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 NA61/SHINE experiment at the CERN SPS is performing a uniqe study of the phase diagram of strongly interacting matter by varying collision energy and nuclear mass number of colliding nuclei. In central Pb+Pb collisions the NA49 experiment found structures in the energy dependence of several observables in the CERN SPS energy range that had been predicted for the transition to a deconfined phase. New measurements of NA61/SHINE find intriguing similarities in p+p interactions for which no deconfinement transition is expected at SPS energies. Possible implications will be discussed.
K+/PI+ at y=0.
K+/PI+ at y=0.
<K+>/<PI+>.
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.
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.
We study the processes $e^+ e^-\to K_S^0 K_L^0 \gamma$, $K_S^0 K_L^0 \pi^+\pi^-\gamma$, $K_S^0 K_S^0 \pi^+\pi^-\gamma$, and $K_S^0 K_S^0 K^+K^-\gamma$, where the photon is radiated from the initial state, providing cross section measurements for the hadronic states over a continuum of center-of-mass energies. The results are based on 469 fb$^{-1}$ of data collected with the BaBar detector at SLAC. We observe the $\phi(1020)$ resonance in the $K_S^0 K_L^0$ final state and measure the product of its electronic width and branching fraction with about 3% uncertainty. We present a measurement of the $e^+ e^-\to K_S^0 K_L^0 $ cross section in the energy range from 1.06 to 2.2 GeV and observe the production of a resonance at 1.67 GeV. We present the first measurements of the $e^+ e^-\to K_S^0 K_L^0 \pi^+\pi^-$, $K_S^0 K_S^0 \pi^+\pi^-$, and $K_S^0 K_S^0 K^+K^-$ cross sections, and study the intermediate resonance structures. We obtain the first observations of \jpsi decay to the $K_S^0 K_L^0 \pi^+\pi^-$, $K_S^0 K_S^0 \pi^+\pi^-$, and $K_S^0 K_S^0 K^+K^-$ final states.
Cross section measurement for PHI(1020).
Mass measurement for PHI(1020).
Measurement of the PHI(1020) width.
The process e+e- --> p anti-p gamma is studied using 469 fb-1 of integrated luminosity collected with the BABAR detector at the PEP-II collider, at an e+e- center-of-mass energy of 10.6 GeV. From the analysis of the p anti-p invariant mass spectrum, the energy dependence of the cross section for e+e- --> p anti-p is measured from threshold to 4.5 GeV. The energy dependence of the ratio of electric and magnetic form factors, |G_E/G_M|, and the asymmetry in the proton angular distribution are measured for p anti-p masses below 3 GeV. We also measure the branching fractions for the decays J/psi --> p anti-p and psi(2S) --> p anti p.
Measurement of the cross section as a function of the invariant mass of the PBAR-P system and the effective form factor for the reaction E+ E- --> PBAR P. The contributions from J/PSI and PSI(25) decaying to PBAR-P have been subtracted. The form factor error is the combined statistical and systematic.
We study the processes e+e- --> K+ K- pi+pi-gamma, K+ K- pi0pi0gamma, and K+ K- K+ K-gamma, where the photon is radiated from the initial state. About 84000, 8000, and 4200 fully reconstructed events, respectively, are selected from 454 fb-1 of BaBar data. The invariant mass of the hadronic final state defines the \epem center-of-mass energy, so that the K+ K- pi+pi- data can be compared with direct measurements of the e+e- --> K+ K- pi+pi- reaction. No direct measurements exist for the e+e- --> K+ K-pi0pi0 or e+e- --> K+ K-K+ K- reactions, and we present an update of our previous result with doubled statistics. Studying the structure of these events, we find contributions from a number of intermediate states, and extract their cross sections. In particular, we perform a more detailed study of the e+e- --> phi(1020)pipigamma reaction, and confirm the presence of the Y(2175) resonance in the phi(1020) f0(980) and K+K-f0(980) modes. In the charmonium region, we observe the J/psi in all three final states and in several intermediate states, as well as the psi(2S) in some modes, and measure the corresponding product of branching fraction and electron width.
The cross section for the reaction E+ E- --> K+ K- PI+ PI- measured with ISR data. Statistical errors only.
Cross section measurements for the reaction E+ E- --> K*(892)0 K- PI+. Statistical errors only.
Cross section measurements for the reaction E+ E- --> PHI PI+ PI-. Statistical errors only.
We report a high-statistics measurement of differential cross sections for the process gamma gamma -> pi^0 pi^0 in the kinematic range 0.6 GeV <= W <= 4.0 GeV and |cos theta*| <= 0.8, where W and theta* are the energy and pion scattering angle, respectively, in the gamma gamma center-of-mass system. Differential cross sections are fitted to obtain information on S, D_0, D_2, G_0 and G_2 waves. The G waves are important above W ~= 1.6 GeV. For W <= 1.6 GeV the D_2 wave is dominated by the f_2(1270) resonance while the S wave requires at least one additional resonance besides the f_0(980), which may be the f_0(1370) or f_0(1500). The differential cross sections are fitted with a simple parameterization to determine the parameters (the mass, total width and Gamma_{gamma gamma}B(f_0 -> pi^0 pi^0)) of this scalar meson as well as the f_0(980). The helicity 0 fraction of the f_2(1270) meson, taking into account interference for the first time, is also obtained.
Differential cross section for W = 0.61, 0.63 and 0.65 GeV.
Differential cross section for W = 0.67, 0.69 and 0.71 GeV.
Differential cross section for W = 0.73, 0.75 and 0.77 GeV.
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.
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