An Axial-Vector Leptophilic Fifth Force Sourced by Solar Neutrinos

We investigate long-range, purely leptophilic axial-vector interactions mediated by a light gauge boson $A'$ that couples to charged leptons and, by weak symmetry, to left-handed neutrinos. We analyze two realizations, a minimal effective model with muon-only couplings and an anomaly-free axial $U(1)'$ with inter-generation cancellations. In both cases, the solar neutrino flux acts as an extended current that sources a macroscopic $A'$ field at Earth, with spatial components aligned along the Sun-Earth direction. This field produces a distinctive signature in storage-ring measurements of the muon anomalous magnetic moment, $(g-2)_\mu$, namely a diurnal, sign-changing contribution that is positive during daytime and negative at night, superimposed on a time-independent positive offset. We obtain bounds $g' \lesssim {O}(10^{-19})$ in both model frameworks for a light, effectively massless mediator. For completeness, we map the solar-neutrino-sourced potential to electron spin-sensor experiments and find $g' \lesssim {O}(10^{-22})$ in the electron channel.