Results are presented on the exclusive production of four-prong final states in photon-photon collisions from the TPC/Two-Gamma detector at the SLAC e+e− storage ring PEP. Measurement of dE/dx and momentum in the time-projection chamber (TPC) provides identification of the final states 2π+2π−, K+K−π+π−, and 2K+2K−. For two quasireal incident photons, both the 2π+2π− and K+K−π+π− cross sections show a steep rise from threshold to a peak value, followed by a decrease at higher mass. Cross sections for the production of the final states ρ0ρ0, ρ0π+π−, and φπ+π− are presented, together with upper limits for φρ0, φφ, and K*0K¯ *0. The ρ0ρ0 contribution dominates the four-pion cross section at low masses, but falls to nearly zero above 2 GeV. Such behavior is inconsistent with expectations from vector dominance but can be accommodated by four-quark resonance models or by t-channel factorization. Angular distributions for the part of the data dominated by ρ0ρ0 final states are consistent with the production of JP=2+ or 0+ resonances but also with isotropic (nonresonant) production. When one of the virtual photons has mass (mγ2=-Q2≠0), the four-pion cross section is still dominated by ρ0ρ0 at low final-state masses Wγγ and by 2π+2π− at higher mass. Further, the dependence of the cross section on Q2 becomes increasingly flat as Wγγ increases.
TAGGED DATA, RESULTS OBTAINED USING TRANSVERSE-TRANSVERSE LUMINOSITY ONLY. DATA FOR Q2=0 ARE FROM UNTAGGED SAMPLE, ERRORS DUE TO RELATIVE NORMALISATION OF THESE SAMPLES IS INCLUDED INTO ERRORS QUOTED.
UNTAGGED DATA.
Using data onvp and\(\bar vp\) charged current interactions from a bubble chamber experiment with BEBC at CERN, the average multiplicities of charged hadrons and pions are determined as functions ofW2 andQ2. The analysis is based on ∼20000 events with incidentv and ∼10000 events with incident\(\bar v\). In addition to the known dependence of the average multiplicity onW2 a weak dependence onQ2 for fixed intervals ofW is observed. ForW>2 GeV andQ2>0.1 GeV2 the average multiplicity of charged hadrons is well described by〈n〉=a1+a2ln(W2/GeV2)+a3ln(Q2/GeV2) witha1=0.465±0.053,a2=1.211±0.021,a3=0.103±0.014 for thevp anda1=−0.372±0.073,a2=1.245±0.028,a3=0.093±0.015 for the\(\bar vp\) reaction.
No description provided.
No description provided.
No description provided.
We have observed 1085 events of the type e + e − → hadrons, in the total centre-of-mass energy range √ s = 1.2 to 3.0 GeV. The energy dependence of the total annihilation cross-section, parametrized in the form σ ( e + e − → hadrons ) = A · s n , is measured to be n = -(1.54 −0.29 +0.17 ) in the above energy range.
RESULTS USING THE (AP P) MODEL WITH PHASE-SPACE CORRECTIONS.
R AS CALCULATED FROM THE TOTAL HADRONIC CROSS SECTION USING THE (AP P) MODEL.
TOTAL CROSS SECTIONS OBTAINED USING THE QUASI-MODEL-INDEPENDENT METHOD ARE TABULATED HERE.
The study of 620 hadron pairs produced in the s -range (1.44−9.0) GeV 2 , has yielded 110 collinear hadronic events. Their identification in terms of π and K mesons allows the determination of the time-like electromagnetic from factors of these pseudoscalar mesons in the above time-like range. The total number of (e + e − ) events observed in the same experimental conditions is 18 048.
No description provided.
We report measurements of the asymmetry A_parallel for inclusive hadron production on longitudinally polarized proton and deuteron targets by circularly polarized photons. The photons were produced via internal and external bremsstrahlung from an electron beam of 48.35 GeV. Asymmetries for both positive and negative signed hadrons, and a subset of identified pions, were measured in the momentum range 10<P<30 GeV at 2.75 and 5.5 degrees. Small non-zero asymmetries are observed for the proton, while the deuteron results are consistent with zero. Recent calculations do not describe the data well.
The asymmetry for polarized photoproduction of inclusive hadrons from a polarized proton target. The errors are statistical only.
The asymmetry for polarized photoproduction of inclusive identified pions from a polarized proton target. The errors are statistical only.
We have measured the production cross section for K s 0 in e + e − annihilation from 3.6 to 5.0 GeV center of mass energy. A substantial increase of the K s 0 yield is observed around 4 GeV in qualitative agreement with the charm hypothesis.
No description provided.
An analysis has been performed of neutrino and antineutrino interactions with protons and neutrons in a deuterium bubble chamber. The interactions under study are quasielastic neutrino-neutron scattering and one-, two- and three-pion production reactions. Results are presented on cross sections, effective mass distributions, resonance production, momentum transfer distributions and coefficients of the decay angular distributions. Where possible, comparisons are made with existing theoretical models and predictions.
Numerical values supplied by A.Tenner. Note - the binning in this table is smaller than in the publication.
Numerical values supplied by A.Tenner. Note - the binning in this table is smaller than in the publication.
Numerical values supplied by A.Tenner. Note - the binning in this table is smaller than in the publication.
We present the first data on photon-photon annihilation into hadrons for CM energies > 1 GeV obtained with the detector PLUTO at the e + e − storage ring PETRA. Cross sections are extracted using an inelastic eγ scattering formalism. The results are compared to expectations from Regge-like models.
DEPENDENCE OF CROSS SECTION FOR ELECTRON-PHOTON SCATTERING (ANALOGOUS TO HAND'S FORMULA) ON VISIBLE HADRONIC ENERGY, CALCULATED BY TAKING PION MASSES FOR ALL CHARGED PARTICLES.
Results on the elastic K − π − scattering have been obtained from a study of the K − π − system in 15 000 events of the type K − p→K − π − p π + at a K − beam momentum of 4.25 GeV/ c . The on-mass-shell values of the spherical harmonic moments of the K − π − scattering angular distribution and the K − π − elastic cross section have been obtained by extrapolation to the pion pole. From these values we determined the s- and p-wave phase shifts δ 0 3 and δ 1 3 as a function of the effective mass of the K − π − system between threshold and 1.25 GeV/ c 2 . The value of | δ 0 3 | is smaller than 17° for all mass values and the existence of a p-wave cannot be neglected. At m K − π − = 1.18 GeV/ c 2 there are two solutions for the phase shifts. On the average, the cross section of the K − π − elastic scattering over the region of the effective mass considered amounts to approximately 2.5 mb.
The errors are statistical.
We present new high statistics data on hadron production in photon-photon reactions. The data are analyzed in terms of an electron-photon scattering formalism. The dependence of the total cross section of Q 2 , the four-momentum transfer squared of the scattered electron, and on the mass W of the hadronic system is investigated. The data are compared to predictions from Vector-Meson Dominance and the quark model.
DEPENDENCE ON VISIBLE HADRONIC INVARIANT MASS.
We have measured the crosss section for the reaction e + e − → 4 π ± in the energy range 1 2–3.0 GeV.No statistically significant evidence for a new vector meson in the ϱ″ region is found.
No description provided.
We study the processes e+ e- --> 3(pi+pi-)gamma, 2(pi+pi-pi0)gamma and K+ K- 2(pi+pi-)gamma, with the photon radiated from the initial state. About 20,000, 33,000 and 4,000 fully reconstructed events, respectively, have been 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 these data can be compared with the corresponding direct e+e- measurements. From the 3(pi+pi-), 2(pi+pi-pi0) and K+ K- 2(pi+pi-) mass spectra, the cross sections for the processes e+ e- --> 3(pi+pi-), e+ e- --> 2(pi+pi-pi0) and e+ e- --> K+ K- 2(pi+pi-) are measured for center-of-mass energies from production threshold to 4.5 GeV. The uncertainty in the cross section measurement is typically 6-15%. We observe the J/psi in all these final states and measure the corresponding branching fractions.
The cross section for E+ E- --> 3PI+ 3PI- as measured with the ISR data. Errors are statistical only.
The cross section for E+ E- --> 2PI+ 2PI- 2PI0 as measured with the ISR data. Errors are statistical only.
None
No description provided.
None
No description provided.
None
No description provided.
None
No description provided.
We have used the momentum spectrum of leptons produced in semileptonic B-meson decays to set a 90%-confidence-level upper limit on Γ(b→ulν)Γ(b→clν) of 4%. We also measure the semileptonic branching fractions of the B meson to be (12.0±0.7±0.5)% for electrons and (10.8±0.6±1.0)% for muons.
No description provided.
No description provided.
None
No description provided.
No description provided.
We have measured the cross section of four charged pion production in photon-photon interactions in the invariant mass range 1.0≦Wγγ≦3.2 GeV and up toQ2=16 GeV2. For 1.2 GeV≦Wγγ≦1.7 GeV the process is dominated by ρ0ρ0 production with a rapid rise in cross section around 1.2 GeV, well below the nominal ρ0ρ0 threshold. The observed distributions in the two particle masses and in the production and decay angles are well described by an incoherent sum of the phase-space subprocesses γγ →ρ0ρ0, →ρ0π+π−, and →π+π−π+π−. A spin-parity analysis of the ρ0ρ0 system showsJP=2+ to dominate, although 0+ is also possible forWγγ≦1.4 GeV. Negative partity states are excluded.
No description provided.
No description provided.
No description provided.
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.
The yields and average transverse momenta of pions, kaons, and antiprotons produced at the Fermilab p¯p collider at s=300, 540, 1000, and 1800 GeV are presented and compared with data from the energies reached at the CERN collider. We also present data on the dependence of average transverse momentum 〈pt〉 and particle ratios as a function of charged particle density dNcdη; data for particle densities as high as six times the average value, corresponding to a Bjorken energy density 6 GeV/fm3, are reported. These data are relevant to the search for quark-gluon phase of QCD.
No description provided.
No description provided.
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.
The integrated number of LAMBDA/C+'s per hadronic event for the continuum at cm energy 10.54 GeV.
We present a measurement of the cross section for hadron production by e+e− annihilation in the vicinity of the previously observed resonance near 3.77 GeV. The data are used to determine the parameters of the ψ(3770) resonance. The values found are: mass, 3764±5 MeV/c2, total width, 23.5±5 MeV, and partial width to electron pairs, 276±50 eV.
PEAK CROSS SECTION FOR D MESON PAIR PRODUCTION AT PSI(3770) RESONANCE. J/PSI, PSI(3684) AND CONTINUUM BACKGROUND (R=2.5) SUBTRACTED.
This paper reports the results of an experiment measuring the parameters of various electroproduction reactions for a range in the electroproduction variables 0.7<Q2<4 GeV2 and 2<W2<16 GeV2. This report is limited to nondiffractive exclusive channels, with detailed results regarding the πΔ final states, statistically limited results for KΛ final states, and upper limits on the production of a number of event topologies containing a single unseen neutral particle.
No description provided.
Measurements of the semileptonic weak-neutral-current reactions νμp→νμp and ν¯μp→ν¯μp are presented. The experiment was performed using a 170-metric-ton high-resolution target detector in the BNL wide-band neutrino beam. High-statistics samples yield the absolute differential cross sections dσ(νμp)/dQ2 and dσ(ν¯μp)/dQ2. A measurement of the axial-vector form factor GA(Q2) is also presented. The results are in good agreement with the standard model SU(2)×U(1). The weak-neutral-current parameter sin2thetaW is determined to be sin2θW=0.220±0.016(stat)−0.031+0.023(syst).
Errors contain both statistics and systematics, except for additional overall normalisation error given above. Neutrino energy is 0 to 5 GeV with peak at 0.8 Gev.
The reaction γ V p → p π + π − was studied in the W , Q 2 region 1.3–2.8 GeV, 0.3–1.4 GeV 2 using the streamer chamber at DESY. A detailed analysis of rho production via γ V p→ ϱ 0 p is presented. Near threshold rho production has peripheral and non-peripheral contributions of comparable magnitude. At higher energies ( W > 2 GeV) the peripheral component is dominant. The Q 2 dependence of σ ( γ V p→ ϱ 0 p) follows that of the rho propagator as predicted by VDM. The slope of d σ /d t at 〈 Q 2 〉 = 0.4 and 0.8 GeV 2 is within errors equal to its value at Q 2 = 0. The overall shape of the ϱ 0 is t dependent as in photoproduction, but is independent of Q 2 . The decay angular distribution shows that longitudinal rhos dominate in the threshold region. At higher energies transverse rhos are dominant. Rho production by transverse photons proceeds almost exclusively by natural parity exchange, σ T N ⩾ (0.83 ± 0.06) σ T for 2.2 < W < 2.8 GeV. The s -channel helicity-flip amplitudes are small compared to non-flip amplitudes. The ratio R = σ L / σ T was determined assuming s -channel helicity conservation. We find R = ξ 2 Q 2 / M ϱ 2 with ξ 2 ≈ 0.4 for 〈 W 〉 = 2.45 GeV. Interference between rho production amplitudes from longitudinal and transverse photons is observed. With increasing energy the phase between the two amplitudes decreases. The observed features of rho electroproduction are consistent with a dominantly diffractive production mechanism for W > 2 GeV.
DIPION CHANNEL CROSS SECTION.
Exclusive rho^+ rho^- production in two-photon collisions involving a single highly-virtual photon is studied with data collected at LEP at centre-of-mass energies 89 GeV < \sqrt{s} < 209 GeV with a total integrated luminosity of 854.7 pb^-1. The cross section of the process gamma gamma^* -> rho^+ rho^- is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 1.2 GeV^2 < Q^2 < 30 GeV^2 and 1.1 GeV < W_gg < 3 GeV. The \rho^+\rho^- production cross section is found to be of the same magnitude as the cross section of the process gamma gamma^* -> rho^0 rho^0, measured in the same kinematic region by L3, and to have similar W_gg and Q^2 dependences.
Cross sections for the reaction E+ E- --> E+ E- RHO+ RHO-. The differentialcross sections are corrected to the centre of each bin.
Cross sections for the two photon production of RHO+ RHO-.
Differential cross section for the process E+ E- --> E+ E- (RHO+ PI- PI0 + RHO+ RHO- PI0 PI0) corrected to bin centre.
We present a measurement of the polarization of Antilambda hyperons produced in nu_mu charged current interactions. The full data sample from the NOMAD experiment has been analyzed using the same V0 identification procedure and analysis method reported in a previous paper for the case of Lambda hyperons. The Antilambda polarization has been measured for the first time in a neutrino experiment. The polarization vector is found to be compatible with zero.
Lambdabar polarization in regions of the Bjorken scaling variable X.
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 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 = 1.33, 1.35 and 1.37 GeV.
Total cross section for the cos(theta*) ranges 0.0 to 0.6 and 0.0 to 0.8.
Short overview of experiments with SND detector at VEPP-2M e^+e^- collider in the energy range 2E = 400 - 1400 MeV and preliminary results of data analysis are presented.
No description provided.
No description provided.
No description provided.
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- --> PHI PI0 with statistical errors only.
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.
Cross section measurements for the reaction E+ E- --> PHI F0(600). Statistical errors only.
The differential cross section for the process $\gamma \gamma \to \eta \pi^0$ has been measured in the kinematic range $0.84 \GeV < W < 4.0 \GeV$, $|\cos \theta^*|<0.8$, where $W$ and $\theta^*$ are the energy and $\pi^0$ (or $\eta$) 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. Clear peaks due to the $a_0(980)$ and $a_2(1320)$ are visible. The differential cross sections are fitted in the energy region $0.9 \GeV < W < 1.46 \GeV$ to obtain the parameters of the $a_0(980)$. Its mass, width and $\Gamma_{\gamma \gamma} \B (\eta \pi^0)$ are measured to be $982.3 ^{+0.6}_{-0.7} ^{+3.1}_{-4.7} \MeV/c^2$, $75.6 \pm 1.6 ^{+17.4}_{-10.0} \MeV$ and $128 ^{+3}_{-2} ^{+502}_{-43} \eV$, respectively. The energy and angular dependences above 3.1 GeV are compared with those measured in the $\pi^0 \pi^0$ channel. The integrated cross section over $|\cos \theta^*|<0.8$ has a $W^{-n}$ dependence with $n = 10.5 \pm 1.2 \pm 0.5$, which is slightly larger than that for $\pi^0 \pi^0$. The differential cross sections show a $\sin^{-4} \theta^*$ dependence similar to $\gamma \gamma \to \pi^0 \pi^0$. The measured cross section ratio, $\sigma(\eta \pi^0)/\sigma(\pi^0 \pi^0) = 0.48 \pm 0.05 \pm 0.04$, is consistent with a QCD-based prediction.
The total cross section integrated over ABS(COS(THETA*)) < 0.8.
The differential cross section as a function of angle for W = 1.33 GeV.
The differential cross section as a function of angle for W = 1.35 GeV.
Data read off graph.
Data read off graph.
No description provided.
The analysis of 1466 events of the type e + e − → μ ± μ ± , in the time-lifke range from 1.44 to 9.00 GeV 2 , sh that the absolute value of the cross-section and its energy dependence follow QED expectations within (± 3.2%) and (± 1.2%), respectively.
The cross section of the reaction $e^+ e^- \to \mu^\pm \mu^\mp$ integrated over the experimental apparatus at 14 values of the colliding beam energy $E$ corresponding to total centre-of-mass energy $\sqrt{s}=2E$ from 1.2 to 3.0 GeV.
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 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 systematic 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 includes all systematic uncertainty given in Table I. The total covariance matrix for the measured cross section can be obtained by adding statistical and systematic covariance matrices.
A precise measurement of the cross section of the process $e^+e^-\to\pi^+\pi^-(\gamma)$ from threshold to an energy of 3GeV is obtained with the initial-state radiation (ISR) method using 232fb$^{-1}$ of data collected with the BaBar detector at $e^+e^-$ center-of-mass energies near 10.6GeV. The ISR luminosity is determined from a study of the leptonic process $e^+e^-\to\mu^+\mu^-(\gamma)\gamma_{\rm ISR}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^+e^-\to\pi^+\pi^-(\gamma)$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi\pi$ cross section from threshold to 1.8GeV is $(514.1 \pm 2.2({\rm stat}) \pm 3.1({\rm syst}))\times 10^{-10}$.
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ The cross section values (nb) for 337 CM energy intervals (GeV) from 0.3 to 3 GeV. The cross section is bare (excluding vacuum polarization) and includes the emission of final state photons. ***WARNING*** The quoted errors are from the diagonal elements of the statistical covariance matrix (reported on the Table titled "Bare cross-section statistical covariance") and added quadratically with the systematic uncertainties (reported in the Table titled "Bare cross-section systematic uncertainties"). These errors can be used when plotting the results as they are representative of the precision achieved. However, any calculation involving the cross section over some energy range MUST use, to be meaningful, the full statistical covariance matrix and the proper correlations of the systematic uncertainties. ***WARNING*** The Bare cross-section statistical covariance is reported as additional resource in YAML, since its size exceeds the maximum size of 10 MB for the library hepdata_lib. It is a statistical covariance matrix, for 337x337 CM energy intervals (GeV), from 0.3 to 3 GeV, matching the ones of this table.
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ systematic uncertainties contributions and total systematic uncertainties, for 337 CM energy intervals (GeV), from 0.3 to 3 GeV. All systematics contributions are each 100% correlated in all energy bins.
Bare cross-section $e^+e^-\rightarrow\pi^+\pi^-(\gamma)$ statistical covariance matrix, for 337x337 CM energy intervals (GeV), from 0.3 to 3 GeV.
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.