Stars as Laboratories for Fundamental Physics - MPP Theory Group

450 Chapter 12
on the process ν e → ν ′ γ. The corresponding limit based on a comparison
between the measured solar neutrino flux and the measured limit
on x- or γ-rays from the quiet Sun is 7×10 9 s/eV, almost 9 orders of
magnitude more restrictive. Moreover, this method is fully analogous
to a laboratory experiment as it is based on a measured neutrino flux
and a measured upper limit photon flux. To a lesser degree this remark
also applies to the even better SN 1987A constraints which are
applicable to all neutrino flavors.
In addition, less directly established particle fluxes can be used such
as those from the stars in the galactic bulge or from all hydrogenburning
stars or supernovae in the universe. Even more indirectly, one
may study the impact of the radiative decay of the cosmic background
sea of neutrinos or axions which are predicted to exist in the framework
of the big-bang theory of the early universe.
Usually, the bounds on ν → ν ′ γ thus obtained are presented as limits
on the radiative decay time τ γ . Even if one does not aim at an immediate
theoretical interpretation, however, the significance of τ γ is limited
because it represents a combination of the final-state phase-space volume
and the matrix element. The latter can be expressed in terms
of an effective transition moment µ eff as in Eq. (7.12) of Sect. 7.2.2.
This moment characterizes the interaction strength independently of
phase-space effects, providing a much more direct link between the experimental
results and an underlying theory.
A “heavy” neutrino ν h with m h > 2m e ≈ 1 MeV can decay into
ν e e + e − . This channel is often included in the notion of “radiative” decays
because relativistic charged leptons cause experimental signatures
similar to γ rays. If this decay proceeds by virtue of a mixing amplitude
U eh between ν h and ν e the rate is given by Eq. (7.9). Therefore, it is
characterized by |U eh | in a phase-space independent way.
If ν e is a mixture of different mass eigenstates, any ν e source such
as a power reactor or the Sun produces all components. If their mass
differences are small one needs to consider in detail the phenomenon of
neutrino oscillations as in Chapter 8. However, if the oscillation length
is much smaller than the distance between the detector and the source,
the neutrino flux can be considered an incoherent mixture of all mass
eigenstates; at a reactor this is the case for ∆m 2 > ∼ 1eV 2 . The flux of
“heavy” neutrinos from a ν e source is then given by
F νh (E ν ) = |U eh | 2 β(E ν ) F νe (E ν ) . (12.1)
The velocity β(E ν ) = (1 − m 2 h/E 2 ν) 1/2 enters from the phase space of
nonrelativistic neutrinos in the production process. From ν e sources