Constraints on flavour-dependent long-range forces from atmospheric neutrino observations at Super-Kamiokande

Abstract

In the minimal standard model it is possible to gauge any one of the following global symmetries in an anomaly free way: (i)$L_{e}-L_μ$, (ii) $L_{e}-L_τ$ or (iii) $L_μ-L_τ$. If the gauge boson corresponding to (i) or (ii) is (nearly) massless then it will show up as a long range composition dependent fifth force between macroscopic objects. Such a force will also influence neutrino oscillations due to its flavour-dependence. We show that the latter effect is quite significant in spite of very strong constraints on the relevant gauge couplings from the fifth force experiments. In particular, the $L_{e}- L_{μ,τ}$ potential of the electrons in the Sun and the earth is shown to suppress the atmospheric neutrino $ν_μ\to ν_τ$ oscillations which have been observed at Super-Kamiokande. The Super-K data of oscillation of multi-GeV atmospheric neutrinos can be used to put an upper bound on coupling $α_{eτ}< 6.4 \times 10^{-52}$ and $α_{eμ}< 5.5 \times 10^{-52}$at 90% CL when the range of the force is the earth-sun distance. This is an improvement by two orders on the earlier fifth force bounds in this range.