Abstract
Cross sections of the process $e^+e^-\to\pi^0\pi^0 J/\psi$ at center-of-mass energies between 3.808 and 4.600 GeV are measured with high precision by using 12.4 $fb^{-1}$ of data samples collected with the BESIII detector operating at the BEPCII collider facility. A fit to the measured energy-dependent cross sections confirms the existence of the charmonium-like state $Y(4220)$. The mass and width of the $Y(4220)$ are determined to be $(4220.4\pm2.4\pm2.3)$ ${\rm MeV}/c^{2}$ and $(46.2\pm4.7\pm2.1)$ MeV, respectively, where the first uncertainties are statistical and the second systematic. The mass and width are consistent with those measured in the process $e^+e^-\to\pi^+\pi^- J/\psi$. The neutral charmonium-like state $Z_c(3900)^0$ is observed prominently in the $\pi^0 J/\psi$ invariant-mass spectrum, and, for the first time, an amplitude analysis is performed to study its properties. The spin-parity of $Z_c(3900)^0$ is determined to be $J^{P}=1^{+}$, and the pole position is $(3893.1\pm2.2\pm3.0)-i(22.2\pm2.6\pm7.0)$ ${\rm MeV}/c^2$, which is consistent with previous studies of electrically charged $Z_c(3900)^\pm$. In addition, cross sections of $e^+e^-\to\pi^0 Z_c(3900)^0\to \pi^0\pi^0 J/\psi$ are extracted, and the corresponding lineshape is found to agree with that of the $Y(4220)$.
Highlights
A charmoniumlike structure with a mass around 4260 MeV=c2 and spin-parity of JPC 1⁄4 1−−, namely the Yð4260Þ, was observed and confirmed in the process eþe− → ðγISRÞπþπ−J=ψ by several experiments [1,2,3]
Where Nobs is the signal yield obtained as described above, Lint is the integrated luminosity, ε is the selection efficiency estimated with signal Monte Carlo (MC) samples modeled according topthffiffie results of the partial-wave analysis (PWA) for those points that fall within s 1⁄4 4.178–4.416 GeV and by PHSP for other energy points with low statistics, ð1 þ δrÞ is the radiative correction factor, ð1 þ δvÞ is the vacuum polarization factor derived from QED calculations [23] and B is the world averaged value [24] of the product branching fractions (BFs) of the intermediate states
For high-statistics c.m. energy points for which PWA is performed, we generate 100 sets of signal MC samples at each c.m. energy point by altering the input parameters with an additional residual generated randomly with a multivariable Gaussian function according to the PWA results, and the resultant standard deviation of detection efficiencies is taken as the systematic uncertainty
Summary
A charmoniumlike structure with a mass around 4260 MeV=c2 and spin-parity of JPC 1⁄4 1−−, namely the Yð4260Þ, was observed and confirmed in the process eþe− → ðγISRÞπþπ−J=ψ by several experiments [1,2,3]. A partial-wave analysis (PWA) [14] showed that the charged charmoniumlike state Zcð3900ÞÆ, observed in decays to πÆJ=ψ in the process eþe− → πþπ−J=ψ [3,15], and to DÃDin the process eþe− → πÆðDÃD Þ∓ [16], has spin-parity JP 1⁄4 1þ. More precise measurements of their resonant parameters, production cross sections, and decay modes, as well as searches for new states, are essential. Studying the neutral decay process eþe− → π0π0J=ψ is a natural way to study the properties of the Yð4220Þ and to search for the charge-neutral isospin partner of the Zcð3900ÞÆ. The production cross sections are measured with high precision, and a PWA is performed to study properties of the Zcð3900Þ0
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