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Constraints on the two-pion contribution to hadronic vacuum polarization
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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, $a_\mu^\text{HVP}$. Lattice-QCD evaluations of the latter indicate that it might be larger than calculated dispersively on the basis of $e^+e^-\to\text{hadrons}$ 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 $e^+e^- \to 2\pi$ process and study the correlations which thereby emerge between $a_\mu^\text{HVP}$, 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 $a_\mu^\text{HVP}$ can be altered substantially, driven by changes in the phase shift and/or the inelastic contribution, and illustrate the ensuing changes in the $e^+e^-\to 2\pi$ 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.
Forward citations
Cited by 6 Pith papers
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Precision evaluation of the $\eta$- and $\eta'$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
A new dispersive analysis of the eta and eta-prime transition form factors gives a_mu(eta-pole) = 14.7(9) x 10^-11 and a_mu(eta'-pole) = 13.5(7) x 10^-11, with combined pseudoscalar poles at 91.2(+2.9,-2.4) x 10^-11.
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Towards testing $(g-2)_\tau$ in $e^+e^-\to\tau^+\tau^-$: radiative corrections and projections for Belle II
A complete one-loop QED calculation for polarized e+e- to tau+tau- is implemented in the McMule Monte-Carlo code, showing that Belle II with a polarized beam could test the tau anomalous magnetic moment at the 10^-5 level.
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Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
Using a dispersive formalism with experimental transition form factors and short-distance constraints, the authors obtain a_mu^HLbL = 101.9(7.9) x 10^-11, halving the previous uncertainty.
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Dispersive analysis of the pion vector form factor without zeros
Imposing the absence of complex zeros in the pion vector form factor reduces the dominant systematic uncertainty and makes the tensions between CMD-3 and other e+e- data sets appear sharper, including in the pion char...
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Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
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Dispersion relation for hadronic light-by-light scattering: subleading contributions
A dispersive evaluation gives a_mu^HLbL subleading = 33.2(7.2) x 10^-11 and total = 101.9(7.9) x 10^-11.
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