Constraints on the two-pion contribution to hadronic vacuum polarization

Colangelo, Gilberto; Hoferichter, Martin; Stoffer, Peter (2021). Constraints on the two-pion contribution to hadronic vacuum polarization. Physics letters. B, 814, p. 136073. Elsevier 10.1016/j.physletb.2021.136073

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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, aHVPμ. 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 aμmeasurement. In this Letter we study to which extent this 2πcontribution 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−→2π process and study the correlations which thereby emerge between aHVPμ, the hadronic running of the fine-structure constant, the P-wave ππphase shift, and the charge radius of the pion. Inelastic effects play an important role, despite being constrained by the Eidelman–Łukaszuk bound. We identify scenarios in which aHVPμcan be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the e+e−→2π 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.

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