Two-pion contribution to hadronic vacuum polarization

Abstract

We present a detailed analysis of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ data up to $\sqrt{s}=1\text{GeV}$ in the framework of dispersion relations. Starting from a family of $\pi \pi$ $P$-wave phase shifts, as derived from a previous Roy-equation analysis of $\pi \pi$ scattering, we write down an extended Omnès representation of the pion vector form factor in terms of a few free parameters and study to which extent the modern high-statistics data sets can be described by the resulting fit function that follows from general principles of QCD. We find that statistically acceptable fits do become possible as soon as potential uncertainties in the energy calibration are taken into account, providing a strong cross check on the internal consistency of the data sets, but preferring a mass of the $\omega$ meson significantly lower than the current PDG average. In addition to a complete treatment of statistical and systematic errors propagated from the data, we perform a comprehensive analysis of the systematic errors in the dispersive representation and derive the consequences for the two-pion contribution to hadronic vacuum polarization. In a global fit to both time- and space-like data sets we find $a_{\mu }^{\pi \pi }{|}_{\le 1\text{GeV}}=495.0(1.5)(2.1)\times 10^{-10}$ and $a_{\mu }^{\pi \pi }{|}_{\le 0.63\text{GeV}}=132.8(0.4)(1.0)\times 10^{-10}$. While the constraints are thus most stringent for low energies, we obtain uncertainty estimates throughout the whole energy range that should prove valuable in corroborating the corresponding contribution to the anomalous magnetic moment of the muon. As side products, we obtain improved constraints on the $\pi \pi$ $P$-wave, valuable input for future global analyses of low-energy $\pi \pi$ scattering, as well as a determination of the pion charge radius, $⟨r_{\pi }^2⟩=0.429(1)(4){\text{fm}}^2$.

40 pages, 16 figures, 13 tables; version published in JHEP

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• Radiative Muon Mass Models and $(g-2{)}_{\mu }$
• On-shell Renormalization with Vector-like Leptons, One-loop Muon-Higgs Coupling and Muon g-2
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$
• Leptonic probes of Alternative Left-Right Symmetric Models
• Lepton $g-2$ and $W$-boson mass anomalies in the DFSZ axion model
• Flavour anomalies meet flavour symmetry
• Contributions to the Muon $g-2$ from a Three-Form Field
• The mass-degenerate SM-like Higgs and anomaly of $(g-2{)}_{\mu }$ in $\mu$-term extended NMSSM
• Flavor- and CP-safe explanation of $g_{\mu }-2$ anomaly
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Muon $g-2$ Anomaly from a Massive Spin-2 Particle
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Round table on Standard Model Anomalies
• Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections
• Dispersive determination of resonances from $\pi \pi$ scattering data
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• A pedagogical review on muon $g-2$
• GM2Calc-2 for the 2HDM
• Unitarity bounds on extensions of Higgs sector
• Systematic analysis of search strategies for $L_{\mu }-L_{\tau }$ gauge bosons at Belle II
• Semi-Visible Dark Photon Phenomenology at the GeV Scale
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Muon g-2 from Millicharged Hidden Confining Sector
• Fermiophobic $Z^{\prime }$ model for simultaneously explaining the muon anomalies $R_{K^{(\ast )}}$ and $(g-2{)}_{\mu }$
• Proton Lifetime in Minimal Supersymmetric SU(5) with Gauge Mediation
• Thermal Leptophilic Light Vector Dark Matter with Spinor Mediator and Muon (g-2) Anomaly
• Theory of Muon g-2
• Evaluation of the three-flavor quark-disconnected contribution to the muon anomalous magnetic moment from experimental data
• Fractionary Charged Particles Confronting Lepton Flavor Violation and the Muon's Anomalous Magnetic Moment
• Probing the muon $g-2$ with future beam dump experiments
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Graph Reinforcement Learning for Exploring BSM Model Spaces
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Pion Interactions and the Standard Model at High Precision
• Explaining the hints for lepton flavour universality violation with three $S_2$ leptoquark generations
• Aligned Zee-Grimus-Neufeld model for $(g-2{)}_{\mu }$
• Subthreshold parameters of $\pi \pi$ scattering revisited
• Flavour anomalies in supersymmetric scenarios with non-minimal flavour violation
• Structure-dependent radiative corrections to $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\gamma$ in the GVMD approach
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints