Stars as Laboratories for Fundamental Physics - MPP Theory Group

260 Chapter 7
The expansion rate and thus the energy density of the universe are
well “measured” at the epoch of nucleosynthesis (T ≈ 0.3 MeV) by
the primordial light-element abundances (Yang et al. 1984). This bigbang
nucleosynthesis (BBN) argument has been used to constrain the
number of light neutrino families to N ν ∼ < 3.4 (Yang et al. 1984; Olive
et al. 1990). Even though the measured Z ◦ decay width has established
N ν = 3 (Particle Data Group 1994) the BBN bound remains of interest
as a mass limit because massive neutrinos contribute more than a massless
one to the expansion rate at BBN. For a lifetime exceeding about
100 s this argument excludes 500 keV ∼ < m ν ∼ < 35 MeV (Kolb et al. 1991;
Dolgov and Rothstein 1993; Kawasaki et al. 1994), with even more restrictive
limits for Dirac neutrinos (Fuller and Malaney 1991; Enqvist
and Uibo 1993; Dolgov, Kainulainen, and Rothstein 1995). In Fig. 7.2
the region thus excluded is hatched and marked “BBN.”
Kawasaki et al. (1994) have considered the majoron mode ν → ν ′ χ
(Sect. 15.7) as a specific model for the neutrino decay. Including the
energy density of the scalar χ they find even more restrictive limits
which exclude the region between the dashed lines in Fig. 7.2.
7.2 Neutrino Mixing and Decay
7.2.1 Flavor Mixing
One of the most mysterious features of the particle zoo is the threefold
repetition of families (or “flavors”) shown in Fig. 7.1. The fermions in
each column have been arranged in a sequence of increasing mass which
appears to be the only significant difference between them. There is no
indication for higher sequential families; the masses of their neutrinos
would have to exceed 1 2 m Z = 46 GeV according to the CERN and SLAC
measurements of the Z ◦ decay width (Particle Data Group 1994). If
the origin of masses is indeed the interaction with the vacuum Higgs
field, the only difference between the fermions of a given column in
Fig. 7.1 is their Yukawa coupling to Φ.
If the only difference between, say, an electron and a muon is the
vacuum refraction, any superposition between them is an equally legitimate
charged lepton except for the practical difficulty of preparing it
experimentally. When such a mixed state propagates, the two components
acquire different phases along the beam exactly like two photon
helicities in an optically active medium, leading to a rotation of the
plane of polarization. Of course, now this “polarization” is understood
in the abstract flavor space rather than in coordinate space.