20 Neutrino Mass Hints at Mirror Symmetry in Nature
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photon spin would be just right to compensate for the spin of the neutrino
(or the helicity which is spin alignment of the neutrino with its direction of
motion). They found that in this decay, only one kind of neutrino, called a
left-handed neutrino, emerged (as already explained, left-handed means the
spin of the neutrino is opposite to the direction in which it is moving). If
mirror symmetry was a good symmetry, an equal number of neutrinos with
both left- and right-handed helicity should have been seen, but they were not.
This proved that the weak interactions do not respect mirror symmetry and
it must have some connection to neutrino helicity. Also it was found that in
all beta decay type processes, only the same left-handed helicity neutrino was
emitted. If a beta decay emitted an electron, the corresponding neutrino would
be an anti-neutrino and its helicity is opposite to that of the the neutrino; thus,
the anti-neutrino would be right-handed. This suggests that the universe only
has left-handed helicity states of neutrino and right-handed helicity states of
anti-neutrino, but not right-handed neutrinos and left-handed anti-neutrinos.
This is a profound discovery, since all other matter particles that we know,
like electrons, protons, etc. have both left- and right-handed helicities. They
are all known to be massive, whereas the neutrinos in the universe have only
one kind of helicity. Why is the neutrino so special?
20.4 Mass and Helicity
Recall our discussion of helicity in Chap. 2. This is a concept which says
how the spin is aligned with respect to its velocity (speed and spin direction
together), and it is a very important concept in theoretical physics. As we will
see, this will help us understand and appreciate the role of neutrino mass in
determining the direction of physics that goes beyond the standard model.
The mass of a fermion i.e. a spin one half particle is intimately connected
to its helicity. This is explained in Fig. 20.1. Let us analyze Fig. 20.1 where the
twirling lines represent the spin direction and the straight line represents the
direction of velocity. The principle of relativity says that if a particle has mass,
it can move at any speed below the speed of light, whereas if a particle has no
mass, it can move only at the speed of light. No less or no more. Now, coming
to the Fig. 20.1, it shows a massive particle moving from left to right at some
speed, with its spin twirling to the left, and this is a particle with left-handed
helicity. But since it has mass, one can look at the same particle from a rapidly
moving train, speeding to the right faster than the particle. From the train, the
particle will look like it is moving to the left, but its twirling direction is still the
same as before. This means that from the moving train, the particle looks right-
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photon spin would be just right to compensate for the spin of the neutrino
(or the helicity which is spin alignment of the neutrino with its direction of
motion). They found that in this decay, only one kind of neutrino, called a
left-handed neutrino, emerged (as already explained, left-handed means the
spin of the neutrino is opposite to the direction in which it is moving). If
mirror symmetry was a good symmetry, an equal number of neutrinos with
both left- and right-handed helicity should have been seen, but they were not.
This proved that the weak interactions do not respect mirror symmetry and
it must have some connection to neutrino helicity. Also it was found that in
all beta decay type processes, only the same left-handed helicity neutrino was
emitted. If a beta decay emitted an electron, the corresponding neutrino would
be an anti-neutrino and its helicity is opposite to that of the the neutrino; thus,
the anti-neutrino would be right-handed. This suggests that the universe only
has left-handed helicity states of neutrino and right-handed helicity states of
anti-neutrino, but not right-handed neutrinos and left-handed anti-neutrinos.
This is a profound discovery, since all other matter particles that we know,
like electrons, protons, etc. have both left- and right-handed helicities. They
are all known to be massive, whereas the neutrinos in the universe have only
one kind of helicity. Why is the neutrino so special?
20.4 Mass and Helicity
Recall our discussion of helicity in Chap. 2. This is a concept which says
how the spin is aligned with respect to its velocity (speed and spin direction
together), and it is a very important concept in theoretical physics. As we will
see, this will help us understand and appreciate the role of neutrino mass in
determining the direction of physics that goes beyond the standard model.
The mass of a fermion i.e. a spin one half particle is intimately connected
to its helicity. This is explained in Fig. 20.1. Let us analyze Fig. 20.1 where the
twirling lines represent the spin direction and the straight line represents the
direction of velocity. The principle of relativity says that if a particle has mass,
it can move at any speed below the speed of light, whereas if a particle has no
mass, it can move only at the speed of light. No less or no more. Now, coming
to the Fig. 20.1, it shows a massive particle moving from left to right at some
speed, with its spin twirling to the left, and this is a particle with left-handed
helicity. But since it has mass, one can look at the same particle from a rapidly
moving train, speeding to the right faster than the particle. From the train, the
particle will look like it is moving to the left, but its twirling direction is still the
same as before. This means that from the moving train, the particle looks right-