Stars as Laboratories for Fundamental Physics - MPP Theory Group

Solar Neutrinos 387
10.7 Spin and Spin-Flavor Oscillations
If the anticorrelation between disk-centered magnetic indicators of solar
activity and the event rate at Homestake is taken seriously, the only
plausible explanation put forth to date is that of magnetically induced
neutrino spin or spin-flavor transitions that were discussed in Sect. 8.4.
It was first pointed out by Voloshin and Vysotskiĭ (1986) that the varying
magnetic-field strength in the solar convective surface layers could
cause a time-varying depletion of the left-handed solar neutrino flux.
A refined discussion was provided by Voloshin, Vysotskiĭ, and Okun
(1986a,b) after whom this mechanism is called the VVO solution to
the solar neutrino problem.
Strong magnetic fields may also exist in the nonconvective interior
of the Sun. In principle, they could also cause magnetic oscillations
and thus reduce the solar neutrino flux (Werntz 1970; Cisneros 1971).
However, the amount of reduction would not be related to the magnetic
activity cycle which is confined to the convective surface layers with an
approximate depth of 0.3R ⊙ ≈ 2×10 10 cm = 200,000 km. The oscillation
length is given by Eq. (8.53) so that over this distance a complete
spin reversal is achieved for
µ ν B T ≈ 3×10 −10 µ B kG, (10.26)
where µ B = e/2m e is the Bohr magneton and B T is the magneticfield
strength perpendicular to the neutrino trajectory. Because the
magnetic field is mainly toroidal, the condition of transversality is automatically
satisfied.
Magnetic spin oscillations in vacuum do not have any energy dependence
and so the solar neutrino flux would be reduced by a common
factor for the entire spectrum. However, a large conversion rate is
only achieved if the spin states are nearly degenerate which is not the
case in media where refractive effects change the dispersion relation of
left-handed neutrinos. In the context of spin-flavor oscillations, degeneracy
can be achieved by a proper combination of medium refraction
and mass differences (resonant spin-flavor oscillations). In this case
the diagonal elements of the neutrino oscillation Hamiltonian involve
energy-dependent terms of the form (m 2 2 − m 2 1)/2E ν , causing a strong
energy dependence of the conversion probability. Therefore, the measured
signals in the detectors as well as the time variation at Homestake
and the absence of such a variation at Kamiokande can all be explained
by a suitable choice of neutrino parameters and magnetic-field profiles