Stars as Laboratories for Fundamental Physics - MPP Theory Group

Neutrino Oscillations 281
and hence does not appear to be an exotic assumption. Whatever the
physical cause of particle masses, it seems unrelated to their gauge interactions!
Expanding the neutrino state in plane waves, each mass
eigenstate propagates as e −i(ωt−ki·x) where k 2 i = ω 2 − m 2 i . Therefore,
the different mass components develop phase differences, causing the
original superposition which formed a ν e to turn partially into other
flavors. Therefore, one can search for the disappearance of neutrinos
of a given flavor from a beam, or one can search for the appearance of
“wrong-flavored” states in a beam. The measured deficit of solar ν e ’s
(Chapter 10) has long been attributed to the oscillation phenomenon
even though a definitive proof is still missing.
Neutrino oscillations effectively measure a phase difference between
two components of a beam, much as the rotation of the plane of polarization
of linearly polarized light represents a phase difference between
the circularly polarized components of a beam in an optically active
medium. This method is sensitive to small differences in the refractive
index of the two components. For example, the Faraday rotation effect
can be used to measure very weak interstellar magnetic fields even
though the interstellar medium is quite dilute. Both for neutrinos and
photons, fine points of the dispersion relation have a significant impact
on the oscillation effect.
Wolfenstein (1978) was the first to recognize that the mediuminduced
modification of the neutrino dispersion relations (Sect. 6.7.1)
is not an academic affair, but rather of immediate relevance for some
neutrino oscillation experiments. In Mikheyev and Smirnov’s (1985)
seminal paper it was shown that oscillations can be “resonant” when a
beam passes through such a density gradient that the flavor branches
of the dispersion relation cross. This Mikheyev-Smirnov-Wolfenstein
(MSW) effect is very important in astrophysics because neutrinos are
naturally produced in the interior of stars and stream through a density
gradient into empty space.
An adiabatic crossing of the dispersion relations has the effect of
interchanging the flavor content of the neutrino flux even if the mixing
angle is very small. This effect is one version of the oscillation solution
of the solar neutrino problem. For suitable parameters it is also significant
in supernovae where different-flavored neutrinos are thought to be
produced with different energy spectra. The MSW effect could swap
the spectral characteristics of the neutrinos emerging from a newborn
neutron star, allowing for a number of fascinating novel effects.
If neutrinos had large magnetic dipole moments they could spinprecess
in magnetic fields. This effect is completely analogous to flavor