Stars as Laboratories for Fundamental Physics - MPP Theory Group

Nonstandard Neutrinos 257
95% CL mass limit of 23.8 MeV on the basis of 25 events of the form
τ → 5πν τ and 5ππ ◦ ν τ where π stands for a charged pion.
Another kinematical method to be discussed in Sect. 11.3.4 uses
the neutrino pulse dispersion from a distant supernova (SN). For ν e the
observed neutrinos from SN 1987A gave m < νe ∼ 20 eV, less restrictive
than the tritium experiments. However, if the neutrino pulse from a
future galactic SN will be detected one may be able to probe even a ν τ
mass down to the cosmologically interesting 30 eV range (Sect. 11.6)!
For Dirac neutrinos there is another essentially kinematical constraint
from the SN 1987A neutrino observations. The sterile ν Dirac
components can be produced in scattering processes by helicity flips.
In a supernova core this effect leads to an anomalous energy drain,
limiting a Dirac mass to be less than a few 10 keV (Sect. 13.8.1).
7.1.4 Neutrinoless Double-Beta Decay
If neutrinos have Majorana masses, lepton number is not conserved as
one cannot associate a conserved “charge” with a Majorana particle.
One observable consequence would be the occurrence of neutrinoless
nuclear decay modes of the form (A, Z) → (A, Z+2) 2e − which would
violate lepton number by two units. There are several isotopes which
can decay only by the simultaneous conversion of two neutrons. Recently
it has become possible to observe the electron spectra from the
standard two-neutrino mode (A, Z) → (A, Z+2) 2e − 2ν e ; for a recent
review see Moe (1995). The decay 76 Ge → 76 Se 2e − 2ν e , for example, is
found to have a half-life of (1.43±0.04 stat ±0.13 syst )×10 21 yr (Beck 1993).
The age of the universe, by comparison, is about 10 10 yr.
In the 0ν decay mode, loosely speaking, one of the emitted Majorana
neutrinos would be reabsorbed as an antineutrino with an amplitude
proportional to m νe ,Majorana and thus a rate proportional to m 2 ν e ,Majorana.
In a measurement of the combined energy spectrum of both electrons
the 0ν mode would show up as a peak at the endpoint. The best
current upper bound is from the Heidelberg-Moscow 76 Ge experiment
which yields m νe ,Majorana < 0.65 eV (Balysh et al. 1995), a number which
will likely improve to 0.2 eV over the next few years. This nominal limit
must be relaxed by as much as a factor of 2−3 for the uncertainty in the
nuclear matrix elements which are needed to translate an experimental
limit on the neutrinoless decay rate into a mass limit.
With neutrino mixing (Sect. 7.2) the other flavors also contribute so
that the bound is really on the quantity ⟨m ν ⟩ ≡ ∑ j λ j |U ej | 2 m j where λ j
is a CP phase equal to ±1, and the sum is to be extended over all two-