Constraints on the two-pion contribution to hadronic vacuum polarization

At low energies hadronic vacuum polarization (HVP) is strongly dominated by two-pion intermediate states, which are responsible for about 70% of the HVP contribution to the anomalous magnetic moment of the muon, a(mu)(HVP). Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of e(+) e(-) -> hadrons data, at a level which would contest the long-standing discrepancy with the a(mu) measurement. In this Letter we study to which extent this 2 pi contribution can be modified without, at the same time, producing a conflict elsewhere in low-energy hadron phenomenology. To this end we consider a dispersive representation of the e(+) e(-) -> 2 pi process and study the correlations which thereby emerge between a(mu)(HVP), the hadronic running of the fine-structure constant, the P-wave pi pi phase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman-Lukaszuk bound. We identify scenarios in which a(mu)(HVP) can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the e(+) e(-) -> 2 pi cross section. In the combined scenario, which minimizes the effect in the cross section, a uniform shift around 4% is required. At the same time both the analytic continuation into the space-like region and the pion charge radius are affected at a level that could be probed in future lattice-QCD calculations. (C) 2021 The Author(s). Published by Elsevier B.V.