In experiments with the CMD-2 detector at the VEPP-2M electron-positron collider at Novosibirsk about 150000 $e^+e^-\to\pi^+\pi^-$ events were recorded in the center-of-mass energy range from 0.61 up to 0.96 GeV. The result of the pion form factor measurement with a 1.4% systematic error is presented. The following values of the $\rho$-meson and $\rho-\omega$ interference parameters were found: $M_\rho=(775.28\pm 0.61\pm 0.20) MeV, \Gamma_\rho=(147.70\pm 1.29 \pm 0.40) MeV, \Gamma(\rho\to e^+e^-)=(6.93\pm 0.11\pm 0.10) keV, Br(\omega\to\pi^+\pi^-) = (1.32\pm 0.23)%$.
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The cross section of the process e+e- -> pi+pi- has been measured using about 114000 events collected by the CMD-2 detector at the VEPP-2M e+e- collider in the center-of-mass energy range from 0.61 to 0.96 GeV. Results of the pion form factor determination with a 0.6% systematic uncertainty are presented. Implications for the hadronic contribution to the muon anomalous magnetic moment are discussed.
Updated measured values of the pion form factor and 'bare' cross section.
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.
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.
We have measured the cross section $\sigma(e^+e^-\to \pi^+\pi^- \gamma)$ at an energy $W=m_\phi=1.02$ GeV with the KLOE detector at the electron-positron collider DA$\Phi$NE. From the dependence of the cross section on the invariant mass of the two-pion system, we extract $\sigma(e^+e^-\to \pi^+\pi^-)$ for the mass range $0.35<s<0.95$ GeV$^2$. From this result, we calculate the pion form factor and the hadronic contribution to the muon anomaly, $a_\mu$.
The differential cross section as a function of the invariant mass of the di-pion system in the angular region THETA(PIPI) <15 DEGREES or THETA(PIPI) >165 DEGREES and THETA(PI) in the region 0 to 180 DEGREES.
The physical cross section for E+ E- --> PI+ PI- including FSR and vacuum polarization effects.
The pion form factor with FSR and vacuum polarization effects removed.
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.
We have measured the cross section $\sigma(e^+e^-\to\pi^+\pi^-\gamma(\gamma))$ at DA$\Phi$NE, the Frascati \phi-factory, using events with initial state radiation photons emitted at small angle and inclusive of final state radiation. We present the analysis of a new data set corresponding to an integrated luminosity of 240 pb$^{-1}$. We have achieved a reduced systematic uncertainty with respect to previously published KLOE results. From the cross section we obtain the pion form factor and the contribution to the muon magnetic anomaly from two pion states in the mass range $0.592 < M_{\pi\pi} < 0.975$ GeV. For the latter we find $\Delta a^{\pi\pi}_\mu = (387.2\pm0.5_{\rm stat}\pm2.4_{\rm exp}\pm2.3_{\rm th})\times 10^{-10}$
Differential cross section for E+ E- --> PI+ PI- GAMMA (GAMMA).
Total cross section for E+ E- --> PI+ PI-.
Pion form factor.
The pion electromagnetic form factor has been measured at the VEPP-2M collider in the c.m. energy range 360 MeV–1400 MeV with the detectors OLYA and CMD. On the basis of all available data for the pion form factor collected in the timelike region, the following values for ρ-meson parameters were obtained: m ρ = 775.9 ± 1.1 MeV, σ ρ = 150.5 ± 3.0 MeV. The ω-meson branching ratio into π + π − pair, electromagnetic radius of the pion, ππ scattering length in the P-wave and the strong interaction contribution to the muon ( g − 2) value were found to be B ωππ = (2.3 ± 0.4)%, 〈 r π 2 〉 = 0.422 ± 0.013 fm 2 , a 1 1 = 0.033 ± 0.033m π −3 , a H = (68.4 ± 1.1) × 10 −9 .
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Experimental data from the OLYA detector
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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.
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