Searching for hadronic scale new forces at (g − 2)μ’s lattice-vs-dispersion front

The anomalous magnetic moment of the muon (amu) serves as a precise test of the quantum nature of the Standard Model (SM) and its extensions. To identify beyond-SM physics, one must subtract the SM contributions, particularly the non-perturbative hadronic vacuum polarization (HVP) component. Two primary methods extract HVP: lattice computations and data-driven dispersion relations, enabling different forms of the “amu" that compare experimental and theoretical predictions. Additionally, comparing these two theoretical predictions forms the “HVP-test,” which is highly sensitive to hadronic-scale new physics. We explore the impact of a light (~ 100 MeV–1 GeV) vector boson on both tests. For a flavor-universal boson, new physics contributions effectively cancel in the amu test when using data-driven HVP. As an illustration of these general results, we consider two models: (i) the dark photon (A') and (ii) a baryon-number-coupled gauge boson (B). Combining these tests allows us to constrain the parameter space of A' and B, complementary to the existing searches.