We report a measurement of the $e^+e^- \to \pi^+\pi^-\pi^0$ cross section in the energy range from 0.62 to 3.50 GeV using an initial-state radiation technique. We use an $e^+e^-$ data sample corresponding to 191 $\text{fb}^{-1}$ of integrated luminosity, collected at a center-of-mass energy at or near the $\Upsilon{(4S)}$ resonance with the Belle II detector at the SuperKEKB collider. Signal yields are extracted by fitting the two-photon mass distribution in $e^+e^- \to \pi^+\pi^-\pi^0\gamma$ events, which involve a $\pi^0 \to \gamma\gamma$ decay and an energetic photon radiated from the initial state. Signal efficiency corrections with an accuracy of 1.6% are obtained from several control data samples. The uncertainty on the cross section at the $\omega$ and $\phi$ resonances is dominated by the systematic uncertainty of 2.2%. The resulting cross sections in the 0.62-1.80 GeV energy range yield $ a_\mu^{3\pi} = [48.91 \pm 0.23~(\mathrm{stat}) \pm 1.07~(\mathrm{syst})] \times 10^{-10} $ for the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment. This result differs by $2.5$ standard deviations from the most precise current determination.
Energy bin range ($\sqrt{s'}$), number of events after unfolding ($N_{\mathrm{unf}}$), corrected efficiency ($\varepsilon$), and cross section ($\sigma_{3\pi}$) for $e^{+}e^{-} \to \pi^{+} \pi^{-} \pi^{0}$ in energy range 0.62--1.05~GeV. The two uncertainties in the cross section are the statistical and systematic contributions. The statistical uncertainties for the unfolding and cross section are square roots of the diagonal components of the unfolding covariance matrix. The image shows Figure 23 in the PRD paper, and the points with error bars indicate the cross section in the table.
Energy bin range ($\sqrt{s'}$), number of events after unfolding ($N_{\mathrm{unf}}$), corrected efficiency ($\varepsilon$), and cross section ($\sigma_{3\pi}$) for $e^{+}e^{-} \to \pi^{+} \pi^{-} \pi^{0}$ in energy range 1.05--3.50~GeV. The two uncertainties in the cross section are the statistical and systematic contributions. The statistical uncertainties for the unfolding and cross section are square roots of the diagonal components of the unfolding covariance matrix. The image shows Figure 23 in the PRD paper, and the points with error bars indicate the cross section in the table.
The statistic covariance matrix for the $e^+e^- \to \pi^+ \pi^- \pi^0$ cross section measurement at the Belle II. The 212 x 212 matrix of the energy ranges from 0.62 to 3.50 GeV. This covariance matrix, obtained by propagating the covariance matrix in the unfolding procedure, shows the total statistical uncertainties for the cross section results.
Measurements of the two-photon interaction e + e − → e + e − + hadrons at s ≃ 91 GeV and s ≃ 183 GeV are presented. The double-tag events, collected with the L3 detector, correspond to interated luminosities of 140 pb −1 at 91 GeV and 52 pb −1 at 183 GeV. The cross-section of γ ∗ γ ∗ collisions has been measured at 〈 Q 2 〉 = 3.5 GeV 2 and 〈 Q 2 〉 = 14 GeV 2 . The data agree well with predictions based on perturbative QCD, while the Quark Parton Model alone is insufficient to describe the data.
No description provided.
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New measurements at a centre-of-mass energy s ≃183 GeV of the hadronic photon structure function F γ 2 ( x ) in the Q 2 interval, 9 GeV 2 ≤ Q 2 ≤30 GeV 2 , are presented. The data, collected in 1997 with the L3 detector, correspond to an integrated luminosity of 51.9 pb −1 . Combining with the data taken at a centre-of-mass energy of 91 GeV, the evolution of F γ 2 with Q 2 is measured in the Q 2 range from 1.2 GeV 2 to 30 GeV 2 . F γ 2 shows a linear growth with ln Q 2 ; the value of the slope α −1 d F γ 2 ( Q 2 )/dln Q 2 is measured in two x bins from 0.01 to 0.2 and is somewhat higher than predicted.
Measured values of F2/ALPHA as a function of x. The second systematic error (DSYS) is that due to the model dependence and is the difference between the results obtained with PHOJET and TWOGAM. The full systematic error is the quadrature sum of the two systematic errors.
The hadronic photon structure function F γ 2 is studied in the reaction e + e − →e + e − hadrons at LEP with the L3 detector. The data, collected from 1991 to 1995 at a centre-of-mass energy s ≃91 GeV, correspond to an integrated luminosity of 140 pb −1 . The photon structure function F γ 2 is measured in the Q 2 interval 1.2 GeV 2 ≤ Q 2 ≤9.0 GeV 2 and the x interval 0.002< x <0.2. F γ 2 shows a linear growth with ln Q 2 . The value of the slope α −1 d F γ 2 ( Q 2 )/dln Q 2 is measured to be 0.079±0.011±0.009.
No description provided.
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The reactions e + e − → e + e − e + e − and e + e − → e + e − μ + μ − , in a single tag configuration, are studied at LEP with the L3 detector. The data set corresponds to an integrated luminosity of 93.7 pb −1 at s =91 GeV. Differential cross sections are measured for 1.4 GeV 2 ≤Q 2 ≤7.6 GeV 2 . The leptonic photon structure function F γ 2 and azimuthal correlations are measured for e + e − → e + e − μ + μ − . The related structure functions F γ A and F γ B , which originate from interference terms of the scattering amplitudes, are determined for the first time.
The systematic and statistical errors added in quadrature. F2(NAME=FA) AND F2(NAME=FB) are related structure functions FA and FB, which originate from inerference terms of the scattering amplitudes. See text for exact definition and details.
We present a measurement of the average b-hadron lifetime τ b at the e + e − collider LEP. Using hadronic Z decays collected in the period from 1991 to 1994, two independent analyses have been performed. In the first one, the b-decay position is reconstructed as a secondary vertex of hadronic b-decay particles. The second analysis is an updated measurement of τ b using the impact parameter of leptons with high momentum and high transverse momentum. The combined result is τ b =[1549±9 (stat) ±15 (syst)] fs . In addition, we measure the average charged b-decay multiplicity 〈 n b 〉 and the normalized average b-energy 〈 x E 〉 b at LEP to be 〈n b 〉=4.90±0.04 (stat)±0.11 (syst), 〈x E 〉 b =0.709±0.004 (stat+syst).
No description provided.
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We report on measurements of e + e − annihilation into hadrons and lepton pairs. The data have been taken with the L3 detector at LEP at center-of-mass energies between 161 GeV and 172 GeV. In a data sample corresponding to 21.2 pb −1 of integrated luminosity 2728 hadronic and 868 lepton-pair events are selected. The measured cross sections and leptonic forward-backward asymmetries agree well with the Standard Model predictions.
No description provided.
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We describe the sample of energetic single-photon events ( E γ > 15 GeV) collected by L3 in the 1991–1993 LEP runs. The event distributions agree with expectations from the Standard Model. The data are used to constrain the ZZ γ coupling and to set an upper limit of 4.1 × 10 −6 , μ B (90% C.L.) on the the magnetic moment of the τ neutrino.
The number of events expected from Standard Model is 8.2. Here UNSPEC is 'invisible' particle.
90 PCT C.L. limit on an anomalous magnetic moment for tau-neutrino from '1GAMMA + nothing' events. Magnetic moment in Bohr magnetons.
We have determined the strong coupling $\as$ from a comprehensive study of energy-energy correlations ($EEC$) and their asymmetry ($AEEC$) in hadronic decays of $Z~0$ bosons collected by the SLD experiment at SLAC. The data were compared with all four available predictions of QCD calculated up to $\Oa2$ in perturbation theory, and also with a resummed calculation matched to all four of these calculations. We find large discrepancies between $\as$ values extracted from the different $\Oa2$ calculations. We also find a large renormalization scale ambiguity in $\as$ determined from the $EEC$ using the $\Oa2$ calculations; this ambiguity is reduced in the case of the $AEEC$, and is very small when the matched calculations are used. Averaging over all calculations, and over the $EEC$ and $AEEC$ results, we obtain $\asz=0.124~{+0.003}_{-0.004} (exp.) \pm 0.009 (theory).$
Statistical errors only.
Statistical errors only.
ALPHAS from the EEC O(ALPHAS**2) measurement.
We present a study of the global event shape variables thrust and heavy jet mass, of energy-energy correlations and of jet multiplicities based on 250 000 hadronic Z 0 decays. The data are compared to new QCD calculations including resummation of leading and next-to-leading logarithms to all orders. We determine the strong coupling constant α s (91.2 GeV) = 0.125±0.003 (exp) ± 0.008 (theor). The first error is the experimental uncertainty. The second error is due to hadronization uncertainties and approximations in the calculations of the higher order corrections.
Measured EEC distribution corrected for detector effects and photon radiation. Errors are combined statistical and systematic uncertainties.
Measured average jet multiplicities for the K_PT algorithm. All numbers are corrected for detector effects and photon radiation. Errors are combined statistical and systematic uncertainties.
Value of strong coupling constant, alpha_s, determined from the data. First error is experimental, the second is theoretical.
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