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, $⟨r_{\pi }^2⟩=0.429(1)(4){\text{fm}}^2$.

arXiv comment40 pages, 16 figures, 13 tables; version published in JHEP

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• The Muon Magnetic Moment and Physics Beyond the Standard Model
• Radiative corrections and Monte Carlo tools for low-energy hadronic cross sections in $e^{+}{e}^{-}$ collisions
• A 17 MeV pseudoscalar and the LSND, MiniBooNE and ATOMKI anomalies
• Muon g-2, Dark Matter and the Higgs mass in No-Scale Supergravity
• Global analysis and LHC study of a vector-like extension of the Standard Model with extra scalars
• Tension between $e^{+}{e}^{-}\to \eta {\pi }^{-}{\pi }^{+}$ and ${\tau }^{-}\to \eta {\pi }^{-}{\pi }^0{\nu }_{\tau }$ data and non-standard interactions
• Current Status of the Muon g-2 Interpretations within Two-Higgs-Doublet Models
• Higgs-mass constraints on a supersymmetric solution of the muon g-2 anomaly
• High-energy frontier of the muon g-2 at a muon collider
• Design and performance of an in-vacuum, magnetic field mapping system for the Muon g-2 experiment
• Anomalous and axial Z' contributions to g-2
• Models with two Higgs doublets and a light pseudoscalar:a portal to dark matter and the possible $(\mathbf{g}-2{)}_{\mu }$ excess
• Leptoquark and vector-like quark extended models as the explanation of the muon $g-2$ anomaly
• Measurement of the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0$ cross section in the energy range 0.62-3.50 GeV at Belle II
• Pion pair production in $e^{+}{e}^{-}$ annihilation at next-to-leading order matched to Parton Shower
• Hadronic light-by-light scattering in the anomalous magnetic moments of electron and $\tau$
• Connecting $(g-2{)}_{\mu }$ to neutrino mass in the extended neutrinophilic 2HDM
• Uncertainty quantification for $\mu \to e$ conversion in nuclei: charge distributions
• Dispersion relations for $B^{-}\to {\ell }^{-}{\bar{\nu }}_{\ell }{\ell }^{\prime -}{\ell }^{\prime +}$ form factors
• Flavor-changing light bosons with accidental longevity
• Minimal Zee model for lepton $g-2$ and $W$-mass shifts
• Gauging lepton flavor SU(3) for the muon $g-2$
• Muon $g-2$ Anomaly and Neutrino Magnetic Moments
• Explaining $g_{\mu }-2$ and $R_{K^{(\ast )}}$ using the light mediators of $U(1{)}_{T3R}$
• Spinning No-Scale $\mathcal{F}$-$SU$(5) in the Right Direction
• Vector leptoquark contributions to lepton dipole moments
• Prospects for ${\gamma }^{\star }{\gamma }^{\star }\to \pi \pi$ via lattice QCD
• A study on the correlation between poles and cuts in $\pi \pi$ scattering
• Secluded Dark Sector and Muon $(g-2)$ in the Light of Fast Expanding Universe
• Anomalous gauge couplings vis-$\grave{a}$-vis $(g-2{)}_{\mu }$ and flavor observables
• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Neutrinophilic DM annihilation in a model with $U(1{)}_{L_{\mu }-L_{\tau }}\times U(1{)}_H$ gauge symmetry
• A model-independent parameterization of $B\to \pi \pi \ell \nu$ decays
• Probing an intrinsically flavorful ALP via tau-lepton flavor physics
• Flavoured $(g-2{)}_{\mu }$ with Dark Lepton Seasoning
• Collider probe of heavy additional Higgs bosons solving the muon $g-2$ and dark matter problems
• Implications of the muon anomalous magnetic moment for the LHC and MUonE
• Monopoles, Exotic states and Muon $g-2$ in TeV scale Trinification
• Disperon QED
• Constraining Low-Scale Flavor Models with $(\mathbf{g}-2{)}_{\mathbf{\mu }}$ and Lepton Flavor Violation
• Gauged $L_e-L_{\mu }-L_{\tau }$ symmetry, fourth generation, neutrino mass and dark matter
• Proton-box contribution to $a_{\mu }^{\mathrm{HLbL}}$
• Singlet Scalars as Dark Matter and the Muon g-2 Anomaly
• Study of pion vector form factor and its contribution to the muon $(g-2)$
• Two-loop contributions of axion-like particles to electromagnetic and chromomagnetic form factors
• Light stringy states and the $g-2$ of the muon
• Machine-Learning Analysis of Radiative Decays to Dark Matter at the LHC
• Resolving Muon g-2 Anomaly With Partial Compositeness
• Enhanced $B_q\to \ell {\ell }^{\prime }$ and $B\to (K,\pi )\ell {\ell }^{\prime }$ in light of $(g-2{)}_{\mu }$
• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
• Improved $K_{e3}$ radiative corrections sharpen the $K_{\mu 2}$--$K_{l3}$ discrepancy
• Muon $g-2$ Anomaly from Vector-like Leptons in a 2-Higgs-doublet + Scalar Singlet Model
• Semi-visible dark photon in a model with vector-like leptons for the $(g-2{)}_{e,\mu }$ and $W$-boson mass anomalies
• An alternative gauged $U(1{)}_R$ symmetric model in light of the CDF II $W$ boson mass anomaly
• Lepton $g-2$ and $W$-boson mass anomalies in the DFSZ axion model
• Contribution of exclusive $({\pi }^0{\pi }^0,{\pi }^0\eta ,\eta \eta )\gamma$ channels to the leading order HVP of the muon $g-2$
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants
• Muon $g-2$ in a 2HDM assisted by inert scalars: probing at the ILC
• Radiative Muon Mass Models and $(g-2{)}_{\mu }$
• On-shell Renormalization with Vector-like Leptons, One-loop Muon-Higgs Coupling and Muon g-2
• Leptonic probes of Alternative Left-Right Symmetric Models
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• The Radiative Flavor Template at the LHC: Lepton non-universality and g-2
• 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
• Flavour anomalies meet flavour symmetry
• Muon $g-2$ Anomaly from a Massive Spin-2 Particle
• Flavor- and CP-safe explanation of $g_{\mu }-2$ anomaly
• Momentum-dependence of $\rho -\omega$ mixing in the pion vector form factor and its effect on $(g-2{)}_{\mu }$
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Dispersive analysis of the $J/\psi \to {\pi }^0{\gamma }^{\ast }$ transition form factor with $\rho$-$\omega$ mixing effects
• A pedagogical review on muon $g-2$
• Muon g-2 from Millicharged Hidden Confining Sector
• Dispersive determination of resonances from $\pi \pi$ scattering data
• Semi-Visible Dark Photon Phenomenology at the GeV Scale
• Hadronic contributions to $a_{\mu }$ within Resonance Chiral Theory
• Systematic analysis of search strategies for $L_{\mu }-L_{\tau }$ gauge bosons at Belle II
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Unitarity bounds on extensions of Higgs sector
• Fermiophobic $Z^{\prime }$ model for simultaneously explaining the muon anomalies $R_{K^{(\ast )}}$ and $(g-2{)}_{\mu }$
• Round table on Standard Model Anomalies
• Analysis of the Pion Electromagnetic Form Factor with Next-to-Next-to-Leading Order QCD Corrections
• GM2Calc-2 for the 2HDM
• Probing the muon $g-2$ with future beam dump experiments
• Subthreshold parameters of $\pi \pi$ scattering revisited
• Proton Lifetime in Minimal Supersymmetric SU(5) with Gauge Mediation
• 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
• Graph Reinforcement Learning for Exploring BSM Model Spaces
• Pion Interactions and the Standard Model at High Precision
• Explaining the hints for lepton flavour universality violation with three $S_2$ leptoquark generations
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Fractionary Charged Particles Confronting Lepton Flavor Violation and the Muon's Anomalous Magnetic Moment
• Theory of Muon g-2
• Evaluation of the three-flavor quark-disconnected contribution to the muon anomalous magnetic moment from experimental data
• Thermal Leptophilic Light Vector Dark Matter with Spinor Mediator and Muon (g-2) Anomaly
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Flavour anomalies in supersymmetric scenarios with non-minimal flavour violation
• Aligned Zee-Grimus-Neufeld model for $(g-2{)}_{\mu }$