Update of Euclidean windows of the hadronic vacuum polarization

We compute the standard Euclidean window of the hadronic vacuum polarization using multiple independent blinded analyses. We improve the continuum and infinite-volume extrapolations of the dominant quark-connected light-quark isospin-symmetric contribution and address additional subleading systematic effects from sea-charm quarks and residual chiral-symmetry breaking from first principles. We find <math display="inline"><msubsup><mi>a</mi><mi mathvariant="normal">μ</mi><mi mathvariant="normal">W</mi></msubsup><mo>=</mo><mn>235.56</mn><mo stretchy="false">(</mo><mn>65</mn><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>50</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math>, which is in <math display="inline"><mn>3.8</mn><mi>σ</mi></math> tension with the recently published dispersive result of <math display="inline"><msubsup><mi>a</mi><mi mathvariant="normal">μ</mi><mi mathvariant="normal">W</mi></msubsup><mo>=</mo><mn>229.4</mn><mo stretchy="false">(</mo><mn>1.4</mn><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>10</mn></mrow></msup></math> [G. Colangelo, A. X. El-Khadra, M. Hoferichter, A. Keshavarzi, C. Lehner, P. Stoffer, and T. Teubner, Phys. Lett. B 833, 137313 (2022)] and in agreement with other recent lattice determinations. We also provide a result for the standard short-distance window. The results reported here are unchanged compared to our presentation at the Edinburgh workshop of the g-2 Theory Initiative in 2022 [C. Lehner, Talk Presented at the 5th Plenary Meeting of the g-2 Theory Initiative in Edinburgh (2022)].