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Based on (10087±44)×106 J/ψ events collected with the BESIII detector, the process J/ψ→γπ+π−η′ is studied using two dominant decay channels of the η′ meson, η′→γπ+π− and η′→ηπ+π−,η→γγ. The X(2600) is observed with a statistical significance larger than 20σ in the π+π−η′ invariant mass spectrum, and it has a strong correlation to a structure around 1.5 GeV/{\it c}2 in the π+π− invariant mass spectrum. A simultaneous fit on the π+π−η′ and π+π− invariant mass spectra with the two η′ decay modes indicates that the mass and width of the X(2600) state are 2617.8±2.1+18.2−1.9 MeV/{\it c}2 and 200±8+20−17 MeV, respectively. The corresponding branching fractions are measured to be B(J/ψ→γX(2600))⋅B(X(2600)→f0(1500)η′)⋅B(f0(1500)→π+π−) = (3.39±0.18+0.91−0.66)×10−5 and B(J/ψ→γX(2600))⋅B(X(2600)→f′2(1525)η′)⋅B(f′2(1525)→π+π−) = (2.43±0.13+0.31−1.11)×10−5, where the first uncertainties are statistical, and the second systematic.
Based on electron-positron collision data collected with the BESIII detector operating at the Beijing Electron Positron Collider II storage rings, the value of R≡σ(e+e−→hadrons)/σ(e+e−→μ+μ−) is measured at 14 center-of-mass energies from 2.2324 to 3.6710 GeV. The resulting uncertainties are less than 3.0%, and are dominated by systematic uncertainties.