Stars as Laboratories for Fundamental Physics - MPP Theory Group

452 Chapter 12
relativistic parent neutrino β = 1 and so the normalized photon energy
distribution corresponding to Eq. (12.2) is
dN γ
= 1 (
1 − α + 2α E )
γ
, 0 < E γ < δ m E ν . (12.4)
dE γ δ m E ν δ m E ν
The decays of Majorana neutrinos or axions (α = 0) produce a boxshaped
spectrum while for α = ±1 it is triangle shaped (Fig. 12.1).
Fig. 12.1. Photon spectrum from the decay of a relativistic neutrino (energy
E ν ) according to Eq. (12.4).
A fraction (m ν /E ν )(d γ /τ γ ) of neutrinos decay before reaching the
detector if the laboratory lifetime is large compared with the decay
path d γ . Here, τ γ is the rest-frame radiative decay time and E ν /m ν
the time dilation factor. Integrating over the neutrino source spectrum
then yields
F γ (E γ ) = m ν
τ γ
∫ ∞ (
dE ν
d γ 1 − α + 2α E )
γ Fν (E ν )
. (12.5)
E γ /δ m δ m δ m E ν
Most sources emit either antineutrinos (for example ν e ’s from a fission
reactor) or neutrinos (for example ν e ’s from the Sun). In these cases
Eq. (12.5) gives us directly the expected γ flux as a function of the assumed
value for α. However, there are some examples for simultaneous
ν and ν sources. In those cases one needs to know which value of α to
use for ν if a certain value for ν has been assumed.
Under very general assumptions the laws of particle physics are
invariant under a simultaneous transformation which takes particles
into antiparticles (charge conjugation C), reflects all spatial coordinates
(parity transformation P), and inverts motions (time reversal T). In this
case the CPT theorem states that the masses and total decay times of
E 2 ν