Stars as Laboratories for Fundamental Physics - MPP Theory Group

272 Chapter 7
coupling in gauge theories were performed by Levine (1966) and Cung
and Yoshimura (1975); for more recent discussions in the framework of
the standard model see Nieves, Pal, and Unger (1983), Nieves (1987),
Dodelson and Feinberg (1991), Liu (1991), Langacker and Liu (1992),
Kuznetsov and Mikheev (1993), and Dicus and Repko (1993). This
two-photon coupling leads to a higher-order contribution to the neutrino
refractive index in a bath of photons (Sect. 6.7.2). However, this
and other consequences do not seem to be important in any astrophysical
or laboratory setting of practical interest.
For neutrinos with masses and mixings there is a decay amplitude
ν → ν ′ γγ which can dominate for a small range of neutrino masses
below m ν = 2m e as discussed by Nieves (1983) and Ghosh (1984).
Explicit results were given in Sect. 7.2.2 above.
One of the photons may represent an external electric or magnetic
field, i.e. one may consider the neutrino decay ν → ν ′ γ in the presence
of a strong external field which would modify the propagators
of the intermediate charged leptons. For very strong fields it appears
that a substantial decay rate can obtain (Gvozdev, Mikheev, and Vassilevskaya
1992a,b, 1993, 1994a,b). From this literature it does not
seem to become entirely clear under which if any circumstances these
results might be of practical interest for, say, the decay of supernova or
neutron-star neutrinos.
7.4 Electromagnetic Processes
The presence of electromagnetic dipole and transition moments implies
that neutrinos couple directly to the electromagnetic field, allowing for
a variety of nonstandard processes (Fig. 7.8). Most obviously, neutrinos
can scatter on electrons by photon exchange. The ν-e scattering cross
section (electrons at rest in the laboratory frame) was given, e.g. by
Vogel and Engel (1989)
dσ
dT = G2 Fm e
2π
[(C V + C A ) 2 + (C V − C A ) 2 (1 − T E ν
) 2
+ (C 2 A − C 2 V ) m eT
E 2 ν
]
+ αµ 2 ν
[ 1
T − 1 E ν
]
, (7.24)
where C V and C A are the weak coupling constants given in Appendix B,
T is the electron recoil energy with the limits 0 ≤ T ≤ 2E 2 ν/(2E ν +m e ),
and µ ν is the neutrino dipole moment.