A precision measurement of the matrix elements for $\eta\to\pi^+\pi^-\pi^0$ and $\eta\to\pi^0\pi^0\pi^0$ decays is performed using a sample of $(10087\pm44)\times10^6$$J/\psi$ decays collected with the BESIII detector. The decay $J/\psi \to \gamma \eta$ is used to select clean samples of 631,686 $\eta\to\pi^+\pi^-\pi^0$ decays and 272,322 $\eta\to\pi^0\pi^0\pi^0$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The non-zero $gX^2Y$ term for the decay mode $\eta\to\pi^+\pi^-\pi^0$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\eta\to\pi^+\pi^-\pi^0$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\eta\to\pi^0\pi^0\pi^0$ decay, and no obvious structure around the $\pi^+\pi^-$ mass threshold is observed.
In Phys. Lett. B 753, 629-638 (2016) [arXiv:1507.08188] the BESIII collaboration published a cross section measurement of the process $e^+e^-\to \pi^+ \pi^-$ in the energy range between 600 and 900 MeV. In this erratum we report a corrected evaluation of the statistical errors in terms of a fully propagated covariance matrix. The correction also yields a reduced statistical uncertainty for the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, which now reads as $a_\mu^{\pi\pi\mathrm{, LO}}(600 - 900\,\mathrm{MeV}) = (368.2 \pm 1.5_{\rm stat} \pm 3.3_{\rm syst})\times 10^{-10}$. The central values of the cross section measurement and of $a_\mu^{\pi\pi\mathrm{, LO}}$, as well as the systematic uncertainties remain unchanged.
Earlier measurements at LEP of isolated hard photons in hadronic Z decays, attributed to radiation from primary quark pairs, have been extended in the ALEPH experiment to include hard photon productioninside hadron jets. Events are selected where all particles combine democratically to form hadron jets, one of which contains a photon with a fractional energyz≥0.7. After statistical subtraction of non-prompt photons, the quark-to-photon fragmentation function,D(z), is extracted directly from the measured 2-jet rate. By taking into account the perturbative contributions toD(z) obtained from anO(ααs) QCD calculation, the unknown non-perturbative component ofD(z) is then determined at highz. Provided due account is taken of hadronization effects nearz=1, a good description of the other event topologies is then found.
We present measurements of the structure function \Ft\ in $e~+p$ scattering at HERA in the range $3.5\;\Gevsq < \qsd < 5000\;\Gevsq$. A new reconstruction method has allowed a significant improvement in the resolution of the kinematic variables and an extension of the kinematic region covered by the experiment. At $ \qsd < 35 \;\Gevsq$ the range in $x$ now spans $6.3\cdot 10~{-5} < x < 0.08$ providing overlap with measurements from fixed target experiments. At values of $Q~2$ above 1000 GeV$~2$ the $x$ range extends to 0.5. Systematic errors below 5\perc\ have been achieved for most of the kinematic region. The structure function rises as \x\ decreases; the rise becomes more pronounced as \qsd\ increases. The behaviour of the structure function data is well described by next-to-leading order perturbative QCD as implemented in the DGLAP evolution equations.
The total cross section fore+e− annihilation into hadrons for center of mass energies from 9.4 to 9.5 GeV has been measured with the nonmagnetic DESY-Heidelberg detector at DORIS. A value ofR=σhad/σµµ=3.8±0.7 for the continuum region around the Υ (9.46) resonance has been determined. The ratioΓeeΓhad/Γtot of electronic, hadronic and total widths has been reevaluated to be (1.00±0.23) keV for the Υ resonance and (0.37±0.16) keV for the Υ′. In addition, a search for directly produced pohotons from Υ decays of the type Υ→γ+gluon+gluon has been performed. The Υ decay into muon pairs has also been searched for.
Using the detector ARGUS at thee+e− storage ring DORIS II, we have investigated inclusive momentum spectra of charged pions, kaons, and protons from decays of the υ(4S) meson. The kaon spectra have been measured in two independent ways, by coherently exploiting the detector's particle identification capabilities, and by detecting decays in-flight. The extracted mean multiplicities for charged hadrons are 7.17±0.05±0.14 pions, 1.56±0.03±0.05 kaons and 0.110±0.010±0.007 protons per υ(4S) decay, where pions and protons fromKso and Δ decays have been subtracted.
The inclusive production cross sections of η′ (958) andfo (975) mesons are measured ine+e− annihilation in the nonresonant continuum around\(\sqrt s= 10\) GeV and in decays of the υ resonances using the ARGUS detector. For η′ (958) mesons, a production ratio of η′ (958)/ηdir=0.35±0.24, with ηdir=η−BR(η′→ηX)·η′, is determined in direct υ(1S) decays, which can be partially explained by the pseudoscalar singlet/octet mixing. Forfo(975) production, we obtain a production ratio offo(975)/p(770)°=0.17±0.030 in direct υ(1S) decays. In its production features, thefo(975) behaves like an ordinary meson, though aK\(\bar K\) molecule nature cannot be excluded. The substantial production yield of thefo(975) meson demonstrates the important effect of feeddown from mesons beyond the basic multiples on pseudoscalar and vector meson production.
The cross sections fore+e−→π+π−π0 ande+e−→ωπ+π− have been measured in the 1.35 ≦\(\sqrt s \) ≦2.4 GeV range from 1900 nb−1 collected by DM2 at DCI. The second process proceeds via a resonant state at ≈- 1660 MeV/c2, ≈- 280 MeV/c2 wide. The first one is larger than a VDM extrapolation from the ω-ϕ peaks and, although does not show any clear structure, is compatible with the presence of the above resonance.
An updated analysis using about 1.5 million events recorded at $\sqrt{s} = M_Z$ with the DELPHI detector in 1994 is presented. Eighteen infrared and collinear safe event shape observables are measured as a function of the polar angle of the thrust axis. The data are compared to theoretical calculations in ${\cal O} (\alpha_s^2)$ including the event orientation. A combined fit of $\alpha_s$ and of the renormalization scale $x_{\mu}$ in $\cal O(\alpha_s^2$) yields an excellent description of the high statistics data. The weighted average from 18 observables including quark mass effects and correlations is $\alpha_s(M_Z^2) = 0.1174 \pm 0.0026$. The final result, derived from the jet cone energy fraction, the observable with the smallest theoretical and experimental uncertainty, is $\alpha_s(M_Z^2) = 0.1180 \pm 0.0006 (exp.) \pm 0.0013 (hadr.) \pm 0.0008 (scale) \pm 0.0007 (mass)$. Further studies include an $\alpha_s$ determination using theoretical predictions in the next-to-leading log approximation (NLLA), matched NLLA and $\cal O(\alpha_s^2$) predictions as well as theoretically motivated optimized scale setting methods. The influence of higher order contributions was also investigated by using the method of Pad\'{e} approximants. Average $\alpha_s$ values derived from the different approaches are in good agreement.
Infrared and collinear safe event shape distributions and their mean values are determined in e+e- collisions at centre-of-mass energies between 45 and 202 GeV. A phenomenological analysis based on power correction models including hadron mass effects for both differential distributions and mean values is presented. Using power corrections, alpha_s is extracted from the mean values and shapes. In an alternative approach, renormalisation group invariance (RGI) is used as an explicit constraint, leading to a consistent description of mean values without the need for sizeable power corrections. The QCD beta-function is precisely measured using this approach. From the DELPHI data on Thrust, including data from low energy experiments, one finds beta_0 = 7.86 +/- 0.32 for the one loop coefficient of the beta-function or, assuming QCD, n_f = 4.75 +/- 0.44 for the number of active flavours. These values agree well with the QCD expectation of beta_0=7.67 and n_f=5. A direct measurement of the full logarithmic energy slope excludes light gluinos with a mass below 5 GeV.
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