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)$L_{e}-L_{\mu}$, (ii) $L_{e}-L_{\tau}$ or (iii) $L_{\mu}-L_{\tau}$. 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 $L_{e}- L_{\mu,\tau}$ potential of the electrons in the Sun and the earth is shown to suppress the atmospheric neutrino $\nu_\mu \to \nu_\tau$ 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 $\alpha_{e\tau}< 6.4 \times 10^{-52}$ and $\alpha_{e\mu}< 5.5 \times 10^{-52}$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.