Constraints on flavor-dependent long range forces from neutrino experiments

We study the impact of flavor-dependent long range leptonic forces mediated by the $L_e-L_\mu$ or $L_e -L_\tau$ gauge bosons on the solar neutrino oscillations, when the interaction range $R_{LR}$ is much larger than the Earth-Sun distance. The solar and atmospheric neutrino mass scales do not get trivially decoupled in this situation even if $\theta_{13}$ is vanishingly small. In addition, for $\alpha \gsim 10^{-52}$ and normal hierarchy, resonant enhancement of $\theta_{13}$ may give rise to strong energy dependent effects on the $\nu_e$ survival probability. A complete three generation analysis of the solar neutrino and KamLAND data gives the $3\sigma$ limits $\alpha_{e\mu} < 3.4 \times 10^{-53}$ and $\alpha_{e\tau} < 2.5 \times 10^{-53}$ when $R_{LR}$ is much smaller than our distance from the galactic center. With larger $R_{LR}$, the collective LR potential due to all the electrons in the galaxy becomes significant and the constraints on $\alpha$ become stronger by upto two orders of magnitude.