its orientation
relative to the spin is reversed for antiparticles. For example, the
neutron cannot be a Majorana fermion among other reasons because it
carries a magnetic moment.
Because the r.h. neutrino components of a given family, if they exist,
are sterile anyway, there is no practical distinction between massless
Dirac and Majorana neutrinos except in a situation where gravitational