Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 477
Fig. 12.15. (The overall factor m −1
ν of Eq. 12.32 is not included, of
course.) Up to neutrino masses of about 10 MeV one may essentially
ignore the nonrelativistic corrections while for larger masses one has to
worry about them. However, because this discussion applies to standard
neutrinos, the largest relevant mass is about 24 MeV and so the
nonrelativistic corrections never overwhelm the result.
12.4.6 Summary of ν → ν ′ γ Limits
In order to summarize the decay limits I begin in Fig. 12.16 with the relevant
regimes of m ν and τ tot . Above the upper dotted line the neutrinos
live long enough so that most of them pass the Earth before decaying
while below the lower dotted line they decay within the envelope of
the progenitor star. In the areas 1 and 5 the photon burst is “short”
(∆t < γ ∼ 10 s), in 2 and 4 it is “intermediate” (10 s < ∼ ∆t < γ ∼ 223.2 s),
and in 3 it is “long” (223.2 s < ∼ ∆t γ ). The exact boundaries as well as
the relevant constraints are summarized in Tab. 12.2. In Fig. 12.17 the
limits on µ eff are summarized as a contour plot.
If one restricts possible neutrino decays to the radiative channel one
has τ tot = τ γ which depends only on µ eff and m ν . Then one may use
directly the upper limits on µ eff given in Tab. 12.2 for the areas 1−3,
depending on the assumed mass. Put another way, the conditions on
τ tot are then automatically satisfied.
These limits certainly apply to ν e as the ν e burst from SN 1987A has
been measured. The fluxes of the other flavors were only theoretically
implied. If they have only standard weak interactions they must have
been emitted approximately with the same efficiency as ν e . Large dipole
moments, however, imply large nonstandard interactions: The same
electromagnetic interaction vertex that allows for radiative decays also
allows for scattering on charged particles by photon exchange! For
MeV energies, for example, the scattering cross section on electrons by
regular weak interactions and that by photon exchange are the same
for µ eff of order 10 −10 µ B . Hence in the lower left corner of Fig. 12.17
the neutrinos would interact much more strongly by photon exchange
than by ordinary weak interactions, causing them to emerge from higher
layers of the SN core than normally assumed. Their fluence and effective
temperature is then much smaller than standard. Put another way, for
µ > eff ∼ 10 −10 µ B the above constraints are not self-consistent (Hatsuda,
Lim, and Yoshimura 1988). However, because large dipole moments can
be constrained by other methods (Sect. 7.5.1) a detailed investigation
of their impact on SN physics is not warranted.