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

In the minimal standard model it is possible to gauge any one of the following global symmetries in an anomaly free way: (i) Le-Lμ, (ii) Le-Lτ or (iii) Lμ-Lτ. 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 Le-Lμ,τ potential of the electrons in the Sun and the Earth is shown to suppress the atmospheric neutrino νμ→ντ 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 αeτ<6.4x10-52 and αeμ<5.5x10-52 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