Exploring Flavor-Dependent Long-Range Forces in Long-Baseline Neutrino Oscillation Experiments

The Standard Model gauge group can be extended with minimal matter content by introducing anomaly free U(1) symmetry, such as $L_e-L_{\mu}$ or $L_e-L_{\tau}$. If the neutral gauge boson corresponding to this abelian symmetry is ultra-light, then it will give rise to flavor-dependent long-range leptonic force, which can have significant impact on neutrino oscillations. For an instance, the electrons inside the Sun can generate a flavor-dependent long-range potential at the Earth surface, which can suppress the $\nu_{\mu} \to \nu_e$ appearance probability in terrestrial experiments. The sign of this potential is opposite for anti-neutrinos, and affects the oscillations of (anti-)neutrinos in different fashion. This feature invokes fake CP-asymmetry like the SM matter effect and can severely affect the leptonic CP-violation searches in long-baseline experiments. In this paper, we study in detail the possible impacts of these long-range flavor-diagonal neutral current interactions due to $L_e-L_{\mu}$ symmetry, when (anti-)neutrinos travel from Fermilab to Homestake (1300 km) and CERN to Pyh\"asalmi (2290 km) in the context of future high-precision superbeam facilities, DUNE and LBNO respectively. If there is no signal of long-range force, DUNE (LBNO) can place stringent constraint on the effective gauge coupling $\alpha_{e\mu} < 1.9 \times 10^{-53}~(7.8 \times 10^{-54})$ at 90% C.L., which is almost 30 (70) times better than the existing bound from the Super-Kamiokande experiment. We also observe that if $\alpha_{e\mu} \geq 2 \times 10^{-52}$, the CP-violation discovery reach of these future facilities vanishes completely. The mass hierarchy measurement remains robust in DUNE (LBNO) if $\alpha_{e\mu} < 5 \times 10^{-52}~(10^{-52})$.