Stars as Laboratories for Fundamental Physics - MPP Theory Group

Neutrino Oscillations 303
It is also instructive to look at a vertical cut through this contour
plot, except that it is more useful to represent it as a function of E ν for
a fixed ∆m 2 rather than the reverse. Both possibilities are equivalent
because what appears is the combination ∆m 2 /2E ν . The result is the
MSW bathtub shown in Fig. 8.10 for ∆m 2 = 3×10 −5 eV 2 and sin 2 2θ 0 =
0.01 which is one set of parameters that might solve the solar neutrino
problem (Chapter 10).
The main point of Fig. 8.10 is that resonant neutrino oscillations
modify the spectrum of observable ν e ’s differently for different energies.
Low-energy neutrinos remain entirely unaffected, intermediate-energy
ones are strongly suppressed, and the effect on high-energy states varies
over a broad interval. There, the shape of the observable spectrum is
modified relative to the source spectrum.
8.3.6 Neutrino Oscillations without Vacuum Mixing
Neutrino oscillations in vacuum or in a medium arise because in the
weak-interaction basis the matrix of effective neutrino masses, Meff,
2
has off-diagonal elements which induce transitions between, say, an
initial ν e and a ν µ . The effect of the medium is to modify the diagonal
elements of this matrix, possibly such that different flavor states become
degenerate, causing the effect of resonant oscillations. Conceivably,
oscillations could occur even if Meff
2 = 0 in vacuum so that in the
standard model there are no off-diagonal terms.
The absence of off-diagonal medium contributions to Meff
2 within
the standard model reflects the absence of flavor-changing neutral currents
(Sect. 7.2). It cannot be excluded experimentally, however, that
for neutrinos such currents exist on some level, implying that a ν e , for
example, sometimes emerges as a ν µ from a collision with another particle.
In the forward direction this would cause an “off-diagonal refractive
index” so that mixing and thus oscillations would be induced by the
medium (Valle 1987; Fukugita and Yanagida 1988). Certain supersymmetric
extensions of the standard model with R-parity breaking predict
such effects (Guzzo, Masiero, and Petcov 1991; Kapetanakis, Mayr, and
Nilles 1992). Therefore, if neutrino oscillations indeed explain the solar
neutrino problem (Chapter 10) this does not inevitably imply neutrino
vacuum masses and mixings—it could also point to the existence of
flavor-changing neutral currents. An analytic description of two-flavor
oscillations for this case was given by Guzzo and Petcov (1991) while a
detailed parameter study for the solution of the solar neutrino problem
was provided by Barger, Phillips, and Whisnant (1991).