Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 467
12.4.3 Radiative Decay Limit: Low-Mass Neutrinos
We are now armed to derive a radiative lifetime limit for low-mass
neutrinos (m < ν ∼ 40 eV) by comparing the expected fluence according to
Eqs. (12.12) and (12.16) for channels 1, 2, and 3 with the observational
upper limits given in Tab. 12.1 for a 10 s time interval surrounding
the observed SN 1987A ν e burst. Depending on the assumed neutrino
spectral distribution which was parametrized by T ν and the anisotropy
parameter α, different channels give the most restrictive limits. These
are shown in Fig. 12.8 as a function of T ν for α = 0, ±1.
For normal neutrinos the relevant temperature range is between
4 and 8 MeV. In Fig. 12.8 a much larger range is shown because one
may also consider the emission of sterile neutrinos or axions from the
deep interior of a SN core where temperatures of several 10 MeV and
Fermi energies of several 100 MeV are available (Sect. 12.4.6).
For Dirac neutrinos the most conservative case is α = −1 where
for 4 MeV < ∼ T < ν ∼ 8 MeV the bound is approximately constant at
τ γ /m ν > 0.8×10 15 s/eV. Therefore, it applies equally to ν e and lowmass
ν µ and ν τ . For Majorana neutrinos (α = 0) the limit is more
restrictive by a factor of 2−3, depending on the assumed T ν . With
Eq. (7.12) the most conservative overall limit 75 (α = −1) translates into
µ eff < 1.5×10 −8 µ B m −2
eV. (12.17)
It applies if the total laboratory lifetime exceeds the time of flight of
5.7×10 12 s from the LMC to us. With a typical E ν = 20 MeV one must
require τ tot /m ν ∼ > 3×10 5 s/eV in the neutrino rest frame.
If the total lifetime is shorter than this limit all neutrinos decay
before they reach the Earth. Therefore, one can only derive a limit on
the branching ratio B γ of the radiative channel. One easily finds that
Eq. (12.13) is to be replaced by
F ′ γ(E γ ) = F ν B γ
∫ ∞
E γ
dE ν (1 − α + 2α E γ /E ν ) Φ ν (E ν )/E ν . (12.18)
Therefore, using the same Boltzmann source spectrum the photon spectrum
is slightly harder. Going through the same steps as before one
finds the upper limits on B γ as a function of the assumed T ν and α
75 Somewhat stronger constraints found in the literature were based on a less detailed
analysis, notably with regard to the spectral dependence and the dependence
on α. Published results are τ γ /m ν > 0.83×10 15 s/eV (von Feilitzsch and Oberauer
1988), 1.7×10 15 (Kolb and Turner 1989), 6.3×10 15 (Chupp, Vestrand, and Reppin
1989), and 2.8×10 15 (Bludman 1992).