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This could be achieved at upgraded present facilities
and novel facilities yet to be built.
Note that the above questions are dealt with globally,
in particular also in the USA and Japan. Fundamental
Symmetries are one of the four key topics recently put
forward by the NSAC Long Range Plan. New facilities
are being set up and planned at e.g. Michigan, TRIUMF,
RIKEN and JPARC and these labs are setting up new
groups and taking new initiatives for fundamental interactions
research. In general this field relies on precision
measurements which requires long beam times and high
particle intensities. But once completed every single
experiment gets visibility and has large impact.
4.5.2 Fundamental Fermions
Neutrino oscillations and
the neutrino mixing matrix
A major advance in our knowledge of neutrino properties
has been made in the last decade after the
discovery of the neutrino oscillation phenomenon by
the Super-Kamiokande experiment in 1998, with an
impact in various fields of physics. Among the numerous
implications are the fact that neutrinos are massive
particles, contrary to what was believed for decades; in
addition, the longstanding problems of the atmospheric
anomaly and of the solar neutrino deficit have now been
solved.
At present the two independent Δm 2 as well as two
out of the three mixing angles have been measured.
However, in spite of the impressive progress made in our
knowledge of neutrino properties, crucial open questions
remain. The main goal of future oscillation experiments
will be to address these key open issues and to determine
the value of the third neutrino mixing angle θ 13 ,
the sign of the atmospheric Δm 2 23 and the value of the
Dirac phase.
Neutrino oscillations turn out to be essential when
neutrinos propagate in astrophysical environments, e.g.
in core-collapse supernovae, in accretion-disks around
black holes, as well as in the early Universe just before
Big-Bang nucleosynthesis. Concerning the solar neutrino
measurements, at present the BOREXINO experiment is
running and has given confirmation of the Large Mixing
Angle solution, of the solar neutrino deficit problem, with
both 7 Be and 8 B neutrinos.
As far as the third mixing angle is concerned, only an
upper limit is available. In the near future three reactor
experiments – Double-Chooz, RENO and Daya Bay –
and the first super-beams experiments (T2K and NOνA)
will be able to measure its value if sin 2 2θ 13 < 0.02. Note
that the combination of the available experimental data
indicates that the value of θ 13 might actually be close to
the present limit.
One of the major important open issues is the possible
existence of CP violation in the lepton sector. A
non-zero Dirac phase introduces a difference between
neutrino and anti-neutrino oscillations. Such an observation
would have an enormous impact in various domains
of physics, from high-energy physics to cosmology. In
particular, it would bring an important element to our
understanding of matter versus anti-matter asymmetry
in the Universe.
Neutrino oscillations and the neutrino mixing matrix
Theoretically the observation of the neutrino oscillations implies that the neutrino interaction (or flavour α) basis
is related to the propagation (or mass i) basis through a unitary matrix called the Maki-Nakagawa-Sakata-
Pontecorvo (MNSP) matrix (Figure 1), the analogue of the Cabibbo-Kobayashi-Maskawa (CKM) matrix in the
quark sector. In recent years the goal of solar, atmospheric, accelerator and reactor experiments has been to
precisely measure the oscillation parameters. These comprise the difference of the neutrino mass eigenstates
2 2 2
mij mi m
j
and the elements of the MNSP matrix U α i . If three active neutrino families are considered such
a matrix depends on three mixing angles and three CP violating phases, one Dirac and two Majorana phases.
The last ones have physical meaning only if neutrinos are Majorana particles, identical to their antiparticles.
Then these phases influence neutrinoless double beta decay and other processes. However, they do not affect
neutrino oscillation, regardless of whether neutrinos are Majorana particles.
Figure 1. The neutrino mixing matrix with the three mixing angles between the different
neutrino generations and the CP violating Dirac phase δ.
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