Study of the process $e^+e^- \to \pi^+\pi^-$ in the energy region 400<\sqrt[]{s}<1000 MeV
TL;DR: The cross section of the process e^+e^-\to \pi^+\pi^- was measured in the SND experiment at the VEPP-2M collider in the energy region 400<\sqrt[]{s}<1000 MeV as discussed by the authors.
Abstract: The cross section of the process e^+e^-\to \pi^+\pi^- was measured in the SND experiment at the VEPP-2M collider in the energy region 400<\sqrt[]{s}<1000 MeV. This measurement was based on about 12.4 \times 10^6 selected collinear events, which include 7.4\times 10^6 e^+e^-\to e^+e^-, 4.5\times 10^6 e^+e^-\to\pi^+\pi^- and 0.5\times 10^6 e^+e^-\to\mu^+\mu^- selected events. The systematic uncertainty of the cross section determination is 1.3 %. The \rho-meson parameters were determined: m_\rho=774.9\pm 0.4\pm 0.5 MeV, \Gamma_\rho=146.5\pm 0.8\pm 1.5 MeV, \sigma(\rho\to\pi^+\pi^-)=1220\pm 7\pm 16 nb as well as the parameters of the G-parity suppressed decay \omega\to\pi^+\pi^-: \sigma(\omega\to\pi^+\pi^-)=29.9\pm 1.4\pm 1.0 nb and \phi_{\rho\omega} = 113.5\pm 1.3\pm 1.7 degree.
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TL;DR: The current status of the Standard Model calculation of the anomalous magnetic moment of the muon is reviewed in this paper, where the authors present a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice approach.
801 citations
TL;DR: In this paper, the authors used a global fit function based on analyticity and unitarity of the underlying ε-gamma-to-3-pi amplitude and its normalization from a chiral low-energy theorem to check the internal consistency of the various ε+e^-to 3-pi data sets.
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 $\phi$, 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 $\gamma^*\to3\pi$ 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 $a_\mu^{3\pi}|_{\leq 1.8\,\text{GeV}}=46.2(6)(6)\times 10^{-10}$ 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 $M_\phi=1019.20(2)(1)\,\text{MeV}$, confirming the tension to the $\omega$ mass as extracted from the $2\pi$ channel.
364 citations
TL;DR: The contribution of the 3π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e+e− → 3π amplitude was studied in this paper.
Abstract: We address the contribution of the 3π channel to hadronic vacuum polarization (HVP) using a dispersive representation of the e+e− → 3π amplitude. This channel gives the second-largest individual contribution to the total HVP integral in the anomalous magnetic moment of the muon (g − 2)μ, both to its absolute value and uncertainty. It is largely dominated by the narrow resonances ω and ϕ, but not to the extent that the off-peak regions were negligible, so that at the level of accuracy relevant for (g − 2)μ 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 γ∗ → 3π 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− → 3π data sets. Overall, we obtain $$ {a}_{\mu}^{3\pi } $$
|≤1.8 GeV = 46.2(6)(6) × 10−10 as our best estimate for the total 3π contribution consistent with all (low-energy) constraints from QCD. In combination with a recent dispersive analysis imposing the same constraints on the 2π channel below 1 GeV, this covers nearly 80% of the total HVP contribution, leading to $$ {a}_{\mu}^{\mathrm{HVP}} $$
= 692.3(3.3) × 10−10 when the remainder is taken from the literature, and thus reaffirming the (g−2)μ anomaly at the level of at least 3.4σ. As side products, we find for the vacuum-polarization-subtracted masses Mω = 782.63(3)(1) MeV and Mϕ = 1019.20(2)(1) MeV, confirming the tension to the ω mass as extracted from the 2π channel.
337 citations
TL;DR: In this paper, a revisited analysis of the theoretical framework was performed to determine the spectral functions of hadronic δ-decays, which can be used to determine hadronic quantities that, due to the nonperturbative nature of long distance QCD, cannot be computed from first principles.
Abstract: Hadronic $\ensuremath{\tau}$ decays provide a clean laboratory for the precise study of quantum chromodynamics (QCD). Observables based on the spectral functions of hadronic $\ensuremath{\tau}$ decays can be related to QCD quark-level calculations to determine fundamental quantities like the strong-coupling constant, parameters of the chiral Lagrangian $\ensuremath{\mid}{V}_{us}\ensuremath{\mid}$, the mass of the strange quark, and to simultaneously test the concept of quark-hadron duality. Using the best available measurements and a revisited analysis of the theoretical framework, the value ${\ensuremath{\alpha}}_{s}({m}_{\ensuremath{\tau}}^{2})=0.345\ifmmode\pm\else\textpm\fi{}{0.004}_{\mathrm{exp}}\ifmmode\pm\else\textpm\fi{}{0.009}_{\mathrm{th}}$ is obtained. Taken together with the determination of ${\ensuremath{\alpha}}_{s}({M}_{Z}^{2})$ from the global electroweak fit, this result leads to the most accurate test of asymptotic freedom: the value of the logarithmic slope of ${\ensuremath{\alpha}}_{s}^{\ensuremath{-}1}(s)$ is found to agree with QCD at a precision of 4%. The $\ensuremath{\tau}$ spectral functions can also be used to determine hadronic quantities that, due to the nonperturbative nature of long-distance QCD, cannot be computed from first principles. An example for this is the contribution from hadronic vacuum polarization to loop-dominated processes like the anomalous magnetic moment of the muon. This article reviews the measurements of nonstrange and strange $\ensuremath{\tau}$ spectral functions and their phenomenological applications.
272 citations
TL;DR: In this article, the anomalous magnetic moment of the muon and the value of the QED coupling at the Z-boson mass were updated, incorporating the new e^+e^- \to \pi\pi data obtained by CMD-2 and KLOE, as well as the corrected SND data.
262 citations