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.
The nature of b-quark jet hadronisation has been investigated using data taken at the Z peak by the DELPHI detector at LEP. Two complementary methods are used to reconstruct the energy of weakly decaying b-hadrons, E^weak_B. The average value of x^weak_B = E^weak_B/E_beam is measured to be 0.699 +/- 0.011. The resulting x^weak_B distribution is then analysed in the framework of two choices for the perturbative contribution (parton shower and Next to Leading Log QCD calculation) in order to extract measurements of the non-perturbative contribution to be used in studies of b-hadron production in other experimental environments than LEP. In the parton shower framework, data favour the Lund model ansatz and corresponding values of its parameters have been determined within PYTHIA~6.156 from DELPHI data: a= 1.84^{+0.23}_{-0.21} and b=0.642^{+0.073}_{-0.063} GeV^-2, with a correlation factor rho = 92.2%. Combining the data on the b-quark fragmentation distributions with those obtained at the Z peak by ALEPH, OPAL and SLD, the average value of x^weak_B is found to be 0.7092 +/- 0.0025 and the non-perturbative fragmentation component is extracted. Using the combined distribution, a better determination of the Lund parameters is also obtained: a= 1.48^{+0.11}_{-0.10} and b=0.509^{+0.024}_{-0.023} GeV^-2, with a correlation factor rho = 92.6%.
The combined unfolded and weighted results, per bin, for $f(x^{\rm weak}_{\rm B})$. Quoted uncertainties have been scaled by 1.31.
The average value of the $x^{\rm weak}_{\rm B}$ distribution.
A study of the inclusive charged hadron production in two-photon collisions is described. The data were collected with the DELPHI detector at LEP II. Results on the inclusive single-particle p_T distribution and the differential charged hadrons dsigma/dp_T cross-section are presented and compared to the predictions of perturbative NLO QCD calculations and to published results.
Differential inclusive DSIG/DPT distribution of charged particles produced in GAMMA* GAMMA* interaction with two pseudorapidity cut offs.
The ZZ production cross section is measured from a data sample corresponding to a total integrated luminosity of 452 pb(-')(1), collected by the ALEPH experiment at LEP at centre-of-mass energies from 192 to 209 GeV. Individual cross sections, ext racted at six centre-of-mass energies, are found to be in agreement with Standard Model calculations. The results are used to set limits on anomalous neutral gauge couplings.
Measured E+ E- --> Z0 Z0 cross sections.
The production of two high-p_T jets in the interactions of quasi-real photons in e+e- collisions at sqrt{s_ee} from 189 GeV to 209 GeV is studied with data corresponding to an integrated e+e- luminosity of 550 pb^{-1}. The jets reconstructed by the k_T cluster algorithm are defined within the pseudo-rapidity range -1 < eta < 1 and with jet transverse momentum, p_T, above 3 GeV/c. The differential di-jet cross-section is measured as a function of the mean transverse momentum ptmean of the jets and is compared to perturbative QCD calculations.
Total cross section for dijet production. Errors are combined statistics and systematics.
Measured dijet production cross section as a function of the mean jet transverse momentum. Errors include both statistics and systematics.
Measured dijet production cross section as a function of jet pseudorapiditydifference. Errors include both statistics and systematics.
Inclusive beauty-quark production in two-photon collisions has been measured at LEP using an integrated luminosity of 698 pb-1 collected by the ALEPH detector with sqrt(s) between 130 and 209 GeV. The b quarks were identified using lifetime information. The cross section is found to be sigma(e+ e- --> e+ e- b \bar{b} X) = (5.4 +/- 0.8 (stat) +/- 0.8 (syst)) pb which is consistent with Next-to-Leading Order QCD.
Cross section for the process E+ E- --> E+ E- BQUARK BQUARKBAR X.
Measurements of inclusive production of the Lambda, Xi- and Xi*(1530) baryons in two-photon collisions with the L3 detector at LEP are presented. The inclusive differential cross sections for Lambda and Xi- are measured as a function of the baryon transverse momentum, pt, and pseudo-rapidity, eta. The mean number of Lambda, Xi- and Xi*(1530) baryons per hadronic two-photon event is determined in the kinematic range 0.4 GeV < pt< 2.5 GeV, |eta| < 1.2. Overall agreement with the theoretical models and Monte Carlo predictions is observed. A search for inclusive production of the pentaquark theta+(1540) in two-photon collisions through the decay theta+ -> proton K0s is also presented. No evidence for production of this state is found.
Differential cross section for LAMBDA production.
Differential cross section for LAMBDA production.
Differential cross section for XI- production.
Measurements of the Xi- and anti-Xi+ masses, mass differences, lifetimes and lifetime differences are presented. The anti-Xi+ sample used is much larger than those used previously for such measurements. In addition, the Xi production rates in Z -> b anti-b and Z -> q anti-q events are compared and the position xi* of the maximum of the xi distribution in Z -> q anti-q events is measured.
Corrected LN(1/X) distribution for (XI- + XIBAR+) production.
Measured and extrapoplated production rates.
Extrapolated production rate in b-bbar events.
Hadron production and lepton-pair production in e+e- collisions are studied with data collected with the L3 detector at LEP at centre-of-mass energies sqrt{s}=192-208GeV. Using a total integrated luminosity of 453/pb, 36057 hadronic events and 12863 lepton-pair events are selected. The cross sections for hadron production and lepton-pair production are measured for the full sample and for events where no high-energy initial-state-radiation photon is emitted prior to the collisions. Lepton-pair events are further investigated and forward-backward asymmetries are measured. Finally, the differential cross sections for electron-positron pair-production is determined as a function of the scattering angle. An overall good agreement is found with Standard Model predictions.
Measured hadron cross section for the inclusive data sample.
Measured hadron cross section for the high-energy data sample.
Measured MU+ MU- cross section for the inclusive data sample.
This paper presents DELPHI measurements and interpretations of cross-sections, forward-backward asymmetries, and angular distributions, for the e+e- -> ffbar process for centre-of-mass energies above the Z resonance, from sqrt(s) ~ 130 - 207 GeV at the LEP collider. The measurements are consistent with the predictions of the Standard Model and are used to study a variety of models including the S-Matrix ansatz for e+e- -> ffbar scattering and several models which include physics beyond the Standard Model: the exchange of Z' bosons, contact interactions between fermions, the exchange of gravitons in large extra dimensions and the exchange of sneutrino in R-parity violating supersymmetry.
Measured cross sections and forward-backward asymmetries for non-radiative E+ E- --> E+ E- events.
Differential cross sections for non-radiative E+ E- --> E+ E- events at centre of mass energy 189 GeV.
Differential cross sections for non-radiative E+ E- --> E+ E- events at centre of mass energy 192 GeV.
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