Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 485
while those produced further away escaped into intergalactic space, a
lifetime below 10 5 × 1 kpc ≈ 10 16 s in the laboratory frame is excluded.
Because SN neutrinos with MeV masses are nearly nonrelativistic the
rest-frame lifetime is identical with the laboratory lifetime to within a
factor of a few, excluding τ < e + e − ∼ 10 15 s.
If the decays occur too close to the source the annihilation with
electrons from the neutrino decay is of some importance (Mohapatra,
Nussinov, and Zhang 1994). Therefore, decay times below about
10 4 s cannot be excluded by the present argument (Dar, Goodman, and
Nussinov 1987).
Actually, the galactic positron flux is thought to be associated with
supernovae, albeit not from ν τ decay but rather from the β + decays
of certain nuclei which are synthesized in a SN explosion (Chan and
Lingenfelter 1993). These authors performed a detailed analysis of the
probability for positrons to escape without annihilation from the SN
environment into the galaxy.
12.5.2 Can the Tau Neutrino Be Heavy
Armed with this result we can return to the question raised in Sect. 7.2.2
if a ν τ with a mass exceeding 2m e is compatible with the cosmological
requirement that such particles and their decay products do not
“overclose” the universe. It turns out that the SN constraints on
ν τ → ν e e + e − presented in this chapter exclude this possibility so that
either ν τ respects the cosmological mass limit of a few 10 eV or else it
must have fast invisible decay channels which inevitably require interactions
beyond the standard model.
In Fig. 12.19 the available constraints on τ e + e− are summarized. The
SN 1987A bound from the absence of a prompt γ burst, the cosmological
requirement, and the above limit from galactic positron annihilation
together exclude the entire range of possible masses and lifetimes. The
margins of overlap are so enormous that each of the arguments has
several orders of magnitude to spare for unaccounted uncertainties.
A heavy standard ν τ is also excluded on the basis of arguments involving
big-bang nucleosynthesis (BBN). The usual limit on the number
of effective neutrino degrees of freedom at nucleosynthesis alone
is enough to reach this conclusion (Sect. 7.1.5). Moreover, charged
leptons and secondary photons from the e + e − decay channel would destroy
some of the synthesized nuclei (Lindley 1979, 1985; Krauss 1984;
Kawasaki, Terasawa, and Sato 1986). The main virtue of the SN limits
is, therefore, that no reference to BBN is required to exclude a heavy ν τ .