Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 455
is no meaningful limit on µ eff from decay experiments. This example
highlights the importance of separating the intrinsic coupling strength,
or the magnitude of the matrix element, from phase-space effects in the
interpretation of such results.
12.2.3 Heavy Neutrinos from Reactors
Considering the decay of ν e into a different neutrino species implies
entertaining the notion of the nonconservation of the electron lepton
number, forcing one to contemplate the possibility of neutrino flavor
mixing as well. Therefore, reactors will be sources for other flavors
and notably of “heavy neutrinos” according to Eq. (12.1). The photon
flux from radiative ν h decays can now be calculated as before, except
that the dwelling time for nonrelativistic ν h ’s in the decay volume is
increased by β −1 so that the velocity cancels between this factor and
Eq. (12.1). However, the photon spectrum shown in Fig. 12.1 must
be modified for the decays of nonrelativistic neutrinos because β < 1
in Eq. (12.3). Therefore, the overall expression for F γ (E γ ) becomes
somewhat more involved.
As long as m < h ∼ 1 MeV one may treat the ν h flux as relativistic.
Then the radiative decay limits are the same as for ν e , except that
they are diminished by the reduced neutrino flux. Thus, the bound
Eq. (12.6) translates into
µ eff < 0.92×10 −13 µ B |U eh | −1 m −2
MeV . (12.7)
With m h up to an MeV this bound has a lot more teeth than the one
on electron neutrinos.
For m h > 2m e ≈ 1 MeV the decays ν h → ν e e + e − will become
kinematically possible and probably dominate. The scintillation counters
that were used to search for decay photons near a power reactor
are equally sensitive to electrons and positrons—for many purposes
relativistic charged particles may be treated almost on the same footing
as γ rays. Therefore, the same Gösgen data have been analyzed
to constrain the mixing amplitude U eh (Oberauer, von Feilitzsch, and
Mössbauer 1987; Oberauer 1992). Even more restrictive limits were
obtained from data taken at the Rovno reactor (Fayons, Kopeykin,
and Mikaelyan 1991), and most recently at the Bugey reactor (Hagner
et al. 1995). Note that in this method the same mixing probability
|U eh | 2 appears in Eq. (12.1) to obtain the ν h flux from a ν e source, and
in Eq. (7.9) to obtain the decay probability. Hence, the expected e + e −
flux is proportional to |U eh | 4 .