An Axial-Vector Leptophilic Fifth Force Sourced by Solar Neutrinos

TL;DR

The paper introduces a purely leptophilic axial-vector fifth force mediated by a light $A'$ that couples axially to charged leptons and left-handed neutrinos, with solar neutrinos acting as an extended Sun–Earth source. It analyzes two anomaly-free realizations ($L^{AV}_\mu$ and $L^{AV}_\mu-L^{AV}_\tau$) and derives the $A'$ field sourced at Earth, leading to a diurnal, sign-changing contribution to the muon anomalous magnetic moment $(g-2)_\mu$ in storage rings, plus a time-independent offset. Using muon $g-2$ data, it derives bounds $g' \lesssim \mathcal{O}(10^{-19})$ for a light mediator, while electron-channel constraints yield $g'_e \lesssim \mathcal{O}(10^{-22})$ via spin-sensor mappings; accounting for day–night modulation strengthens these muon bounds by about an order of magnitude. The work highlights the potential for time-domain particle-physics probes leveraging solar neutrino fluxes to constrain new long-range forces and underscores model independence via anomaly-free charge patterns. Overall, the solar-neutrino–sourced axial-vector interaction provides a novel avenue to test leptophilic new physics with current and near-future precision experiments.

Abstract

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, $(g-2)_μ$, 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.

Figures (4)

• Figure 1: The averaged oscillation probability for solar neutrinos with different propagation length. The green (red, and blue) solid line represents the probability that electron neutrino oscillate to electron (muon, and tau) neutrino. The integration region have a center value at $E_\nu = \bar{E}_{\mathrm{pp}}=$ 0.267 MeV together with a width $\Delta E_\nu = 1$ keV in both side. The gray dashed (dotted) line represents the radii of Sun (Earth obit).
• Figure 2: The oscillation probability for solar neutrinos the oscillation probability is given by Eq. \ref{['eq:solar_probability']}, therefore it do not have any information of $r$. However, as such equation is usually used to calculate the oscillation probability at Earth, maybe we can take $r = 1$ AU as a function of neutrino energy. The red (blue) solid line represents the probability that electron neutrino oscillate to muon (tau) neutrino. The gray dashed (dotted) line represents the maximal (averaged) energy of pp chain neutrino.
• Figure 3: The variation of the frequency respect to times in $L^{\rm AV}_\mu$ model. The red (blue) line represents the variation from $\delta \omega_z$ (${|\delta \vec{\omega}|^2}/{2 |\vec{\omega}|}$). Here we take $m_{A'} = 0$ and $g'_{\mu} = 10^{-18}$.
• Figure 4: Constraint to the $L^{\rm AV}_\mu$ model (red) and $L^{\rm AV}_\mu - L^{\rm AV}_\tau$ model from muon $g-2$ experiment Muong-2:2025xyk. The solid (dashed) line represent the constraint (not) considering the daily modulation.