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.
Using data collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider, we measure the energy dependence of the $e^+e^- \to h_b(nP)\pi^+\pi^-$ $(n=1,2)$ cross sections from thresholds up to $11.02\,$GeV. We find clear $\Upsilon(10860)$ and $\Upsilon(11020)$ peaks with little or no continuum contribution. We study the resonant substructure of the $\Upsilon(11020) \to h_b(nP)\pi^+\pi^-$ transitions and find evidence that they proceed entirely via the intermediate isovector states $Z_b(10610)$ and $Z_b(10650)$. The relative fraction of these states is loosely constrained by the current data: the hypothesis that only $Z_b(10610)$ is produced is excluded at the level of 3.3 standard deviations, while the hypothesis that only $Z_b(10650)$ is produced is not excluded at a significant level.
Center-of-mass energies, integrated luminosities and Born cross sections for all energy points. The first uncertainty in the energy is uncorrelated, the second is correlated. The three uncertainties in the cross sections are statistical, uncorrelated systematic and correlated systematic.
Measurements of inclusive differential cross sections for charged pion and kaon production in electron-positron annihilation have been carried out at a center-of-mass energy of Q = 10.52 GeV. The measurements were performed with the Belle detector at the KEKB electron-positron collider using a data sample containing 113 million e+e- -> qqbar events, where q={u,d,s,c}. We present charge-integrated differential cross sections d\sigma_h+-/dz for h+- = pi+-, K+- as a function of the relative hadron energy z = 2*E_h / sqrt{s} from 0.2 to 0.98. The combined statistical and systematic uncertainties for pi+- (K+-) are 4% (4%) at z ~ 0.6 and 15% (24%) at z ~ 0.9. The cross sections are the first measurements of the z-dependence of pion and kaon production for z > 0.7 as well as the first precision cross section measurements at a center-of-mass energy far below the Z^0 resonance used by the experiments at LEP and SLC.
Measured charged-integrated differential cross sections for charged pion and kaon production as a function of the fractional hadron energy Z (=2*Eh/sqrt(s)).
A search for charmonium and other new states is performed in a study of exclusive initial-state-radiation production of D Dbar events from electron-positron annihilations at a center-of-mass energy of 10.58 GeV. The data sample corresponds to an integrated luminosity of 384 fb-1 and was recorded by the BABAR experiment at the PEP-II storage ring. The D Dbar mass spectrum shows clear evidence of the psi(3770) plus other structures near 3.9, 4.1, and 4.4 GeV/c^2. No evidence for Y(4260) -> D Dbar is observed, leading to an upper limit of B(Y(4260) -> D Dbar)/B(Y(4260) -> J/psi pi+ pi-) < 1.0 at 90 % confidence level.
Measured cross section for D0 DBAR0 and D+ D- production. Bins with no data are shown with a 'dash'.
This paper reports measurements of processes: e+e- -> gamma KsK+pi-, e+e- -> gamma K+K-pi0, e+e- -> gamma phi eta, and e+e- -> gamma phi pi0. The initial state radiated photon allows to cover the hadronic final state in the energy range from thresholds up to ~4.6 GeV. The overall size of the data sample analyzed is 232 fb-1, collected by the BaBar detector running at the PEP-II e+e- storage ring. From the Dalitz plot analysis of the KsK+pi- final state, moduli and relative phase of the isoscalar and the isovector components of the e+e- -> K K*(892) cross section are determined. Parameters of phi and rho recurrences are also measured, using a global fitting procedure which exploits the interconnection among amplitudes, moduli and phases of the e+e- -> KsK+pi-, K+K-pi0, phi eta final states. The cross section for the OZI-forbidden process e+e- -> phi pi0, and the J/psi branching fractions to KK*(892) and K+K-eta are also measured.
The cross section for E+ E- --> K0S K+ PI- + CC with statistical errors only.
The cross section for E+ E- --> K+ K- PI0 with statistical errors only.
The cross section for E+ E- --> PHI PI0 with statistical errors only.
We study the processes $e^+ e^-\to 2(\pi^+\pi^-)\pi^0\gamma$, $2(\pi^+\pi^-)\eta\gamma$, $K^+ K^-\pi^+\pi^-\pi^0\gamma$ and $K^+ K^-\pi^+\pi^-\eta\gamma$ with the hard photon radiated from the initial state. About 20000, 4300, 5500 and 375 fully reconstructed events, respectively, are selected from 232 fb$^{-1}$ of BaBar data. The invariant mass of the hadronic final state defines the effective $e^+ e^-$ center-of-mass energy, so that the obtained cross sections from the threshold to about 5 GeV can be compared with corresponding direct \epem measurements, currently available only for the $\eta\pi^+\pi^-$ and $\omega\pi^+\pi^-$ submodes of the $e^+ e^-\to 2(\pi^+\pi^-)\pi^0$ channel. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from $e^+ e^-\to\omega(782)\pi^+\pi^-$ and study the $\omega(1420)$ and $\omega(1650)$ resonances. In the charmonium region, we observe the $J/\psi$ in all these final states and several intermediate states, as well as the $\psi(2S)$ in some modes, and we measure the corresponding branching fractions.
Measured cross section for E+ E- --> 2(PI+ PI-) PI0 with statistical errorsonly.
Measured cross section for E+ E- --> ETA PI+ PI- with statistical errors only.
Measured cross section for E+ E- --> OMEGA PI+ PI- with statistical errors only.
We study the processes $e^+ e^-\to K^+ K^- \pi^+\pi^-\gamma$, $K^+K^-\pi^0\pi^0\gamma$ and $K^+ K^- K^+ K^-\gamma$, where the photon is radiated from the initial state. About 34600, 4400 and 2300 fully reconstructed events, respectively, are selected from 232 \invfb of \babar data. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy, so that the $K^+ K^- \pi^+\pi^-\gamma$ data can be compared with direct measurements of the $e^+ e^-\to K^+K^- \pipi$ reaction/ no direct measurements exist for the $e^+ e^-\to K^+ K^- \pi^0\pi^0$ or $\epem\to K^+ K^- K^+ K^-$ reactions. Studying the structure of these events, we find contributions from a number of intermediate states, and we extract their cross sections where possible. In particular, we isolate the contribution from $e^+ e^-\to\phi(1020) f_{0}(980)$ and study its structure near threshold. In the charmonium region, we observe the $J/\psi$ in all three final states and several intermediate states, as well as the $\psi(2S)$ in some modes, and measure the corresponding branching fractions. We see no signal for the Y(4260) and obtain an upper limit of $\BR_{Y(4260)\to\phi\pi^+\pi^-}\cdot\Gamma^{Y}_{ee}<0.4 \ev$ at 90% C.L.
Measurement of the E+ E- --> K+ K- PI+ PI- cross section. Statistical errors only.
Measurement of the E+ E- --> K(892)0 K PI cross section. Statistical errors only.
Measurement of the E+ E- --> PHI PI+ PI- cross section. Statistical errors only.
We report the observation of $\e^+e^-\to \phi\eta$ near $\sqrt{s}$ = 10.58 GeV with 6.5 $\sigma$ significance in the $K^+K^-\gamma\gamma$ final state in a data sample of 224 $fb^{-1}$ collected by the BaBar experiment at the PEP-II $e^+e^-$ storage rings. We measure the restricted radiation-corrected cross section to be $\sigma(\e^+e^- \to \phi \eta) =$$2.1\pm 0.4 (\mathrm{stat})\pm 0.1(\mathrm{syst}) \mathrm{fb}$ within the range $|\cos\theta^*| < 0.8$, where $\theta^*$ is the center-of-mass polar angle of the $\phi$ meson. The $\phi$ meson is required to be in the invariant mass range of 1.008 $< m_{\phi} <$ 1.035 \gevcc. The radiation-corrected cross section in the full $\cos\theta^*$ range is extrapolated to be $2.9\pm 0.5 (\mathrm{stat})\pm 0.1(\mathrm{syst}) \mathrm{fb}$.
Radiation corrected cross section in the limited cos(theta) range and extrapolated to the full range assuming a 1+ cos(theta)**2 dependence.
We present a measurement of the cross section of the process $e^+e^-\to\pi^+pi^-\psi(2S)$ from threshold up to 8 GeV center-of-mass energy using events containing initial-state radiation, produced at the PEP-II $e^+e^-$ storage rings. The study is based on 298 fb$^{-1}$ of data recorded with the BaBar detector. A structure is observed in the cross-section not far above threshold, near 4.32 GeV. We also investigate the compatibility of this structure with the Y(4260) previously reported by this experiment.
The measured c.m. energy dependence of the cross section with statistical errors only.. Bins with no recorded data are shown as a 'dash'.
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.
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