162
R. N. Mohapatra
to have very similar values to the mass of the neutrino, observed in oscillation
experiments. Therefore, there may be a connection between the two. The current size of the cosmological constant deduced from cosmological expansion
is ∼(10
−3 )
4 eV
4 and the value of the heaviest neutrino that is oscillating is
∼10
−2 eV, leading to such speculations. There is yet no theoretical basis for
such speculation. We will of course not know for a while whether any of these
or even the other theories about the origin of neutrino masses are right. The
first requirement for this is to establish whether the neutrino is indeed its own
anti-particle.
21.4 Testing Majorana Nature of Neutrinos
in Experiments
Physics is an experimental science. In particular, experiments need to establish
whether the neutrinos are Dirac or Majorana particles. Each possibility has its
distinct implications: for example, the idea of understanding the origin using
the seesaw mechanism discussed above depends very much on the assumption
that neutrinos are Majorana type. So how do we really test this idea? It is clear
that if neutrinos are Majorana fermions, the lepton number marker that was
discussed above is broken by two units. This breaking is weak. So for most
purposes, it will appear as if the lepton number is not broken, but there will
be situations where such a small effect can possibly show up and we need to
look for such places.
One of the ways the weak force manifests itself is via the decay of nuclei to
another nuclei with one higher atomic number (i.e., Z → Z + 1), and the
fundamental process is n → p +e
−
+ ¯
ν e where the neutron that decays resides
inside the nucleus. An example of such a decay is: Co
60
→ Ni
60
+ e
−
+ ¯
ν e
and there are many other examples in nature. (Co
60 decay is nowadays used in
cancer therapy). These processes are called single beta decays, denoting the fact
that there is only a single electron emitted per decay. Such decays cannot tell
whether the neutrino is a Dirac or Majorana fermion. In these processes, the
decaying nucleus is called the mother nucleus and the final nucleus is called is
the daughter nucleus.
However, there can be processes where there can be the emission of two
neutrinos if the single beta decay happens twice inside a nucleus. These
processes are called double beta decays. In such a decay, two neutrons inside
the nucleus decay simultaneously, instead of just one. There are examples of
nuclei where the single beta decay is forbidden by energy considerations, i.e.
R. N. Mohapatra
to have very similar values to the mass of the neutrino, observed in oscillation
experiments. Therefore, there may be a connection between the two. The current size of the cosmological constant deduced from cosmological expansion
is ∼(10
−3 )
4 eV
4 and the value of the heaviest neutrino that is oscillating is
∼10
−2 eV, leading to such speculations. There is yet no theoretical basis for
such speculation. We will of course not know for a while whether any of these
or even the other theories about the origin of neutrino masses are right. The
first requirement for this is to establish whether the neutrino is indeed its own
anti-particle.
21.4 Testing Majorana Nature of Neutrinos
in Experiments
Physics is an experimental science. In particular, experiments need to establish
whether the neutrinos are Dirac or Majorana particles. Each possibility has its
distinct implications: for example, the idea of understanding the origin using
the seesaw mechanism discussed above depends very much on the assumption
that neutrinos are Majorana type. So how do we really test this idea? It is clear
that if neutrinos are Majorana fermions, the lepton number marker that was
discussed above is broken by two units. This breaking is weak. So for most
purposes, it will appear as if the lepton number is not broken, but there will
be situations where such a small effect can possibly show up and we need to
look for such places.
One of the ways the weak force manifests itself is via the decay of nuclei to
another nuclei with one higher atomic number (i.e., Z → Z + 1), and the
fundamental process is n → p +e
−
+ ¯
ν e where the neutron that decays resides
inside the nucleus. An example of such a decay is: Co
60
→ Ni
60
+ e
−
+ ¯
ν e
and there are many other examples in nature. (Co
60 decay is nowadays used in
cancer therapy). These processes are called single beta decays, denoting the fact
that there is only a single electron emitted per decay. Such decays cannot tell
whether the neutrino is a Dirac or Majorana fermion. In these processes, the
decaying nucleus is called the mother nucleus and the final nucleus is called is
the daughter nucleus.
However, there can be processes where there can be the emission of two
neutrinos if the single beta decay happens twice inside a nucleus. These
processes are called double beta decays. In such a decay, two neutrons inside
the nucleus decay simultaneously, instead of just one. There are examples of
nuclei where the single beta decay is forbidden by energy considerations, i.e.