The cross section of the process $e^+ e^-\to\pi^+\pi^-$ has been measured in the Spherical Neutral Detector (SND) experiment at the VEPP-2000 $e^+e^-$ collider VEPP-2000 in the energy region $525 <\sqrt[]{s} <883$ MeV. The measurement is based on data with an integrated luminosity of about 4.6 pb$^{-1}$. The systematic uncertainty of the cross section determination is 0.8 % at $\sqrt{s}>0.600$ GeV. The $\rho$ meson parameters are obtained as $m_\rho = 775.3\pm 0.5\pm 0.6$ MeV, $\Gamma_\rho = 145.6\pm 0.6\pm 0.8$ MeV, $B_{\rho\to e^+ e^-}\times B_{\rho\to\pi^+\pi^-} = (4.89\pm 0.02\pm 0.04)\times 10^{-5}$, and the parameters of the $e^+ e^-\to\omega\to\pi^+\pi^-$ process, suppressed by $G$-parity, as $B_{\omega\to e^+ e^-}\times B_{\omega\to\pi^+\pi^-}= (1.32\pm 0.06\pm 0.02)\times 10^{-6} $ and $\phi_{\rho\omega} = 110.7\pm 1.5\pm1.0$ degrees.
The Born cross section of the process e+e- -> pi+pi- taking into account the radiative corrections due to the initial and final state radiation.
Measured value of the pion form factor
The bare e+e- -> pi+pi- undressed cross without vacuum polarization, but with the final state radiative correction.
In Phys. Lett. B 753, 629-638 (2016) [arXiv:1507.08188] the BESIII collaboration published a cross section measurement of the process $e^+e^-\to \pi^+ \pi^-$ in the energy range between 600 and 900 MeV. In this erratum we report a corrected evaluation of the statistical errors in terms of a fully propagated covariance matrix. The correction also yields a reduced statistical uncertainty for the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, which now reads as $a_\mu^{\pi\pi\mathrm{, LO}}(600 - 900\,\mathrm{MeV}) = (368.2 \pm 1.5_{\rm stat} \pm 3.3_{\rm syst})\times 10^{-10}$. The central values of the cross section measurement and of $a_\mu^{\pi\pi\mathrm{, LO}}$, as well as the systematic uncertainties remain unchanged.
Results of the BESIII measurement of the cross section $\sigma^{\rm bare}_{\pi^+\pi^-(\gamma_{\rm FSR})} \equiv \sigma^{\rm bare}(e^+e^-\rightarrow\pi^+\pi^-(\gamma_{\rm FSR}))$ and the squared pion form factor $|F_\pi|^2$. The errors are statistical only. The value of $\sqrt{s'}$ represents the bin center. The 0.9$\%$ systematic uncertainty is fully correlated between any two bins.
Results for the bare cross section $\sigma^\text{bare}_{\pi^+\pi^-}$ and the pion form factor together with their statistical uncertainties. The systematical uncertainties are given by 0.9% (see <a href="https://inspirehep.net/literature/1385603">arXiv:1507.08188</a>).
Bare cross section $\sigma^\mathrm{bare}(e^+e^-\to\pi^+\pi^-(\gamma_\mathrm{FSR}))$ of the process $e^+e^-\to\pi^+\pi^-$ measured using the initial state radiation method. The data is corrected concerning final state radiation and vacuum polarization effects. The final state radiation is added using the Schwinger term at born level.
The cross section of the process e+e-\to\mu+\mu- was measured in the SND experiment at the VEPP-2M e+e- collider in the energy region \sqrt{s}=980, 1040 -- 1380 MeV. The event numbers of the process e+e-\to\mu+\mu- were normalized to the integrated luminosity measured using e+e-\to e+e- and e+e-\to\gamma\gamma processes. The ratio of the measured cross section to the theoretically predicted value is 1.006\pm 0.007 \pm 0.016 and 1.005 \pm 0.007 \pm 0.018 in the first and second case respectively. Using results of the measurements, the electromagnetic running coupling constant \alpha in the energy region \sqrt{s}=1040 -- 1380 MeV was obtained <1/\alpha> = 134.1\pm 0.5 \pm 1.2 and this is in agreement with theoretical expectation.
The E+ E- --> MU+ MU- cross section obtained using the (GAMMA GAMMA) luminosity measurement.
The measured E+ E- --> E+ E- cross section in the electron angle 30 to 150 degrees.
Three-jet production in deep inelastic ep scattering and photoproduction was investigated with the ZEUS detector at HERA using an integrated luminosity of 127 pb-1. Measurements of differential cross sections are presented as functions of angular correlations between the three jets in the final state and the proton-beam direction. These correlations provide a stringent test of perturbative QCD and show sensitivity to the contributions from different colour configurations. Fixed-order perturbative QCD calculations assuming the values of the colour factors C_F, C_A and T_F as derived from a variety of gauge groups were compared to the measurements to study the underlying gauge group symmetry. The measured angular correlations in the deep inelastic ep scattering and photoproduction regimes are consistent with the admixture of colour configurations as predicted by SU(3) and disfavour other symmetry groups, such as SU(N) in the limit of large N.
Integrated 3-jet photoproduction cross section.
Integrated 3-jet cross sections in NC DIS.
Normalized differential 3-jet photoproduction cross section as a function of THETA(H).
We present a measurement of the pion form factor based on e+e- annihilation data from the CMD-2 detector in the energy range 0.6<sqrt(s)<1.0 GeV with a systematic uncertainty of 0.8%. A data sample is five times larger than that used in our previous measurement.
Measured values of the pion form factor. The errors are statistical only.
Measured value of the bare PI+ PI- cross section including corrections for radiative effects but excluding corrections for vacuum polarization effects. The errors are statistical only.
The cross section of the process e+e- -> pi+pi- has been measured at the CMD-2 detector in the 370-520 MeV center-of-mass (c.m.) energy range. A systematic uncertainty of the measurement is 0.7 %. Using all CMD-2 data on the pion form factor, the pion electromagnetic radius was calculated. The cross section of muon pair production was also determined.
The measured Born muon pair production cross section. Errors are statistical only.
The measured pion form factor. The errors are statistical only.
The measured bare PI+ PI- production cross section. This is corrected for radiative effects but excludes a correction for vacuum polarization effects. The errors are statistical only.
In experiment with the SND detector at VEPP-2M $e^+e^-$ collider the $e^+e^-\to\eta\gamma$ cross section was measured in the energy range $E$=0.60--1.38 GeV with the integrated luminosity of 27.8 pb$^{-1}$. The measured cross section is well described by the vector meson dominance model with contributions from the $\rho(770)$, $\omega(783)$, $\phi(1020)$, $\rho^{\prime}(1465)$ resonances and agrees with results of previous measurements. The decay probabilities $\BR(\phi\to\eta\gamma)$, $\BR(\omega\to\eta\gamma)$ and $\BR(\rho\to\eta\gamma)$ were measured with the accuracies better than or comparable to the world averages.
Cross section from the ETA --> 3PI0 decay mode.
Cross section from the ETA --> PI+ PI- PI0 decay mode.
The cross section for the process $e^+e^-\to\pi^+\pi^-$ is measured in the c.m. energy range 1.04-1.38 GeV from 995 000 selected collinear events including 860000 $e^+e^-$ events, 82000 $\mu^+\mu^-$ events, and 33000 $\pi^+\pi^-$ events. The systematic and statistical errors of measuring the pion form factor are equal to 1.2-4.2 and 5-13%, respectively.
Measured value of the pion form factor with statistical errors only.
Measured value of the pion form factor
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.
Cross section taking into account the radiative corrections due to the initial and final state radiation.
Cross section and form factor after the radiative corrections have been undressed.
Undressed cross without vacuum polarization but with the final state radiation.
Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2.
Production cross section as a function of Q**2. Differential cross sectionsare corrected to the centre of each bin.
Production cross section for two-photon data as a function of Q**2.
Production cross section as a function of W.
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