Stars as Laboratories for Fundamental Physics - MPP Theory Group

264 Chapter 7
however, the three-neutrino channel remains forbidden by the absence
of flavor-changing neutral currents because the flavor content of ν and
ν ′ in Fig. 7.5 must remain unaltered by the Z ◦ vertex. Therefore, in
the standard model low-mass neutrinos can decay only by higher-order
(radiative) amplitudes.
“Heavy” neutrinos ν h with m h > 2m e ≈ 1 MeV may decay at treelevel
through the channel ν h → ν e e + e − at a rate
1
τ e + e − = |U eh | 2 G 2 F
3 (4π) 3 m5 h Φ(m h )
= |U eh | 2 3.5×10 −5 s −1 m 5 MeV Φ(m h ), (7.9)
where U eh is the mixing amplitude between ν h and ν e , G F is the Fermi
constant, and m MeV ≡ m h /MeV. The phase-space factor is (Shrock
1981)
Φ(m h ) = (1 − 4a) 1/2 (1 − 14a − 2a 2 − 12a 3 )
+ 24a 2 (1 − a 2 ) ln
with a ≡ m 2 e/m 2 h; it is shown in Fig. 7.6.
1 + (1 − 4a)1/2
1 − (1 − 4a) 1/2 (7.10)
Fig. 7.6. Phase space factor for ν h → ν e e + e − according to Eq. (7.10).
The one- and two-photon decay modes arise in the standard model
with mixed neutrinos from the amplitudes shown in Fig. 7.7. Turn first
to the one-photon decay ν i → ν j γ with the neutrino masses m i > m j .