Neutrino Propagation in a Strongly Magnetized Medium

Abstract

We derive general expressions at the one-loop level for the coefficients of the covariant structure of the neutrino self-energy in the presence of a constant magnetic field. The neutrino energy spectrum and index of refraction are obtained for neutral and charged media in the strong-field limit ($M_W\gg \sqrt{B}\gg m_e,T,\mu ,|\mathbf{p}|$) using the lowest Landau level approximation. The results found within the lowest Landau level approximation are numerically validated, summing in all Landau levels, for strong $B\gg T^2$ and weakly-strong $B\gtrsim T^2$ fields. The neutrino energy in leading order of the Fermi coupling constant is expressed as the sum of three terms: a kinetic-energy term, a term of interaction between the magnetic field and an induced neutrino magnetic moment, and a rest-energy term. The leading radiative correction to the kinetic-energy term depends linearly on the magnetic field strength and is independent of the chemical potential. The other two terms are only present in a charged medium. For strong and weakly-strong fields, it is found that the field-dependent correction to the neutrino energy in a neutral medium is much larger than the thermal one. Possible applications to cosmology and astrophysics are considered.

23 pages, 4 figures. Corrected misprints in references

References in corpus (7)

• The Magnetized Universe
• Generation of large scale magnetic fields at recombination epoch
• Spontaneous rotational symmetry breaking and roton like excitations in gauged sigma-model at finite density
• Electroweak phase diagram at finite lepton number density
• Spontaneous symmetry breaking in gauge theories via Bose-Einstein condensation
• Neutrinos under Strong Magnetic Fields
• Chiral fermion mass and dispersion relations at finite temperature in the presence of hypermagnetic fields

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