Stars as Laboratories for Fundamental Physics - MPP Theory Group

Radiative Particle Decays 451
one can then derive limits on U eh for any ν h , even a hypothetical sterile
one, if m h ∼ > 1 MeV because it is the same mixing amplitude that allows
for its production in the source and for its ν h → ν e e − e + decay.
In the following I will discuss radiative lifetime limits from different
sources approximately in the order of available decay paths, from laboratory
experiments (a few meters) to the radius of the visible universe
(about 10 10 light years).
12.2 Laboratory Experiments
12.2.1 Spectrum of Decay Photons
Perhaps the simplest neutrino source to use for laboratory experiments
is a nuclear power reactor which produces a strong ν e flux from the weak
decays of the uranium and plutonium fission products. If a γ detector
is placed at a certain distance from the reactor core one may assume
that the local neutrino flux F ν (E ν ) is known (units cm −2 s −1 MeV −1 ).
As a first step one then needs to compute the expected flux F γ (E γ ) of
photons from the decay ν → ν ′ γ. The result will also apply to stationary
stellar sources such as the Sun while for the short neutrino burst
from SN 1987A one needs to derive a separate expression (Sect. 12.4).
Because the decay is a dipole transition, the general form of the
photon angular distribution in the rest frame of the parent neutrino is
dN γ /d cos ϑ = 1 (1 − α cos ϑ), (12.2)
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where ϑ is the angle between the ν spin polarization vector and the
photon momentum. For Majorana neutrinos the decay is isotropic,
independently of their polarization, and thus α = 0. Similarly for
axion decays, a → γγ, as these particles have no spin so that in their
rest frame no spatial direction is favored. For polarized Dirac neutrinos
the possible parameter range is −1 ≤ α ≤ 1.
The decay photon has an energy ω = δ m m ν /2 in the rest frame of
the parent neutrino—see Eq. (7.12). If it is emitted in a direction θ
with regard to the laboratory direction of motion, the energy in the
laboratory frame is E γ = ω (E ν + p ν cos θ)/m ν . Hence,
E γ = 1 2 δ m E ν (1 + β cos θ), (12.3)
where β = p ν /E ν = (1 − m 2 ν/Eν) 2 1/2 is the neutrino velocity. For a lefthanded
parent neutrino the spin is polarized opposite to its momentum
so that cos θ = − cos ϑ and dN γ /d cos θ = 1 (1 + α cos θ). For a very
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