Long-range lepton flavor interactions and neutrino oscillations

Recent results from the MINOS accelerator neutrino experiment suggest a possible difference between ν_μ and ν_μ disappearance oscillation parameters, which one may ascribe to a new long-distance potential acting on neutrinos. As a specific example, we consider a model with gauged B-Lₑ-2L_τ number that contains an extremely light new vector boson m_Z^'<10^-18 eV and extraordinarily weak coupling α^'10^-52 (or larger m_Z^' if cosmology bounds on neutrino decay apply). In that case, differences between ν_μ→ν_τ and ν_μ→ν_τ oscillations can result from a long-range potential due to neutrons in the Earth and the Sun that distinguishes ν_μ and ν_τ on Earth, with a potential difference of ~6×10^-14 eV, and changes sign for antineutrinos. We show that existing solar, reactor, accelerator, and atmospheric neutrino oscillation constraints can be largely accommodated for values of parameters that help explain the possible MINOS anomaly by this new physics, although there is some tension with atmospheric constraints. A long-range interaction, consistent with current bounds, could have very pronounced effects on atmospheric neutrino disappearance in the 15--40 GeV range that will be studied with the IceCube DeepCore array, currently in operation, and can have a significant effect on future high-precision long-baseline oscillation experiments that aim for ±1% sensitivity, in ν_μ and ν_μ disappearance, separately. Together, these experiments can extend the reach for new long-distance effects well beyond current bounds and test their relevance to the aforementioned MINOS anomaly. We also point out that long-range potentials originating from the Sun could lead to annual modulations of neutrino data at the percent level, due to the variation of the Earth-Sun distance. A similar phenomenology is shown to apply to other potential new gauge symmetries such as L-3L_τ and B-3L_τ.