Determine the Z–Z′ mixing factor controlling the neutron-sourced long-range potential in Lμ−Lτ models

Determine the value of the neutral-boson mixing combination (ξ − sinθ_W χ) between Z and Z′ that sets the strength of the four-fermion interaction J′_σ J_3^σ and thereby the neutron-sourced long-range matter potential in gauged L_μ−L_τ symmetry, in order to quantify its impact on neutrino oscillations.

Background

For the L_μ−L_τ symmetry, ordinary matter contains no μ or τ charges, so the dominant long-range potential arises via Z–Z′ mixing rather than direct Z′ exchange. The relevant strength depends on the mixing factor (ξ − sinθ_W χ), multiplying the standard and new currents.

Although there are indirect upper limits, the actual value of this mixing factor remains undetermined. The authors therefore place bounds on the effective coupling g_{Z′}(ξ − sinθ_W χ), highlighting the need to determine the mixing to fully characterize the interaction.