Constraining Ultra-Light Vector Bosons via Solar Neutrino Oscillations: The Gauged $L_{\mu }-L_{\tau }$ Model and Prospects for JUNO and XLZD

Abstract

We present an extension of the Standard Model based upon the gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ symmetry, featuring an ultra-light vector boson that couples to the difference of muon and tau lepton numbers. This anomaly-free construction, historically motivated by the muon's anomalous magnetic moment, is employed here as an independent phenomenological framework for solar neutrino physics. Through kinetic mixing with the photon, the $Z^{\prime }$ boson generates an effective matter potential within the solar interior, thereby modifying neutrino flavour oscillations via the Mikheyev--Smirnov--Wolfenstein mechanism. Utilising recent solar neutrino measurements from Borexino, SNO, and Super-Kamiokande, together with an up-to-date standard solar model, we constrain the boson mass to be below $5.7\times 10^{-17}\mathrm{eV}$, a potential ultra-light dark matter candidate. The optimal model, with coupling parameter ${\eta }_o\approx -2$, yields ${\chi }_{\nu }^2=2.7$, compared with ${\chi }_{\nu }^2=3.1$ for the standard three-flavour scenario. This best fit corresponds to an effective four-fermion coupling $g_{Z^{\prime }}^2\epsilon /m_{Z^{\prime }}^2\approx 6.6\times 10^{-23}{\mathrm{eV}}^{-2}$, approximately $5.7$ times the Fermi constant, equivalent for $\epsilon \approx 1$ and a reference mediator mass of $1\mathrm{eV}$ to a gauge coupling $g_{Z^{\prime }}\approx 8\times 10^{-12}$. We also present projections for forthcoming experiments: the Jiangmen Underground Neutrino Observatory (JUNO), operating since August 2025 with world-leading precision on oscillation parameters, together with the XLZD consortium, should substantially refine these constraints. Such ultra-light particles may address long-standing discrepancies in galaxy simulations within the cold dark matter paradigm, whilst terrestrial long-baseline neutrino experiments provide complementary probes of this parameter space.

9 pages, 6 figures, accepted for publication in Phys. Rev. D