20 Neutrino Mass Hints at Mirror Symmetry in Nature
153
Fig. 20.2 A particle without mass always travels with the speed of light, the highest
speed possible in the universe, and therefore does not have a state with opposite spinspeed relation (chirality)
contradicting the theory of relativity, whereas all other particles in the standard
model which have mass appear have to have both left and right helicity states,
to be in agreement with the theory of relativity. The discovery of neutrino
mass therefore means that at least some right-handed neutrino helicity states
must be present in nature. This is a major change to our thinking about the
neutrino, caused by the discovery of neutrino oscillation.
20.5 Mirror Reflection and Neutrino States and
Nature of Weak Force
Under mirror reflection (also known as parity), the left-handed helicity state
of a fermion goes to the right helicity state. The left-handed helicity neutrino
participates in weak forces as described by the standard model, whereas the
right-handed helicity neutrino does not since it never appears in any weak
decay. For example, if somehow a left helicity neutrino produced in beta decay
is “rotated” into a right helicity neutrino (also called right-handed neutrino),
the later suddenly will not have any weak force and will move around freely.
This is a peculiarity of the weak force.
A curious thing about forces is that the ones that respect mirror reflection
symmetry (as do the strong force, electric force, etc.) are the ones coupled to
particles with mass which have both the left and right helicity states present
in the universe. And also, they couple to both helicity states of these particles
with equal strength. These forces (strong, electromagnetic) do not affect the
neutrinos which come only in the left-handed helicity. On the other hand,
the weak force which breaks mirror reflection symmetry couples not only to
all other fermions just mentioned which have mass, but also to the neutrino
which in the standard model has only left-handed helicity. The weak force law
states that it couples asymmetrically to all the particles.
Thus it is plausible to assume that since neutrinos have mass, there is a
right-handed neutrino, and therefore at some higher energy scale not yet
explored, the weak force behaves more like the other forces and becomes mirror
153
Fig. 20.2 A particle without mass always travels with the speed of light, the highest
speed possible in the universe, and therefore does not have a state with opposite spinspeed relation (chirality)
contradicting the theory of relativity, whereas all other particles in the standard
model which have mass appear have to have both left and right helicity states,
to be in agreement with the theory of relativity. The discovery of neutrino
mass therefore means that at least some right-handed neutrino helicity states
must be present in nature. This is a major change to our thinking about the
neutrino, caused by the discovery of neutrino oscillation.
20.5 Mirror Reflection and Neutrino States and
Nature of Weak Force
Under mirror reflection (also known as parity), the left-handed helicity state
of a fermion goes to the right helicity state. The left-handed helicity neutrino
participates in weak forces as described by the standard model, whereas the
right-handed helicity neutrino does not since it never appears in any weak
decay. For example, if somehow a left helicity neutrino produced in beta decay
is “rotated” into a right helicity neutrino (also called right-handed neutrino),
the later suddenly will not have any weak force and will move around freely.
This is a peculiarity of the weak force.
A curious thing about forces is that the ones that respect mirror reflection
symmetry (as do the strong force, electric force, etc.) are the ones coupled to
particles with mass which have both the left and right helicity states present
in the universe. And also, they couple to both helicity states of these particles
with equal strength. These forces (strong, electromagnetic) do not affect the
neutrinos which come only in the left-handed helicity. On the other hand,
the weak force which breaks mirror reflection symmetry couples not only to
all other fermions just mentioned which have mass, but also to the neutrino
which in the standard model has only left-handed helicity. The weak force law
states that it couples asymmetrically to all the particles.
Thus it is plausible to assume that since neutrinos have mass, there is a
right-handed neutrino, and therefore at some higher energy scale not yet
explored, the weak force behaves more like the other forces and becomes mirror