Dispersive determinations of lattice HVP window quantities for muon g-2

We report on recent dispersive determinations of contributions to $a^{\rm HVP}_\mu$, the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon. The results provide data-driven determinations of components which are separately calculated and summed to produce the alternate lattice determination, with the goal of clarifying the region (or regions) in the dispersive spectrum responsible for recently observed discrepancies between lattice and dispersive results. Dispersive results are presented for the isospin-limit, light-quark-connected (lqc) and strange-connected-plus-full-𝑢𝑑𝑠-disconnected (s+lqd) components of, in addition to $a^{\rm HVP}_\mu$ itself, various “windowed” versions thereof. The discrepancy between lattice and dispersive results is shown to lie almost entirely in the lqc component, and to be largest for those observables that weight most heavily contributions from the $\rho$ peak region. We also show that all the observed discrepancies are removed if, in the dispersive determinations, recently released CMD-3 results for the $𝑒+𝑒−\rightarrow \pi^+\pi^-$ cross sections are used, in the region covered by the CMD-3 data, in place of the combination of results from previous experiments employed in the 2020 𝑔−2 Theory Initiative white paper assessment.