Three-pion contribution to hadronic vacuum polarization

Abstract

We address the contribution of the $3\pi$ channel to hadronic vacuum polarization (HVP) using a dispersive representation of the $e^{+}{e}^{-}\to 3\pi$ amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon $(g-2{)}_{\mu }$, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances $\omega$ and $\varphi$, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for $(g-2{)}_{\mu }$ an analysis of the available data as model independent as possible becomes critical. Here, we provide such an analysis based on a global fit function using analyticity and unitarity of the underlying ${\gamma }^{\ast }\to 3\pi$ amplitude and its normalization from a chiral low-energy theorem, which, in particular, allows us to check the internal consistency of the various $e^{+}{e}^{-}\to 3\pi$ data sets. Overall, we obtain $a_{\mu }^{3\pi }{|}_{\le 1.8\text{GeV}}=46.2(6)(6)\times 10^{-10}$ as our best estimate for the total $3\pi$ contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the $2\pi$ channel below $1\text{GeV}$, this covers nearly $80\%$ of the total HVP contribution, leading to $a_{\mu }^{\text{HVP}}=692.3(3.3)\times 10^{-10}$ when the remainder is taken from the literature, and thus reaffirming the $(g-2{)}_{\mu }$ anomaly at the level of at least $3.4\sigma$. As side products, we find for the vacuum-polarization-subtracted masses $M_{\omega }=782.63(3)(1)\text{MeV}$ and $M_{\varphi }=1019.20(2)(1)\text{MeV}$, confirming the tension to the $\omega$ mass as extracted from the $2\pi$ channel.

arXiv comment24 pages, 1 figure; Appendix B added; version published in JHEP

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• Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II
• Flavoured $(g-2{)}_{\mu }$ with Dark Lepton Seasoning
• Implications of the muon anomalous magnetic moment for the LHC and MUonE
• Monopoles, Exotic states and Muon $g-2$ in TeV scale Trinification
• Constraining Low-Scale Flavor Models with $(\mathbf{g}-2{)}_{\mathbf{\mu }}$ and Lepton Flavor Violation
• Scalar leptoquark and vector-like quark extended models as the explanation of the muon $g-2$ anomaly: bottom partner chiral enhancement case
• Collider probe of heavy additional Higgs bosons solving the muon $g-2$ and dark matter problems
• An alternative gauged $U(1{)}_R$ symmetric model in light of the CDF II $W$ boson mass 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
• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
• Gauged $L_e-L_{\mu }-L_{\tau }$ symmetry, fourth generation, neutrino mass and dark matter
• Resolving Muon g-2 Anomaly With Partial Compositeness
• Recent Developments of Muon g-2 from Lattice QCD
• Semi-visible dark photon in a model with vector-like leptons for the $(g-2{)}_{e,\mu }$ and $W$-boson mass anomalies
• Singlet Scalars as Dark Matter and the Muon g-2 Anomaly
• Muon $g-2$ Anomaly from Vector-like Leptons in a 2-Higgs-doublet + Scalar Singlet Model
• Enhanced $B_q\to \ell {\ell }^{\prime }$ and $B\to (K,\pi )\ell {\ell }^{\prime }$ in light of $(g-2{)}_{\mu }$
• Machine-Learning Analysis of Radiative Decays to Dark Matter at the LHC
• Light stringy states and the $g-2$ of the muon
• Proton-box contribution to $a_{\mu }^{\mathrm{HLbL}}$
• Flavour anomalies meet flavour symmetry
• Lepton $g-2$ and $W$-boson mass anomalies in the DFSZ axion model
• Muon $g-2$ in a 2HDM assisted by inert scalars: probing at the ILC
• Model-independent extrapolation of MUonE data with Padé and D-Log approximants
• The Radiative Flavor Template at the LHC: Lepton non-universality and g-2
• On-shell Renormalization with Vector-like Leptons, One-loop Muon-Higgs Coupling and Muon g-2
• Leptonic probes of Alternative Left-Right Symmetric Models
• 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
• Muon $g-2$ Anomaly from a Massive Spin-2 Particle
• Extracting the chiral anomaly from $e^{+}{e}^{-}\to 3\pi$
• Contribution of exclusive $({\pi }^0{\pi }^0,{\pi }^0\eta ,\eta \eta )\gamma$ channels to the leading order HVP of the muon $g-2$
• Flavor- and CP-safe explanation of $g_{\mu }-2$ anomaly
• Fermiophobic $Z^{\prime }$ model for simultaneously explaining the muon anomalies $R_{K^{(\ast )}}$ and $(g-2{)}_{\mu }$
• Tau data-driven evaluation of the Hadronic Vacuum Polarization
• Semi-Visible Dark Photon Phenomenology at the GeV Scale
• Tensor Meson Pole contributions to the HLbL piece of $a_{\mu }$ within R$\chi$T
• Unitarity bounds on extensions of Higgs sector
• Muon g-2 from Millicharged Hidden Confining Sector
• GM2Calc-2 for the 2HDM
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Systematic analysis of search strategies for $L_{\mu }-L_{\tau }$ gauge bosons at Belle II
• Round table on Standard Model Anomalies
• Pion Interactions and the Standard Model at High Precision
• Probing the muon $g-2$ with future beam dump experiments
• Flavour anomalies in supersymmetric scenarios with non-minimal flavour violation
• Graph Reinforcement Learning for Exploring BSM Model Spaces
• Explaining the hints for lepton flavour universality violation with three $S_2$ leptoquark generations
• Proton Lifetime in Minimal Supersymmetric SU(5) with Gauge Mediation
• Fractionary Charged Particles Confronting Lepton Flavor Violation and the Muon's Anomalous Magnetic Moment
• Aligned Zee-Grimus-Neufeld model for $(g-2{)}_{\mu }$
• Theory of Muon g-2
• Tau Data-Based Evaluations of the hadronic vacuum polarization contribution to the muon $g-2$
• Thermal Leptophilic Light Vector Dark Matter with Spinor Mediator and Muon (g-2) Anomaly