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R. N. Mohapatra
Fig. 20.1 A particle with mass can flip its relative speed direction with respect to spin
handed. Thus a left-handed particle became a right-handed particle. Since the
theory of relativity says that physics does not change from one moving frame
to another, both helicity states must be realized in nature. The cartoon shows
both the states below the picture, to indicate that a massive spin half state must
have both left- and right-handed helicity states. We will call the right-handed
helicity and left-handed helicity states mass partners.
There can be another way two opposite helicity fermions can come about:
recall the discussion of anti-matter which said that matter and anti-matter have
opposite attributes. In other words, if a matter fermion has left-handed helicity,
the anti-matter fermion will have right-handed helicity. So in principle, a
matter fermion and anti-matter fermion can together form a mass, even if
the right-handed fermion does not exist as a separate state in the universe. In
this case the particle and its anti-particle will be mass partners. The problem
however is that, if a particle has electric charge, then the anti-matter has
opposite charge and therefore they cannot be mass partners, because by going
to a rapidly moving frame, one can break electric charge conservation, contrary
to all observations. However for neutrinos which do not have electric charge,
no such problem arises. Such masses are called Majorana masses and are
discussed in a few subsections later in this chapter.
Now look at Fig. 20.2 where a spin half particle without mass has its spin
and velocity shown. This particle is moving at the speed of light and is a
left-handed fermion (or neutrino). Since no train can travel faster than light,
the left-handed helicity particle will always remain left-handed in any frame,
no matter how fast it moves. That means that to describe the physics of
such a particle, one needs to have only one state in the universe. This is the
story of a massless neutrino i.e. it exists only as a left-handed state without
R. N. Mohapatra
Fig. 20.1 A particle with mass can flip its relative speed direction with respect to spin
handed. Thus a left-handed particle became a right-handed particle. Since the
theory of relativity says that physics does not change from one moving frame
to another, both helicity states must be realized in nature. The cartoon shows
both the states below the picture, to indicate that a massive spin half state must
have both left- and right-handed helicity states. We will call the right-handed
helicity and left-handed helicity states mass partners.
There can be another way two opposite helicity fermions can come about:
recall the discussion of anti-matter which said that matter and anti-matter have
opposite attributes. In other words, if a matter fermion has left-handed helicity,
the anti-matter fermion will have right-handed helicity. So in principle, a
matter fermion and anti-matter fermion can together form a mass, even if
the right-handed fermion does not exist as a separate state in the universe. In
this case the particle and its anti-particle will be mass partners. The problem
however is that, if a particle has electric charge, then the anti-matter has
opposite charge and therefore they cannot be mass partners, because by going
to a rapidly moving frame, one can break electric charge conservation, contrary
to all observations. However for neutrinos which do not have electric charge,
no such problem arises. Such masses are called Majorana masses and are
discussed in a few subsections later in this chapter.
Now look at Fig. 20.2 where a spin half particle without mass has its spin
and velocity shown. This particle is moving at the speed of light and is a
left-handed fermion (or neutrino). Since no train can travel faster than light,
the left-handed helicity particle will always remain left-handed in any frame,
no matter how fast it moves. That means that to describe the physics of
such a particle, one needs to have only one state in the universe. This is the
story of a massless neutrino i.e. it exists only as a left-handed state without