Stars as Laboratories for Fundamental Physics - MPP Theory Group

340 Chapter 9
Because Y νe is about Y L /4, lepton number and energy are lost at
about a rate of sin 2 2θ 0 10 10 s −1 . Because the SN 1987A signal lasted
for several seconds, a conflict with these observations is avoided if
sin 2 2θ 0 ∼ < 10 −10 (9.78)
(Kainulainen, Maalampi, and Peltoniemi 1991; Raffelt and Sigl 1993).
If m > νx ∼ 1 MeV the assumed mixing with ν e allows for decays ν x →
ν e e − e + and ν x → ν e e − e + γ. The resulting γ signal from the SN 1987A
ν x flux (Sect. 12.4.7) does not allow for a dramatic improvement of
the bound Eq. (9.78). However, the decay argument does exclude the
possibility of a mixing angle so large that even the “sterile” ν x would
be trapped by virtue of its mixing with ν e .
The case of ∆m 2 < ∼ (100 keV) 2 is complicated because neutrinos in a
certain energy range below their Fermi surface encounter a ν e -ν x mixing
resonance. This implies that during the SN infall phase a large amount
of lepton number can be lost. The impact on the equation of state
can be strong enough to prevent a subsequent explosion. Shi and Sigl
(1994) found that this argument requires sin 2 2θ < 0 ∼ 10 −8 keV 2 /∆m 2 for
∆m 2 > ∼ (1 keV) 2 . They found additional constraints from the anomalous
contribution to the cooling by ν x emission.
These are all limits on the mixing of a sterile neutrino with ν e , the
only case that has been studied in the literature. Historically, this is
related to the now forgotten episode of the 17 keV neutrino which for
some time seemed to exist and which could have been a sterile neutrino
mixed with ν e . However, similar limits can be derived for ν µ -ν x or ν τ -ν x
mixing. The main difference is that the nonelectron neutrinos would
not normally obtain a chemical potential so that only a thermal ν µ and
ν τ population can be converted. A typical temperature is 30 MeV or
more, the average energy of a thermal population of relativistic fermions
is about 3T > ∼ 100 MeV, so there will be a significant thermal muon
population (m µ = 106 MeV). Thus sterile states can be produced in
charged-current muon scatterings in analogy to the above discussion
of ν x production involving electron scattering. The resulting limit on
the mixing angle may be slightly weaker than in the ν e -ν x case, but it
will be of the same general order of magnitude. 52 For ν τ -ν x mixing the
situation is different in that there are no thermally excited τ leptons.
Still, any reaction that produces ν τ ν τ pairs can also produce ν x and ν x
particles.
52 This remark is relevant in the context of recent speculations about the existence
of a 34 MeV sterile neutrino (Barger, Phillips, and Sarkar 1995) as an explanation of
an anomaly observed in the KARMEN experiment (KARMEN Collaboration 1995).