Constraints on the two-pion contribution to hadronic vacuum polarization

Gilberto Colangelo,Martin Hoferichter,Peter Stoffer

doi:10.1016/j.physletb.2021.136073

Gilberto Colangelo, Martin Hoferichter + Show 1 more

Open Access

https://doi.org/10.1016/j.physletb.2021.136073

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Abstract

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, aμHVP. 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 aμ measurement. In this Letter we study to which extent this 2π 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−→2π process and study the correlations which thereby emerge between aμHVP, the hadronic running of the fine-structure constant, the P-wave ππ phase 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 aμHVP 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−→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.

Highlights

In view of recent hints from lattice-QCD calculations that its contribution to the anomalous magnetic moment of the muon could be much larger than obtained from e+e− → hadrons cross-section data, with most of the changes concentrated at low energies
We relied on a dispersive representation of the pion vector form factor and studied which of its parameters could be varied without contradicting other low-energy observables besides the e+e− → 2π cross section itself
We identified three scenarios: (1) where only the elastic π π phase shift, or (2) where only inelastic effects, or

Summary

Introduction

The uncertainty in the Standard Model prediction for the anomalous magnetic moment of the muon [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28]. Electroweak fits due to its impact on the hadronic running of the fine-structure constant α [46,47,48,49] These analyses have shown that to avoid a significant tension with electroweak precision data, the changes to the hadronic cross sections need to be concentrated at low energies, at least below 2 GeV, a scenario indicated by Ref. The fact that these data, which have reached a remarkable level of precision, typically below 1%, can be well described by this highly constrained representation, is a nontrivial test on their quality Within this framework it is possible to address the question which changes become possible without violating analyticity and unitarity and without incurring other tensions elsewhere—besides those with the e+e− → 2π cross-section data. The comparison of the resulting predictions for the e+e− → 2π cross section to data allows us to quantify by how much the experimental cross sections would need to be changed to accommodate such an increase in aHμVP

The pion vector form factor

Changing HVP

Constraints due to the EŁ bound

Impact on the phase shift and cross section

Findings

Declaration of competing interest