Leptophilic Interactions in Nuclear Energy Density Functional Theory

We develop a unified theoretical framework that embeds a light leptophilic vector boson into nuclear energy density functional (EDF) theory. Starting from an underlying leptophilic gauge interaction, the mediator is integrated out in the static limit, yielding an effective current–current interaction that couples proton and lepton densities. This interaction is incorporated self-consistently into relativistic mean-field equations, defining a leptophilic extension of conventional nuclear EDFs. The resulting leptophilic EDF induces correlated modifications of proton and lepton chemical potentials, directly affecting beta equilibrium in dense matter. In uniform matter, these effects lead to percent-level changes in the proton fraction, symmetry energy, and equation of state within phenomenologically allowed parameter ranges. In finite nuclei, the modified proton mean field generates shifts of $10^{-3}$–$10^{-2},\mathrm{fm}$ in neutron-skin thicknesses, comparable to current experimental sensitivities. Our results demonstrate that light leptophilic interactions leave coherent and experimentally accessible imprints on both nuclear structure and dense-matter observables. The framework introduced here provides a controlled and realistic extension of nuclear EDF theory, enabling nuclear systems to serve as laboratories for probing new physics in the leptonic sector.

💡 Research Summary

The authors present a comprehensive theoretical framework that incorporates a light leptophilic vector boson, denoted Zℓ, into nuclear energy‑density‑functional (EDF) theory. Starting from a U(1)′ℓ gauge sector in which charged leptons (e, μ, τ) and optionally their neutrinos carry a universal vector charge, the boson couples to a leptonic current with strength gℓ. A small kinetic‑mixing parameter ε between the hypercharge gauge field and Zℓ induces an effective coupling gp≈ε e to the proton current, allowing the new interaction to affect hadronic systems without violating existing constraints.

In the static limit, where the typical nuclear momentum kF is much smaller than the boson mass mZℓ (chosen in the 5–100 MeV range), the heavy vector field can be integrated out. This yields a non‑local current–current term proportional to the Yukawa Green’s function. For mZℓ≫kF the interaction becomes effectively local, leading to an additional energy‑density contribution

E_Zℓ = ½ mZℓ⁻²