We report a measurement of the differential cross section of $\pi^0$ pair production in single-tag two-photon collisions, $\gamma^* \gamma \to \pi^0 \pi^0$, in $e^+ e^-$ scattering. The cross section is measured for $Q^2$ up to 30 GeV$^2$, where $Q^2$ is the negative of the invariant mass squared of the tagged photon, in the kinematic range 0.5 GeV < W < 2.1 GeV and $|\cos \theta^*|$ < 1.0 for the total energy and pion scattering angle, respectively, in the $\gamma^* \gamma$ center-of-mass system. The results are based on a data sample of 759 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The transition form factor of the $f_0(980)$ and that of the $f_2(1270)$ with the helicity-0, -1, and -2 components separately are measured for the first time and are compared with theoretical calculations.
$W$ dependence of the differential cross section ${\rm d}\sigma/{\rm d}|\cos\theta^*|$ in five $|\cos\theta^*|$ bins for $Q^2$=3.45 GeV$^2$.
$W$ dependence of the differential cross section ${\rm d}\sigma/{\rm d}|\cos\theta^*|$ in five $|\cos\theta^*|$ bins for $Q^2$=4.46 GeV$^2$.
$W$ dependence of the differential cross section ${\rm d}\sigma/{\rm d}|\cos\theta^*|$ in five $|\cos\theta^*|$ bins for $Q^2$=5.47 GeV$^2$.
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.
We report a high-statistics measurement of the differential cross section of the process gamma gamma --> K^0_S K^0_S in the range 1.05 GeV <= W <= 4.00 GeV, where W is the center-of-mass energy of the colliding photons, using 972 fb^{-1} of data collected with the Belle detector at the KEKB asymmetric-energy e^+ e^- collider operated at and near the Upsilon-resonance region. The differential cross section is fitted by parameterized S-, D_0-, D_2-, G_0- and G_2-wave amplitudes. In the D_2 wave, the f_2(1270), a_2(1320) and f_2'(1525) are dominant and a resonance, the f_2(2200), is also present. The f_0(1710) and possibly the f_0(2500) are seen in the S wave. The mass, total width and product of the two-photon partial decay width and decay branching fraction to the K bar{K} state Gamma_{gamma gamma}B(K bar{K}) are extracted for the f_2'(1525), f_0(1710), f_2(2200) and f_0(2500). The destructive interference between the f_2(1270) and a_2(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states chi_{c0} and chi_{c2} are updated. Possible contributions from the chi_{c0}(2P) and chi_{c2}(2P) states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel eta_c --> K^0_S K^0_S is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.
The W dependence of the cross section after integrating up to |cosTheta*|<0.8 and 0.6.
The cos(Theta*) dependence of the differential cross section for the W ranges 1.10-1.11, 1.11-1.12 and 1.12-1.13.
The cos(Theta*) dependence of the differential cross section for the W ranges 1.13-1.14, 1.14-1.15 and 1.15-1.16.
We report the first measurement of the differential cross section for the process gamma gamma --> eta eta in the kinematic range above the eta eta threshold, 1.096 GeV < W < 3.8 GeV over nearly the entire solid angle range, |cos theta*| <= 0.9 or <= 1.0 depending on W, where W and theta* are the energy and eta scattering angle, respectively, in the gamma gamma center-of-mass system. The results are based on a 393 fb^{-1} data sample collected with the Belle detector at the KEKB e^+ e^- collider. In the W range 1.1-2.0 GeV/c^2 we perform an analysis of resonance amplitudes for various partial waves, and at higher energy we compare the energy and the angular dependences of the cross section with predictions of theoretical models and extract contributions of the chi_{cJ} charmonia.
Total cross section.
Angular dependence of the differential cross section for the W range 1.096 to 1.120 GeV.
Angular dependence of the differential cross section for the W range 1.120 to 1.160 GeV.
The cross sections for the reactions $e^+e^- \to \phi\eta, \quad \phi\eta', \quad \rho\eta, \quad \rho\eta'$ have been measured using a data sample of 516 fb$^{-1}$ collected with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. The corresponding values of the cross sections are: $1.4 \pm 0.4 \pm 0.1$ fb $(\phi\eta)$, $5.3 \pm 1.1 \pm 0.4$ fb $(\phi\eta')$, $3.1 \pm 0.5 \pm 0.1$ fb $(\rho\eta)$ and $3.3 \pm 0.6 \pm 0.2$ fb $(\rho\eta')$. The energy dependence of the cross sections is presented using Belle measurements together with those of CLEO and BaBar.
Radiativity corrected cross section.
The differential cross sections for the process $\gamma \gamma \to \pi^0 \pi^0$ have been measured in the kinematic range 0.6 GeV $< W < 4.1$ GeV, $|\cos \theta^*|<0.8$ in energy and pion scattering angle, respectively, in the $\gamma\gamma$ center-of-mass system. The results are based on a 223 fb$^{-1}$ data sample collected with the Belle detector at the KEKB $e^+ e^-$ collider. The differential cross sections are fitted in the energy region 1.7 GeV $< W <$ 2.5 GeV to confirm the two-photon production of two pions in the G wave. In the higher energy region, we observe production of the $\chi_{c0}$ charmonium state and obtain the product of its two-photon decay width and branching fraction to $\pi^0\pi^0$. We also compare the observed angular dependence and ratios of cross sections for neutral-pion and charged-pion pair production to QCD models. The energy and angular dependence above 3.1 GeV are compatible with those measured in the $\pi^+\pi^-$ channel, and in addition we find that the cross section ratio, $\sigma(\pi^0\pi^0)/\sigma(\pi^+\pi^-)$, is $0.32 \pm 0.03 \pm 0.05$ on average in the 3.1-4.1 GeV region.
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 a measurement of the exclusive \$e^+e^- \to \Lambda_c^+ \Lambda_c^-$ cross section as a function of center-of-mass energy near the $\Lambda_c^+ \Lambda_c^-$ threshold. A clear peak with a significance of $8.8\sigma$ is observed in the $\Lambda_c^+ \Lambda_c^-$ invariant mass distribution just above threshold. With an assumption of a resonance origin for the observed peak, a mass and width of $M=(4634^{+8}_{-7} \mathrm{(stat.)} ^{+5}_{-8} \mathrm{(sys.)})\mevc$ and $\Gamma_{\mathrm{tot}}=(92^{+40}_{-24} \mathrm{(stat.)}^{+10}_{-21} \mathrm{(sys.)})\mev$ are determined. The analysis is based on a study of events with initial-state-radiation photons in a data sample collected with the Belle detector at the $\Upsilon(4S)$ resonance and nearby continuum with an integrated luminosity of 695 $\mathrm{fb}^{-1}$ at the KEKB asymmetric-energy $e^+e^_$ collider.
Cross section for the exclusive process E+ E- --> LAMBDA/C+ LAMBDA/CBAR-.
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 measurements of the exclusive cross section for $e^+e^- \to D \overline D $, where $D=D^0$ or $D^+$, in the center-of-mass energy range from the $D \overline D $ threshold to $5\mathrm{GeV}/c^2$ with initial-state radiation. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of $673$ $\mathrm{fb}^{-1}$.
Cross section of E+ E- --> D0 DBAR0.
Cross section of E+ E- --> D+ D-.
We report the first observation of e+e- -> Upsilon(1S)pi+pi-, Upsilon(2S)pi+pi-, and first evidence for e+e- -> Upsilon(3S)pi+pi-, Upsilon(1S)K+K-, near the peak of the Upsilon(5S) resonance at sqrt{s}~10.87 GeV. The results are based on a data sample of 21.7 fb^-1 collected with the Belle detector at the KEKB e+e- collider. The observed cross-sections are sigma(Upsilon(1S)pi+pi-) = 1.61+-0.10(stat)+-0.12(sys) pb and sigma(Upsilon(2S)pi+pi-) = 2.35+-0.19(stat)+-0.32(sys) pb. Attributing these signals to the Upsilon(5S) resonance, the partial widths Gamma(Upsilon(5S)->Upsilon(1S)pi+pi-) = 0.59+-0.04(stat)+-0.09(sys) MeV and Gamma(Upsilon(5S)->Upsilon(2S)pi+pi-) = 0.85+-0.07(stat)+-0.16(sys) MeV are inferred. These are much larger than any partial widths for previously observed Upsilon(nS) -> Upsilon(1S)pi+pi-, Upsilon(2S)pi+pi- decays.
Cross section for the final state UPSI(1S) PI+ PI-.
Cross section for the final state UPSI(2S) PI+ PI-.
Cross section for the final state UPSI(3S) PI+ PI-.
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