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Implications of SU(2)_L x U(1) Symmetry for SIM(2) Invariant Neutrino Masses

Alan Dunn·Thomas Mehen
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Abstract

We consider SU(2)_L x U(1) gauge invariant generalizations of a nonlocal, Lorentz violating mass term for neutrinos that preserves a SIM(2) subgroup. This induces Lorentz violating effects in QED as well as tree-level lepton family number violating interactions. Measurements of g_e - 2 with trapped electrons severely constrain possible SIM(2) mass terms for electrons which violate C invariance. We study Lorentz violating effects in a C invariant and SIM(2) invariant extension of QED. We examine the Lorentz violating interactions of nonrelativistic electrons with electromagnetic fields to determine their impact on the spectroscopy of hydrogen-like atoms and g_e - 2 measurements with trapped electrons. Generically, Lorentz violating corrections are suppressed by m_ν^2/m_e^2 and are within experimental limits. We study one-loop corrections to electron and photon self-energies and point out the need for a prescription to handle IR divergences induced by the nonlocality of the theory. We also calculate the tree level contribution to μto e + γfrom SIM(2) invariant mass terms.

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Alan Dunn, Thomas Mehen. 2006-10-16. Implications of SU(2)_L x U(1) Symmetry for SIM(2) Invariant Neutrino Masses. https://arxiv.org/abs/hep-ph/0610202

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