Particle Physics Booklet - Particle Data Group - Lawrence Berkeley ...

13. Neutrino mixing 193
13. NEUTRINO MASS, MIXING, AND OSCILLATIONS
Written May 2010 by K. Nakamura (IPMU, U. Tokyo and KEK) and
S.T. Petcov (SISSA/INFN, Trieste and IPMU, U. Tokyo).
I. Massive neutrinos and neutrino mixing. It is a well-established
experimental fact that the neutrinos and antineutrinos which take part
in the standard charged current (CC) and neutral current (NC) weak
interaction are of three varieties (types) or flavours: electron, νe and ¯νe,
muon, νμ and ¯νμ, and tauon, ντ and ¯ντ . The notion of neutrino type or
flavour is dynamical: νe is the neutrino which is produced with e + ,or
produces an e− , in CC weak interaction processes, etc. The flavour of
a given neutrino is Lorentz invariant. Among the three different flavour
neutrinos and antineutrinos, no two are identical.
The experiments with solar, atmospheric, reactor and accelerator
neutrinos [4–16,20,21,22] have provided compelling evidences for the
existence of neutrino oscillations [17,18], transitions in flight between
the different flavour neutrinos νe, νμ, ντ (antineutrinos ¯νe, ¯νμ, ¯ντ ),
caused by nonzero neutrino masses and neutrino mixing. The existence of
oscillations implies that if a given flavour neutrino, say νμ, withenergy
E is produced in some weak interaction process, the probability that it
will change into a different flavour neutrino, say ντ , after traveling a
sufficiently large distance L, P (νμ → ντ ; E,L), is different from zero. If
the νμ → ντ oscillation or transition probability P (νμ → ντ ; E,L) �= 0,the
probability that νμ will not change into a neutrino of a different flavour,
i.e., the“νμsurvival probability”, P (νμ → νμ; E,L), will be smaller than
one. One would observe a “disappearance” of muon neutrinos on the way
from the νμ source to the detector if only νμ are detected and they take
part in oscillations.
Oscillations of neutrinos are a consequence of the presence of neutrino
mixing, or lepton mixing, in vacuum. In the formalism used to construct
the Standard Model, this means that the LH flavour neutrino fields νlL(x), which enter into the expression for the lepton current in the CC weak
interaction Lagrangian, are given by:
νlL(x) = �
Ulj νjL(x), l = e, μ, τ, (13.1)
j
where νjL(x) is the LH component of the field of a neutrino νj possessing a
mass mj and U is a unitary matrix - the neutrino mixing matrix [1,17,18].
Eq. (13.1) implies that the individual lepton charges Ll, l = e, μ, τ, arenot
conserved.
All neutrino oscillation data, except for the LSND result [23], can be
described assuming 3-neutrino mixing in vacuum. The number of massive
neutrinos νj, n, can, in general, be bigger than 3 if, e.g., there exist sterile
neutrinos [1] and they mix with the flavour neutrinos. It follows from the
current data that at least 3 of the neutrinos νj, sayν1, ν2, ν3, mustbe
light, m1,2,3 � 1 eV, and must have different masses, m1 �= m2 �= m3. At
present there are no compelling experimental evidences for the existence
of more than 3 light neutrinos.
Being electrically neutral, the massive neutrinos νj can be Dirac or
Majorana particles [27,28]. The first possibility is realized when there
exists a lepton charge L carried by νj (e.g., L = Le + Lμ + Lτ , L(νj) =1),
which is conserved by the particle interactions. The neutrino νj has a
distinctive antiparticle ¯νj: ¯νj differs from νj by the value of L it carries