Stars as Laboratories for Fundamental Physics - MPP Theory Group

Particle Dispersion and Decays in Media 239
this process is kinematically forbidden. However, longitudinal electromagnetic
excitations (plasmons), which exist only in the medium,
propagate such that for some momenta ω 2 − k 2 < 0 (space-like fourmomentum),
allowing for Cherenkov emission. One finds statements
in the literature that the neutrino energy transfer to the medium by
this process exceeded the transfer by (incoherent) ν-e scattering (e.g.
Oraevskiĭ and Semikoz 1984; Oraevskiĭ, Semikoz, and Smorodinskiĭ
1986; Semikoz 1987a). This is in conflict with the discussion of Kirzhnits,
Losyakov, and Chechin (1990) who found on general grounds that
the energy loss of a neutrino propagating in a stable medium was always
bounded from above by the collisional energy loss, apart from a
factor of order unity. Granting this, the Cherenkov process does not
seem to be of great practical importance.
If neutrinos have masses and mix, decays of the form ν 2 → ν 1 γ are
possible in vacuum, and can be kinematically possible in a medium if
the photon “effective mass” does not exceed the neutrino mass difference
m 2 − m 1 . If kinematically allowed, this decay receives a contribution
from the medium-induced coupling which may far exceed the
vacuum decay rate. Explicit calculations were performed by a number
of authors 36 who unfortunately ignored the kinematic constraint
imposed by the photon dispersion relation. This is not a reasonable
approximation in view of the relatively small neutrino masses that remain
of practical interest. Further, in order to judge the importance
of the medium-induced decay it is not relevant to compare with the
vacuum decay rate, but rather one should compare with the collisional
transition rate ν 2 e → eν 1 (mediated by photon exchange) which is the
process with which the coherent reaction directly competes.
The photon decay as well as the Cherenkov process and the mediuminduced
neutrino decay all have in common that the neutrino couples
to an electromagnetic field which is a freely propagating wave, obeying
the dispersion relation in the medium which is ω 2 − k 2 = π T,L (ω, k)
for transverse and longitudinal excitations, respectively. However, one
may also consider the effect of a static external electric or magnetic
field. 37 To this end, one must take the static limit ω → 0 of the
vertex functions Λ αβ
V,A(ω, k). For an external static electric field the
only nonvanishing component of the vector potential A µ is A 0 . Then
36 D’Olivo, Nieves, and Pal (1990); Kuo and Pantaleone (1990); Giunti, Kim, and
Lam (1991).
37 This issue has been investigated in many works, e.g. Oraevskiĭ and Semikoz
(1985, 1987), Semikoz (1987a,b), Nieves and Pal (1989c, 1994), Semikoz and
Smorodinskiĭ (1988, 1989), and D’Olivo, Nieves, and Pal (1989).