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.
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.
We report on a high statistics measurement of the total and differential cross sections of the process gamma gamma -> pi^+ pi^- in the pi^+ pi^- invariant mass range 0.8 GeV/c^2 < W < 1.5 GeV/c^2 with 85.9 fb^{-1} of data collected at sqrt{s}=10.58 GeV and 10.52 GeV with the Belle detector. A clear signal of the f_0(980) resonance is observed in addition to the f_2(1270) resonance. An improved 90% confidence level upper limit Br.(eta'(958) -> pi^+ pi^-) < 2.9 x 10^{-3} is obtained for P- and CP-violating decay of the eta'(958) meson using the most conservative assumption about the interference with the background.
Total cross section.
No description provided.
No description provided.
The reaction $^2$H$(e,e^\prime p)n$ has been studied with full kinematic coverage for photon virtuality $1.75
Recoil neutron momentum distributions.
Recoil neutron angular distributions for neutron momenta in the range 400 to 600 MeV.
Recoil neutron angular distributions for neutron momenta in the range 200 to 300 MeV.
$K^0_SK^0_S$ production in two-photon collisions has been studied using a 397.6 fb$^{-1}$ data sample collected with the Belle detector at the KEKB $e^+e^-$ collider. For the first time the cross sections are measured in the two-photon center-of-mass energy range between 2.4 GeV and 4.0 GeV and angular range $|\cos\theta^*|<0.6$. Combining the results with measurements of $\gamma\gamma\to K^+K^-$ from Belle, we observe that the cross section ratio $\sigma(K^0_SK^0_S)/\sigma(K^+K^-)$ decreases from ~0.13 to ~0.01 with increasing energy. Signals for the $\chi_{c0}$ and $\chi_{c2}$ charmonium states are also observed.
Total cross section for the process GAMMA GAMMA --> K0S K0S.
Angular distribution of the cross section in the W range 2.4 to 2.5 GeV.
Angular distribution of the cross section in the W range 2.5 to 2.6 GeV.
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.
We study the process $e^+e^-\to\pi^+\pi^-\pi^+\pi^-\gamma$, with a hard photon radiated from the initial state. About 60,000 fully reconstructed events have been selected from 89 $fb^{-1}$ of BaBar data. The invariant mass of the hadronic final state defines the effective \epem center-of-mass energy, so that these data can be compared with the corresponding direct $e^+e^-$ measurements. From the $4\pi$-mass spectrum, the cross section for the process $e^+e^-\to\pi^+\pi^-\pi^+\pi^-$ is measured for center-of-mass energies from 0.6 to 4.5 $GeV/c^2$. The uncertainty in the cross section measurement is typically 5%. We also measure the cross sections for the final states $K^+ K^- \pi^+\pi^-$ and $K^+ K^- K^+ K^-$. We observe the $J/\psi$ in all three final states and measure the corresponding branching fractions. We search for X(3872) in $J/\psi (\to\mu^+\mu^-) \pi^+\pi^-$ and obtain an upper limit on the product of the $e^+e^-$ width of the X(3872) and the branching fraction for $X(3872) \to J/\psi\pi^+\pi^-$.
Measured PI+ PI- PI+ PI- cross sections. The errors are statistical only.
Measured K+ K- PI+ PI- cross sections. The errors are statistical only.
Measured K+ K- K+ K- cross sections. The errors are statistical only.
The process e+e- --> pi+ pi- pi0 gamma has been studied at a center-of-mass energy near the Y(4S) resonance using a 89.3 fb-1 data sample collected with the BaBar detector at the PEP-II collider. From the measured 3pi mass spectrum we have obtained the products of branching fractions for the omega and phi mesons, B(omega --> e+e-)B(omega --> 3pi)=(6.70 +/- 0.06 +/- 0.27)10-5 and B(phi --> e+e-)B(phi --> 3pi)=(4.30 +/- 0.08 +/- 0.21)10-5, and evaluated the e+e- --> pi+ pi- pi0 cross section for the e+e- center-of-mass energy range 1.05 to 3.00 GeV. About 900 e+e- --> J/psi gamma --> pi+ pi- pi0 gamma events have been selected and the branching fraction B(J/psi --> pi+ pi- pi0)=(2.18 +/- 0.19)% has been measured.
The measured 3PI mass spectrum calculated for a 25 MeV bin size.
The cross section of the process e+ e- --> pi0 pi0 gamma has been measured in the c.m. energy range 600--970 MeV with the CMD-2 detector. The following branching ratios have been determined: B(rho --> pi0 pi0 gamma) =(5.2^{+1.5}_{-1.3} +- 0.6)x10^{-5} and B(omega --> pi0 pi0 gamma) =(6.4^{+2.4}_{-2.0} +- 0.8)x10^{-5}. Evidence for the rho --> f0(600) gamma decay has been obtained: B(rho --> f0(600) gamma) = (6.0^{+3.3}_{-2.7}\pm 0.9)x10^{-5}. From a search for the process e+ e- --> eta pi0 gamma the following upper limit has been obtained: B(omega --> eta pi0 gamma) < 3.3 10^{-5} at 90% CL.
The Born and 'bare' cross sections.
The cross section of the process e+ e- --> omega pi0 --> pi0 pi0 gamma has been measured in the c.m. energy range 920-1380 MeV with the CMD-2 detector. Its energy dependence is well described by the interference of the rho(770) and rho'(1450) mesons decaying to omega pi0. Upper limits for the cross sections of the direct processes e+ e- --> pi0 pi0 gamma, eta pi0 gamma have been set.
Measurement of the Born cross section and the 'Bare' cross section of the process E+ E- --> OMEGA < PI0 GAMMA > PI0.
Upper limits for the non OMEGA PI0 cross section.
Upper limits of the ETA PI0 GAMMA cross section.
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