Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 461
12.3.2 Heavy Neutrino Admixtures
In full analogy to the case of reactor experiments the solar bound
Eq. (12.10) can be reinterpreted as a limit on radiative decays of heavy
ν e admixtures. To this end one interprets m eV = m h /eV and introduces
the factor |U eh | −1 on the r.h.s. of Eq. (12.10). It must be stressed, however,
that this simple procedure is only applicable to m < h ∼ 30 keV
because the main part of the solar neutrino spectrum is relatively soft.
In the remaining range of interest, 30 keV < ∼ m < h ∼ 1 MeV, the ν h flux is
partly suppressed. Moreover, a large fraction of it will be nonrelativistic
or only moderately relativistic so that the flux of decay photons will
have a nonnegligible angular divergence. The detectors used to derive
the constraints shown in Fig. 12.4 had a limited forward aperture of
about 0.15 sr, relevant in the energy range 18−185 keV (Peterson et al.
1966), and 1 sr, relevant in the energy range 163−774 keV (Frost et al.
1966). Therefore, a certain part of the photon flux that would have
come from angles relatively far away from the Sun would have been cut
out, weakening the bounds on radiative decays of ν h .
For m h > 2m e one would, again, expect the decay ν h → ν e e + e −
to dominate. For m h up to about 14 MeV one may use the 8 B neutrinos
from the Sun as a source spectrum. The flux of interplanetary
positrons from cosmic ray secondaries is measured to be approximately
10 −4 cm −2 s −1 sr −1 MeV −1 at kinetic energies of about 5 MeV. Interpreting
this flux as an upper limit to possible decay positrons from
solar neutrinos, Toussaint and Wilczek (1981) derived
|U eh | 2 ∼ < ⎧
⎪⎨
⎪ ⎩
2×10 −4 (m h = 2 MeV),
2×10 −5 (m h = 5 MeV),
3×10 −6 (m h = 10 MeV).
(12.11)
Because they used the theoretically expected rather than the experimentally
measured solar 8 B neutrino flux I have discounted their original
numbers by a factor of 3. These bounds are included in Fig. 12.3;
in the applicable mass range they are more restrictive than those from
laboratory experiments. They are valid only if the ν h flux is not diminished
by invisible decay channels on its way between Sun and Earth, i.e.
the total ν h (laboratory) lifetime must exceed about 500 s. Because in
the mass range of a few MeV the time dilation factor for about 10 MeV
neutrinos is not large, the bounds apply for total ν h lifetimes exceeding
about 100 s. Such “long-lived” MeV-mass neutrinos are in conflict with
the big-bang nucleosynthesis constraints shown in Fig. 7.2.