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 measurement of the vector to pseudoscalar conversion decay $\phi \to \pi^0 e^+e^-$ with the KLOE experiment is presented. A sample of $\sim 9500$ signal events was selected from a data set of 1.7 fb$^{-1}$ of $e^+e^-$ collisions at $\sqrt{s} \sim m_{\phi}$ collected at the DA$\Phi$NE $e^+e^-$ collider. These events were used to obtain the first measurement of the transition form factor $| F_{\phi \pi^0}(q^2) |$ and a new measurement of the branching ratio of the decay: $\rm{BR}\,(\phi \to \pi^0 e^+e^-) = (\,1.35 \pm 0.05^{\,\,+0.05}_{\,\,-0.10}\,) \times 10 ^{-5}$. The result improves significantly on previous measurements and is in agreement with theoretical predictions.
KLOE measurement of the transition form factor $| F_{\phi \, \pi^0}(q^2) |$ of the $\phi \to \pi^0 e^+e^-$ decay.
The NA62 experiment collected a large sample of charged kaon decays in 2007 with a highly efficient trigger for decays into electrons. A measurement of the $\pi^0$ electromagnetic transition form factor slope parameter from $1.11\times10^{6}$ fully reconstructed $K^\pm \to \pi^\pm \pi^0_D, \pi^0_D \to e^+ e^-\gamma$ events is reported. The measured value $a = (3.68 \pm 0.57)\times10^{-2}$ is in good agreement with theoretical expectations and previous measurements, and represents the most precise experimental determination of the slope in the time-like momentum transfer region.
Number of reconstructed data events and MC events as a function of the Dalitz kinematic variable $x=(M_{ee}/M_{\pi^0})^2$. The MC events are reweighted to correspond to a TFF slope a=0. The MC sample is not normalized to the size of the data. The values of $x$ quoted in the table are the barycenters of the 50 variable size bins.
The $e^+e^-\to K^+K^-$ cross section and charged-kaon electromagnetic form factor are measured in the $e^+e^-$ center-of-mass energy range ($E$) from 2.6 to 8.0 GeV using the initial-state radiation technique with an undetected photon. The study is performed using 469 fb$^{-1}$ of data collected with the BABAR detector at the PEP-II $e^+e^-$ collider at center-of-mass energies near 10.6 GeV. The form factor is found to decrease with energy faster than $1/E^2$, and approaches the asymptotic QCD prediction. Production of the $K^+K^-$ final state through the $J/\psi$ and $\psi(2S)$ intermediate states is observed. The results for the kaon form factor are used together with data from other experiments to perform a model-independent determination of the relative phases between single-photon and strong amplitudes in $J/\psi$ and $\psi(2S)\to K^+K^-$ decays. The values of the branching fractions measured in the reaction $e^+e^- \to K^+K^-$ are shifted relative to their true values due to interference between resonant and nonresonant amplitudes. The values of these shifts are determined to be about $\pm5\%$ for the $J/\psi$ meson and $\pm15\%$ for the $\psi(2S)$ meson.
The $K^+K^-$ invariant-mass interval ($M_{K^+K^-}$), number of selected events ($N_{\rm sig}$) after background subtraction, detection efficiency ($\varepsilon$), ISR luminosity ($L$), measured $e^+e^-\to K^+K^-$ cross section ($\sigma_{K^+K^-}$), and the charged-kaon form factor ($|F_K|$). For the number of events and cross section. For the form factor, we quote the combined uncertainty. For the mass interval 7.5 - 8.0 GeV/$c^2$, the 90$\%$ CL upper limits for the cross section and form factor are listed.
We report the first observation of the Dalitz decay $\eta' \to \gamma e^+e^-$, based on a data sample of 1.31 billion $J/\psi$ events collected with the BESIII detector. The $\eta'$ mesons are produced via the $J/\psi \to \gamma \eta'$ decay process. The ratio $\Gamma(\eta' \to \gamma e^+ e^-)/\Gamma(\eta'\to\gamma\gamma)$ is measured to be $(2.13\pm0.09(\text{stat.})\pm0.07(\text{sys.}))\times10^{-2}$. This corresponds to a branching fraction ${\cal B}(\eta' \to \gamma e^+e^-)= (4.69 \pm0.20(\text{stat.})\pm0.23(\text{sys.}))\times10^{-4}$. The transition form factor is extracted and different expressions are compared to the measured dependence on the $e^+e^-$ invariant mass. The results are consistent with the prediction of the Vector Meson Dominance model.
Fitted ($n^{\text{obs}}_i$) and efficiency-corrected ($n^{\text{corr}}_i$) signal yields for the eight $M(e^+e^-)$ bins, and ratios ($r_i$). The uncertainties are statistical only.
Values of $|F|^2$ in each $M(e^+e^-)$ bin.
Using data samples collected with the BESIII detector at the BEPCII collider, we measure the Born cross section of $e^{+}e^{-}\rightarrow p\bar{p}$ at 12 center-of-mass energies from 2232.4 to 3671.0 MeV. The corresponding effective electromagnetic form factor of the proton is deduced under the assumption that the electric and magnetic form factors are equal $(|G_{E}|= |G_{M}|)$. In addition, the ratio of electric to magnetic form factors, $|G_{E}/G_{M}|$, and $|G_{M}|$ are extracted by fitting the polar angle distribution of the proton for the data samples with larger statistics, namely at $\sqrt{s}=$ 2232.4 and 2400.0 MeV and a combined sample at $\sqrt{s}$ = 3050.0, 3060.0 and 3080.0 MeV, respectively. The measured cross sections are in agreement with recent results from BaBar, improving the overall uncertainty by about 30\%. The $|G_{E}/G_{M}|$ ratios are close to unity and consistent with BaBar results in the same $q^{2}$ region, which indicates the data are consistent with the assumption that $|G_{E}|=|G_{M}|$ within uncertainties.
Summary of the Born cross section $\sigma_\text{Born}$, the effective FF $|G|$, and the related variables used to calculate the Born cross sections at the different c.m.energies $\sqrt{s}$, where $N_\text{obs}$ is the number of candidate events, $N_\text{bkg}$ is the estimated background yield, $\varepsilon^\prime=\varepsilon\times(1+\delta)$ is the product of detection efficiency $\varepsilon$ and the radiative correction factor $(1+\delta)$, and $L$ is the integrated luminosity. The first errors are statistical, and the second systematic.
Electron-proton elastic scattering cross sections have been measured at squared four-momentum transfers q 2 of 0.67, 1.00, 1.17, 1.50, 1.75, 2.33 and 3.00 (GeV/ c ) 2 and Electron scattering angles θ e between 10° and 20° and at about 86° in the laboratory. The proton electromagnetic form factors G E p and G M p were determined. The results indicate that G E p ( q 2 ) decreases faster with increasing q 2 than G M p ( q 2 ). Quasi-elastic electron-deuteron cross sections have been determined at values of q 2 = 0.39, 0.565, 0.78, 1.0 and 1.5 (GeV/ c ) 2 and scattering angles between 10° and 12°. At q 2 = 0.565 (GeV/ c 2 data have also been taken with θ e = 35° and at q 2 = 1.0 and 1.5 (GeV/ c ) 2 with θ e = 86°. Electron-proton as well as electron-neutron scattering cross sections have been deduced by the ratio method. The theoretical uncertainties of this procedure are shown to be small by comparison of the bound with the free proton cross sections. The magnetic form factor of the neutron G M n derived from the data is consistent with the scaling law. The charge form factor of the neutron is found to be small.
Axis error includes +- 2.1/2.1 contribution (NORMALISATION ERROR).
Axis error includes +- 2.1/2.1 contribution (NORMALISATION ERROR).
Axis error includes +- 2.1/2.1 contribution (NORMALISATION ERROR).
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 e+e- -> p anti-p cross section is determined over a range of p anti-p masses, from threshold to 4.5 GeV/c^2, by studying the e+e- -> p anti-p gamma process. The data set corresponds to an integrated luminosity of 232 fb^-1, collected with the BABAR detector at the PEP-II storage ring, at an e+e- center-of-mass energy of 10.6 GeV. The mass dependence of the ratio of electric and magnetic form factors, |G_E/G_M|, is measured for p anti-p masses below 3 GeV/c^2: its value is found to be significantly larger than 1 for masses up to 2.2 GeV/c^2. We also measure J/psi -> p anti-p and psi(2S) -> p anti-p branching fractions and set an upper limit on Y(4260) -> p anti-p production and decay.
The cross section and effective form factor for E+ E- --> PBAR P.
The cross section and effective form factor for E+ E- --> PBAR P.
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.
Neutral-kaon decays to π e ν were analysed to determine the q 2 dependence of the K 0 e3 electroweak form factor f + . Based on 365 612 events, this form factor was found to have a linear dependence on q 2 with a slope λ + =0.0245±0.0012 stat ±0.0022 syst .
The Q2 dependence of FORMFACTOR+ is usually approximated as: FORMFACTOR+(Q2) = CONST * ( 1 + Q2 * CONST(NAME=LAMBDA+)/M(C=PI)**2).
Fermilab experiment E835 has measured the cross section for the reaction p ̄ p→e + e − at s =11.63, 12.43, 14.40 and 18.22 GeV 2 . From the analysis of the 66 observed events new high-precision measurements of the proton magnetic form factor are obtained.
The measured cross section in the kinematic range defined by COS(THETA).
The proton magnetic form factor calculated assuming the equality of the electric and magnetic form factors.
The proton magnetic form factor calculated assuming a negligible electric contribution.
Tensor polarization observables (t20, t21 and t22) have been measured in elastic electron-deuteron scattering for six values of momentum transfer between 0.66 and 1.7 (GeV/c)^2. The experiment was performed at the Jefferson Laboratory in Hall C using the electron HMS Spectrometer, a specially designed deuteron magnetic channel and the recoil deuteron polarimeter POLDER. The new data determine to much larger Q^2 the deuteron charge form factors G_C and G_Q. They are in good agreement with relativistic calculations and disagree with pQCD predictions.
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The cross section for the reaction p¯p→e+e− has been measured at s=8.8, 10.8, 12.4, 13.1, and 14.4 GeV2 by Fermilab experiment E835. A non-magnetic spectrometer is used to identify the e+e− final states generated by the antiproton beam intersecting an internal hydrogen gas jet target. From the analysis of the 144 observed events, new high-precision measurements of the proton magnetic form factor for timelike momentum transfers are obtained.
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Assuming ABS(FORMFACTOR(NAME=ELECTRIC)) = ABS(FORMFACTOR(NAME=MAGNETIC)).
Neglecting contribution for FORMFACTOR(NAME=ELECTRIC).
Two samples of exclusive semileptonic decays, 579 B 0 → D ∗+ ℓ − ν ℓ events and 261 B 0 → D + ℓ − ν ℓ events, are selected from approximately 3.9 million hadronic Z decays collected by the ALEPH detector at LEP. From the reconstructed differential decay rate of each sample, the product of the hadronic form factor F (ω) at zero recoil of the D (∗)+ meson and the CKM matrix element | V cb | are measured to be F D ∗+ (1)|V cb | = (31.9 ± 1.8 stat ± 1.9 syst ) × 10 −3 , F D + (1)| V cb | = (27.8 ± 6.8 stat ± 6.5 syst ) × 10 −3 . The ratio of the form factors F D + (1) and F D ∗+ (1) is measured to be F D + (1) F D ∗+ (1) = 0.87 ± 0.22 stat ± 0.21 syst . A value of | V cb | is extracted from the two samples, using theoretical constraints on the slope and curvature of the hadronic form factors and their normalization at zero recoil, with the result | V cb | = (34.4 ± 1.6 stat ± 2.3 syst ± 1.4 th ) × 10 −3 . The branching fractions are measured from the two integrated spectra to be Br ( B 0 → D ∗+ ℓ − ν ℓ ) = (5.53 ± 0.26 stat ±0.52 syst ) %, Br ( B 0 → D ∗+ ℓ − ν ℓ ) = (2.35 ± 0.20 stat ± 0.44 syst ) %.
The formfactors are evaluated at zero recoil of D meson. Two different methods are used (see text for details). VCB is the KCM matrix element. The formfactor fitted to dependence: FF(OM) = FF(1)*(1-CONST*(OM-1)).
VCB is the KCM matrix element.
VCB is the KCM matrix element.
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We present measurement of the π0γ*γ, ηγ*γ and η′γ*γ form factors. The π0-form factor is for the first time observed in the space-like region. The transition form factor of the η-meson is determined from its decay modes π+π−π0, π+π−γ and the neutral decay mode γγ. The decay of the η′ is observed in the decay channels ργ, ηπ+π− with η→γγ and in the four charged prong final state stemming from ηπ+π− with the η decaying into π+π−(π0/γ). All form factors agree well with a simple ρ-pole predicted by the vector meson dominance model and also with the QCD inspired Brodsky-Lepage model.
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The H2(e,e’n)1H quasielastic cross section was measured at Q2 values of 0.109, 0.176, and 0.255 (GeV/c)2. The neutron detection efficiency was determined by the associated particle technique with the H2(γ,pn) reaction for each of the three neutron kinetic energies. These H2(e,e’n) measurements of the coincidence cross sections are the first at low Q2. The cross sections are sensitive primarily to the neutron magnetic form factor GMn at these kinematics. The extracted GMn values have smaller uncertainties than previous data and are consistent with the dipole parametrization at the two higher momentum transfers; at the lowest momentum transfer, the value of GMn is ∼10% higher than the dipole value.
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The decay τ−→π−−+vτ has been studied using data collected with the OPAL detector at LEP during 1992 and 1993. The hadronic structure functions for this decay are measured model independently assuming G-parity invariance and neglecting scalar currents. Simultaneously the parity violating asymmetry parameter is determined to be\(\gamma VA = 1.08 _{ - 0.41- 0.25}^{ + 0.46+ 0.14} \), consistent with the Standard Model prediction of γVA=1 for left-handed tau neutrinos. Models of Kühn and Santamaria and of Isgur et al. are used to fit distributions of the invariant 3π mass as well as 2π mass projections of the Dalitz plot. The model dependent mass and width of thea1 resonance are measured to be\(m_{a_1 }= 1.266 \pm 0.014_{ - 0.002}^{ + 0.012} \) GeV and\(\Gamma _{a_1 }= 0.610 \pm 0.049_{ - 0.019}^{ + 0.053} \) GeV for the Kühn and Santamaria model and\(m_{a_1 }= 1.202 \pm 0.009_{ - 0.001}^{ + 0.009} \) GeV and\(\Gamma _{a_1 }= 0.422 \pm 0.023_{ - 0.004}^{ + 0.033} \) GeV for the Isgur et al. model. The model dependent values obtained for the parity violating asymmetry parameter are γVA=0.87±0.27−0.06+0.05 for the Kühn and Santamaria model and γVA=1.10±0.31−0.14+0.13 for the Isgur et al. model. Within the Isgur et al. model the ratio of theS-andD-wave amplitudes is measured to beD/S=−0.09±0.03±0.01.
See paper for definition of four weak decay formfactors : wa, wc, wd, we. For TAU+-.
Here ASYM is parity violating asymmetry parameter gamma_VA = 2g_v*g_A/(g_v **2+g_A**2) (see paper).
We report the results of a pion-electron scattering experiment to measure the charge radius of the pion. The experiment was performed in a 50 GeV/ c negative, unseparated beam at the IHEP accelerator, Serpukhov, and has been briefly reported in an earlier publication [1]. A magnetic spectrometer instrumented with wire spark chambers was used to record the incident pion trajectory and the angles and momenta of the scattered particles. Events are reconstructed by detailed trackfinding programs, and a set of kinematic and geometric cuts define the elastic sample. Electrons are identified both by kinematic criteria and pulse height information from total absorption lead glass Čerenkov counters. The final elastic sample consisted of 40 000 πe events in the region of four-momentum transfer squared 0.013 (GeV/ c ) 2 ⩽ q 2 ⩽ 0.036 (GeV/ c ) 2 . A full error matrix fit to the form factors of the pion gave the r.m.s. charge radius of the pion: 〈r π 2 〉 1 2 = (0.78 −0.10 +0.09 ) fm .
Axis error includes +- 0.7/0.7 contribution (DUE TO ACCIDENTAL ANTI-COINCIDENCES).
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Electron-proton elastic-scattering cross sections have been measured at the Stanford Linear Accelerator Center for four-momentum transfers squared q 2 from 1.0 to 25.0 (GeVc)2. The electric (GEp) and magnetic (GMp) form factors of the proton were not separated, since angular distributions were not measured at each q 2. However, values for GMp were derived assuming various relations between GEp and GMp. Several theoretical models for the behavior of the proton magnetic form factor at high values of q 2 are compared with the data.
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The proton form factors GE(q2) and GM(q2) are determined at q2 = 75fm−2.
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