Stars as Laboratories for Fundamental Physics - MPP Theory Group

Chapter 6
Particle Dispersion and
Decays in Media
Dispersion effects in media have a significant impact on the propagation
of some low-mass particles (photons, neutrinos) while others are
left unaffected (axions and other Nambu-Goldstone bosons). The relationship
between forward scattering and refraction is derived, and the
dispersion relations for photons and neutrinos are thoroughly studied.
Modified particle dispersion relations allow certain decay processes to
occur in media that cannot occur in vacuum, notably the photon decay
γ → νν which dominates the neutrino emissivity in a wide range
of temperatures and densities (“plasma process”). Other examples are
the neutrino and majoron decay ν → νχ and χ → νν, respectively.
The rates for such processes are derived. The plasma process allows
one to derive the most restrictive limits on neutrino magnetic dipole
moments. Screening effects in reactions involving Coulomb scattering,
and neutrino electromagnetic form factors in media are discussed.
6.1 Introduction
Particles are the quantized excitations of certain fields—photons of the
electromagnetic field, electrons of the electron field, and so forth. It
is usually convenient to expand these fields in plane waves characterized
by frequencies ω and wave vectors k; the excitations of these modes
then exhibit a temporal and spatial behavior proportional to e −i(ωt−k·x) .
The frequency for a given wave number is determined by the dispersion
relation. Because (ω, k) is a four-vector, and because of Lorentz
invariance, in vacuum the quantity ω 2 − k 2 = m 2 is the same for all
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