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R. N. Mohapatra
for the development of science. But, then there are geniuses like Galileo and Newton.
Well, Ettore was one of them. Majorana had what no one else in the world had.
21.3 Seesaw and Majorana Neutrino Mass
Every child has played with a seesaw with their elder siblings. When the elder
sibling sits down on one side, the child goes up because he or she is lighter and
comes down as the heavier sibling lets the seesaw up. The seesaw has a fulcrum
which stays fixed in the middle. The important thing is that seesaw needs two
people. The way small neutrino mass is understood, it precisely involves a
“heavier sibling” and a “fulcrum.” If the neutrino is a Majorana particle, i.e. it
is its own anti-particle, it can form a mass by itself by taking the left-handed
helicity particle and paring it with a right-handed anti-particle (recall that for
a fermon to get mass, it needs a left-handed helicity to pair up with a righthanded helicity particle). It would not have been possible if the mirror partner
of the neutrino was not its own anti-particle. The fulcrum in this case is the
mass that combines the left-handed neutrino with the right-handed mirror
partner. The technical name for the fulcrum is the Dirac mass of the neutrino.
The result is that the light partner gets a small mass which gets smaller as
the mass of the right helicity neutrino gets bigger, just like in a seesaw. The
heavier the heavy sibling, the higher goes the lighter sibling on the other side.
See the figure below for a picturesque description of this. This mechanism was
discovered independently by several groups in 1977 and 1979 [75]. From the
picture, one can imagine that if the fulcrum is higher, the right-handed heavy
neutrino goes deeper which could be thought of as having a higher mass. This
is precisely what happens mathematically, i.e. if the Dirac mass is bigger, the
right-handed neutrino mass which is called the seesaw mass has to be larger.
There are four types of seesaw models: they are called Type I, II, III seesaw
and inverse seesaw.
1
A conceptual beauty of the seesaw mechanism in the left-right symmetric
models is that it explains why we see only left-handed V − A currents in
low energy weak processes, being linked to the small mass of the neutrino.
In the seesaw mechanism, the heavier the mass of the right-handed neutrino,
the more mirror symmetry is broken and the more dominant weak process is
the V − A current process. It is quite elegant that the small neutrino mass
explains why we do not see right-handed weak force at low energy processes,
1 This author started calling the first two seesaw types already being discussed in the 1990s as type I and
II seesaw, following the nomenclature in superconductivity and supernovae, and the names seem to have
stuck.
R. N. Mohapatra
for the development of science. But, then there are geniuses like Galileo and Newton.
Well, Ettore was one of them. Majorana had what no one else in the world had.
21.3 Seesaw and Majorana Neutrino Mass
Every child has played with a seesaw with their elder siblings. When the elder
sibling sits down on one side, the child goes up because he or she is lighter and
comes down as the heavier sibling lets the seesaw up. The seesaw has a fulcrum
which stays fixed in the middle. The important thing is that seesaw needs two
people. The way small neutrino mass is understood, it precisely involves a
“heavier sibling” and a “fulcrum.” If the neutrino is a Majorana particle, i.e. it
is its own anti-particle, it can form a mass by itself by taking the left-handed
helicity particle and paring it with a right-handed anti-particle (recall that for
a fermon to get mass, it needs a left-handed helicity to pair up with a righthanded helicity particle). It would not have been possible if the mirror partner
of the neutrino was not its own anti-particle. The fulcrum in this case is the
mass that combines the left-handed neutrino with the right-handed mirror
partner. The technical name for the fulcrum is the Dirac mass of the neutrino.
The result is that the light partner gets a small mass which gets smaller as
the mass of the right helicity neutrino gets bigger, just like in a seesaw. The
heavier the heavy sibling, the higher goes the lighter sibling on the other side.
See the figure below for a picturesque description of this. This mechanism was
discovered independently by several groups in 1977 and 1979 [75]. From the
picture, one can imagine that if the fulcrum is higher, the right-handed heavy
neutrino goes deeper which could be thought of as having a higher mass. This
is precisely what happens mathematically, i.e. if the Dirac mass is bigger, the
right-handed neutrino mass which is called the seesaw mass has to be larger.
There are four types of seesaw models: they are called Type I, II, III seesaw
and inverse seesaw.
1
A conceptual beauty of the seesaw mechanism in the left-right symmetric
models is that it explains why we see only left-handed V − A currents in
low energy weak processes, being linked to the small mass of the neutrino.
In the seesaw mechanism, the heavier the mass of the right-handed neutrino,
the more mirror symmetry is broken and the more dominant weak process is
the V − A current process. It is quite elegant that the small neutrino mass
explains why we do not see right-handed weak force at low energy processes,
1 This author started calling the first two seesaw types already being discussed in the 1990s as type I and
II seesaw, following the nomenclature in superconductivity and supernovae, and the names seem to have
stuck.