Data-based determination of the isospin-limit light-quark-connected contribution to the anomalous magnetic moment of the muon

We describe how recent determinations of exclusive-mode contributions to $a_{\mu }^{\mathrm{L}\mathrm{O},\mathrm{H}\mathrm{V}\mathrm{P}}$, the leading-order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, can be used to provide, up to small electromagnetic (EM) corrections accessible from the lattice, a data-based dispersive determination of $a_{\mu }^{\mathrm{l}\mathrm{q}\mathrm{c};\mathrm{I}\mathrm{L}}$, the isospin-limit, light-quark-connected contribution to $a_{\mu }^{\mathrm{L}\mathrm{O},\mathrm{H}\mathrm{V}\mathrm{P}}$. Such a determination is of interest in view of the existence of a number of lattice results for this quantity, emerging evidence for a tension between lattice and dispersive determinations of $a_{\mu }^{\mathrm{L}\mathrm{O},\mathrm{H}\mathrm{V}\mathrm{P}}$, and the desire to clarify the source of this tension. Taking as input for the small EM correction that must be applied to the purely data-driven dispersive determination the result $-0.93(58)\times {10}^{-10}$ obtained in a recent BMW lattice study, we find $a_{\mu }^{\mathrm{l}\mathrm{q}\mathrm{c};\mathrm{I}\mathrm{L}}$ to be $635.0(2.7)\times {10}^{-10}$ if the results of Keshavarzi, Nomura and Teubner are used for the exclusive-mode contributions and $638.4(4.1)\times {10}^{-10}$ if instead those of Davier, Höcker, Malaescu and Zhang are used.