Stars as Laboratories for Fundamental Physics - MPP Theory Group

456 Chapter 12
In Fig. 12.3 the excluded range of masses and mixing angles 71 is
shown together with similar constraints from other neutrino sources.
The reactor bounds are weaker than those from the Sun and SN 1987A,
but they remain important because of the short decay path involved!
If one accepts the big-bang nucleosynthesis bounds (Sect. 7.1.5) the ν τ
total lifetime must be so short that it would not escape from the mantle
of a SN before decaying, and perhaps not even from the Sun.
12.2.4 Neutrinos from a Beam Stop
Another powerful laboratory source for both ν e ’s and ν µ ’s is a beam
stop where neutrinos are produced from the decay of stopped pions,
π + → µ + ν µ and the subsequent decay of stopped muons, µ + → e + ν e ν µ .
In a recent experiment of this sort (Krakauer et al. 1991), the neutrino
intensity was 4.3×10 13 ν µ /s with a total of 8.52×10 19 ν µ . In these
decays the ν µ has a fixed energy of (m 2 π − m 2 µ)/2m π = 29.8 MeV
while the other normalized spectra are (3/Y 4 )(3Y − 2E ν )Eν 2 for ν µ
and (12/Y 4 )(Y − E ν )Eν 2 for ν e with Y ≡ 1m 2 µ = 52.8 MeV. For ν e ,
the 90% CL radiative lifetime limit as a function of the “anisotropy
parameter” α is τ γ /m νe > (15.9 + 9.8α + 0.3α 2 ) s/eV, somewhat less
restrictive than the reactor results.
For ν µ and ν µ one obtains slightly different limits because of the
different source spectra. Under the assumption of CP invariance the
radiative lifetimes for ν µ and ν µ are the same. In this case the combined
limit is τ γ /m νµ > (36.3 + 21.65α + 0.75α 2 ) s/eV while the individual
limits are about half this value. In terms of an effective transition
moment the most conservative case (α = −1) yields
µ eff < 0.11 µ B m −2
eV. (12.8)
For the admixture of other mass eigenstates this result may be translated
in a fashion analogous to the discussion of reactor neutrinos.
Beam-stop neutrinos from meson decays may also be used to constrain
the e + e − decays of heavy admixtures. Because of the larger
amount of available energy one may probe higher masses for ν h while
the reactor bounds drop out above a few MeV because of the relatively
soft spectrum. In Fig. 12.3 the most restrictive such constraints are
summarized.
71 It is customary to display |U eh | 2 when constraining the mixing parameters of
heavy, decaying neutrinos while one shows sin 2 2θ eh for light, oscillating neutrinos
as in Chapter 8. For easier comparison I always use the mixing angle. Recall that
|U eh | = sin θ eh so that for small mixing angles sin 2 2θ eh = 4|U eh | 2 .