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 modification of the production of $J/\psi$, $\psi(\mathrm{2S})$, and $\mit{\Upsilon}(n\mathrm{S})$ ($n = 1, 2, 3$) in $p$+Pb collisions with respect to their production in $pp$ collisions has been studied. The $p$+Pb and $pp$ datasets used in this paper correspond to integrated luminosities of $28$ $\mathrm{nb}^{-1}$ and $25$ $\mathrm{pb}^{-1}$ respectively, collected in 2013 and 2015 by the ATLAS detector at the LHC, both at a centre-of-mass energy per nucleon pair of 5.02 TeV. The quarkonium states are reconstructed in the dimuon decay channel. The yields of $J/\psi$ and $\psi(\mathrm{2S})$ are separated into prompt and non-prompt sources. The measured quarkonium differential cross sections are presented as a function of rapidity and transverse momentum, as is the nuclear modification factor, $R_{p\mathrm{Pb}}$ for $J/\psi$ and $\mit{\Upsilon}(\mathrm{1S})$. No significant modification of the $J/\psi$ production is observed while $\mit{\Upsilon}(\mathrm{1S})$ production is found to be suppressed at low transverse momentum in $p$+Pb collisions relative to $pp$ collisions. The production of excited charmonium and bottomonium states is found to be suppressed relative to that of the ground states in central $p$+Pb collisions.
Summary of results for cross-section of non-prompt J/psi decaying to a muon pair in pp collisions at 5.02 TeV in nb/GeV. Uncertainties are statistical and systematic, respectively.
Summary of results for cross-section of non-prompt psi(2S) decaying to a muon pair in pp collisions at 5.02 TeV in nb/GeV. Uncertainties are statistical and systematic, respectively.
Summary of results for cross-section of prompt J/psi decaying to a muon pair in pp collisions at 5.02 TeV in nb/GeV. Uncertainties are statistical and systematic, respectively.
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