Coordinate-space calculation of the window observable for the hadronic vacuum polarization contribution to
En-Hung Chao (Physics Department, Columbia University, New York, New York 10027, USA, PRISMA+ Cluster of Excellence & Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany); Harvey B. Meyer (GSI Helmholtzzentrum für Schwerionenforschung, D-64291 Darmstadt, Germany, PRISMA+ Cluster of Excellence & Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany, Helmholtz Institut Mainz, Staudingerweg 18, D-55128 Mainz, Germany); Julian Parrino (PRISMA+ Cluster of Excellence & Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, D-55099 Mainz, Germany)
The “intermediate window quantity” of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon allows for a high-precision comparison between the data-driven approach and lattice QCD. The existing lattice results, which presently show good consistency among each other, are in strong tension with the data-driven determination. In order to check for a potentially common source of systematic error of the lattice calculations, which are all based on the time-momentum representation (TMR), we perform a calculation using a Lorentz-covariant coordinate-space (CCS) representation. We present results for the isovector and the connected strange-quark contributions to the intermediate window quantity at a reference point in the plane, in the continuum and infinite-volume limit, based on four different lattice spacings. Our results are in good agreement with those of the recent TMR-based Mainz-CLS publication.
