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.
A precise measurement of the cross section of the process $e^+e^-\to\pi^+\pi^-(\gamma)$ from threshold to an energy of 3GeV is obtained with the initial-state radiation (ISR) method using 232fb$^{-1}$ of data collected with the BaBar detector at $e^+e^-$ center-of-mass energies near 10.6GeV. The ISR luminosity is determined from a study of the leptonic process $e^+e^-\to\mu^+\mu^-(\gamma)\gamma_{\rm ISR}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^+e^-\to\pi^+\pi^-(\gamma)$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi\pi$ cross section from threshold to 1.8GeV is $(514.1 \pm 2.2({\rm stat}) \pm 3.1({\rm syst}))\times 10^{-10}$.
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ The cross section values (nb) for 337 CM energy intervals (GeV) from 0.3 to 3 GeV. The cross section is bare (excluding vacuum polarization) and includes the emission of final state photons. ***WARNING*** The quoted errors are from the diagonal elements of the statistical covariance matrix (reported the Table titled "Bare cross-section statistical covariance") and added quadratically with the systematic uncertainties (reported in the Table titled "Bare cross-section systematic uncertainties"). These errors can be used when plotting the results as they are representative of the precision achieved. However, any calculation involving the cross section over some energy range MUST use, to be meaningful, the full statistical covariance matrix and the proper correlations of the systematic uncertainties. ***WARNING***
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ systematic uncertainties contributions and total systematic uncertainties, for 337 CM energy intervals (GeV), from 0.3 to 3 GeV. All systematics contributions are each 100% correlated in all energy bins.
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ statistical covariance matrix, for 337x337 CM energy intervals (GeV), from 0.3 to 3 GeV.
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 present measurements of the total production rates and momentum distributions of the charmed baryon $\Lambda_c^+$ in $e^+e^- \to$ hadrons at a center-of-mass energy of 10.54 GeV and in $\Upsilon(4S)$ decays. In hadronic events at 10.54 GeV, charmed hadrons are almost exclusively leading particles in $e^+e^- \to c\bar{c}$ events, allowing direct studies of $c$-quark fragmentation. We measure a momentum distribution for $\Lambda_c^+$ baryons that differs significantly from those measured previously for charmed mesons. Comparing with a number of models, we find none that can describe the distribution completely. We measure an average scaled momentum of $\left< x_p \right> = 0.574\pm$0.009 and a total rate of $N_{\Lambda c}^{q\bar{q}} = 0.057\pm$0.002(exp.)$\pm$0.015(BF) $\Lambda_c^+$ per hadronic event, where the experimental error is much smaller than that due to the branching fraction into the reconstructed decay mode, $pK^-\pi^+$. In $\Upsilon (4S)$ decays we measure a total rate of $N_{\Lambda c}^{\Upsilon} = 0.091\pm$0.006(exp.)$\pm$0.024(BF) per $\Upsilon(4S)$ decay, and find a much softer momentum distribution than expected from B decays into a $\Lambda_c^+$ plus an antinucleon and one to three pions.
LAMBDA/C+ differential production rate per hadronic event for the continuum at cm energy 10.54 GeV.
The integrated number of LAMBDA/C+'s per hadronic event for the continuum at cm energy 10.54 GeV.
LAMBDA/C+ differential production rate per UPSILON(4S) decay at cm energy 10.58 GeV.
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 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.
The processes e+ e- --> eta gamma, e+ e- --> pi0 gamma --> 3 gamma have been studied in the c.m. energy range 600--1380 MeV with the CMD-2 detector. The following branching ratios have been determined: Br(rho --> eta gamma) = (3.21 +- 1.39 +- 0.20)x 10^{-4}; Br(omega --> eta gamma) = (4.44 + 2.29 -1.83 +- 0.28)x 10^{-4}; Br(phi --> eta gamma) = (1.373 +- 0.014 +- 0.085)x 10^{-2}; Br(rho --> pi0 gamma) = (6.21 +1.28 - 1.18 +- 0.39)x 10^{-4}; Br(omega --> pi0 gamma) = (9.06 +- 0.20 +- 0.57)x 10^{-2}; Br(phi --> pi0 gamma) = (1.258 +- 0.037 +- 0.077)x 10^{-3};
Born cross section for the process E+ E- --> ETA GAMMA.
Born cross section for the process E+ E- --> PI0 GAMMA.
The cross section of the process e+ e- --> pi0 pi0 gamma has been measured in the c.m. energy range 600--970 MeV with the CMD-2 detector. The following branching ratios have been determined: B(rho --> pi0 pi0 gamma) =(5.2^{+1.5}_{-1.3} +- 0.6)x10^{-5} and B(omega --> pi0 pi0 gamma) =(6.4^{+2.4}_{-2.0} +- 0.8)x10^{-5}. Evidence for the rho --> f0(600) gamma decay has been obtained: B(rho --> f0(600) gamma) = (6.0^{+3.3}_{-2.7}\pm 0.9)x10^{-5}. From a search for the process e+ e- --> eta pi0 gamma the following upper limit has been obtained: B(omega --> eta pi0 gamma) < 3.3 10^{-5} at 90% CL.
The Born and 'bare' cross sections.
The cross section of the process $e^+e^-\to \pi^+\pi^-\pi^0$ was measured in the Spherical Neutral Detector (SND) experiment at the VEPP-2M collider in the energy region $\sqrt[]{s}$ below 980 MeV. This measurement was based on about $1.2 \times 10^6$ selected events. The obtained cross section was analyzed together with the SND and DM2 data in the energy region $\sqrt[]{s}$ up to 2 GeV. The $\omega$-meson parameters: $m_\omega=782.79\pm 0.08\pm 0.09$ MeV, $\Gamma_\omega=8.68\pm 0.04\pm 0.15$ MeV and $\sigma(\omega\to 3\pi)=1615\pm 9\pm 57$ nb were obtained. It was found that the experimental data cannot be described by a sum of only $\omega$, $\phi$, $\omega^\prime$ and $\omega^{\prime\prime}$ resonances contributions. This can be interpreted as a manifestation of $\rho\to 3\pi$ decay, suppressed by $G$-parity, with relative probability $B(\rho\to 3\pi) = (1.01\pm^{0.54}_{0.36}\pm 0.034) \times 10^{-4}$.
Measurements of the E+ E- --> PI+ PI- PI0 cross section.
Results of the study of the e+e-->pi0 gamma process with SND detector at VEPP-2M collider in the c.m.s. energy range sqrt(s)=0.60-0.97 GeV are presented. Using 36513 selected events corresponding to a total integrated luminosity of 3.4 pb^-1 the e+e-->pi0 gamma cross section was measured. The energy dependence of the cross section was analyzed in the framework of the vector meson dominance model. The data are well described by a sum of phi,omega,rho0->pi0 gamma decay contributions with measured decay probabilities: Br(omega->pi0 gamma)=(9.34+-0.15+-0.31)% and Br(rho0->pi0 gamma)=(5.15+-1.16+-0.73)*10^-4 . The rho-omega relative interference phase is phi(rho,omega}=(-10.2+-6.5+-2.5) degree.
Measured E+ E- --> PI0 GAMMA cross section.
Total cross section into OMEGA and RHO0 channels.
The e+e- -> pi0 pi0 gamma process was studied in the SND experiment at VEPP-2M e+e- collider in the energy region 0.60-0.97 GeV. From the analysis of the energy dependence of measured cross section the branching ratios B(omega -> pi0 pi0 gamma)= (6.6 +1.4-0.8(stat) +-0.6(syst))x10^-5 and B(rho -> pi0 pi0 gamma)=(4.1 +1.0-0.9(stat) +-0.3(syst))x10^-5 were obtained.
Measured values of the cross section.
The cross section of the process e+ e- ---> eta gamma has been measured in the 600-1380 MeV c.m. energy range with the CMD-2 detector. The following branching ratios have been determined: B(rho ---> eta gamma) = (3.28 +- 0.37 +- 0.23) 10^{-4}, B(omega ---> eta gamma) = (5.10 +- 0.72 +- 0.34) 10^{-4}, B(phi --> eta gamma) = (1.287 +- 0.013 +- 0.063) 10^{-2}. Evidence for the rho'(1450) ---> eta gamma decay has been obtained for the first time.
The measured Born cross section for the ETA GAMMA final state.
Using 3.07 ${pb}^{-1}$ of data collected in the energy range 0.60-0.97 GeV by CMD-2, about 150 events of the process $\epm \to \pch$ have been selected. The energy dependence of the cross section agrees with the assumption of the $a_1(1260) \pi$ intermediate state which is dominant above 1 GeV. For the first time \fourpi events are observed at the $\rho$ meson energy. Under the assumption that all these events come from the $\rho$ meson decay, the value of the cross section at the $\rho$ meson peak corresponds to the following decay width: \Gamma(\rho^0 \to \fourpi) = (2.8 \pm 1.4 \pm 0.5) {keV} or to the branching ratio B(\rho^0 \to \fourpi) = (1.8 \pm 0.9 \pm 0.3) \cdot 10 ^{-5}.
Measured cross section.
Resonance production in the γγ reactionse+e−→e+e+e−π0π0 ande+e−π0η has been studied with the JADE detector at PETRA. The decay widths into γγ of thef2(1270),a0(980) anda2(1320) were measured to be\(\Gamma _{\gamma \gamma } (f_2 (1270)) = 3.19 \pm 0.09_{ - 0.38}^{ + 0.22} \) Kev,Γλλ(a0(980))=0.28±0.04±0.10 KeV/BR(a0(980)→π0η) andΓλλ(a2(1320))=1.01±0.14±0.22KeV. For thef0(975) andf4(2050) upper limits of the widths were obtained,Γλλ(f0(975))<0.6 KeV, andΓλλ(f4(2050))<1.1 KeV, both at the 95% C.L. Assuming that the spin 0 background under thef2(1270) is small, thef2(1270) was found to be produced exclusively in a helicity 2 state. The helicity 0 contribution is <15% at the 95% C.L. The cross section forλλ→π0π0 in the mass range 2.0–3.5 GeV/c2 was measured for the first time. Since the cross section forλλ→π+π− is a factor ∼2 larger, ππ production in this range can be interpreted as taking place via isospin 0 production.
Cross section for ABS(COS(THETA*)) < 0.3.
Cross section under assumptions of spin 2, helicity 2 production.
Cross section under assumption of spin 0 production.
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