The Cross Section Measurement Of Process E~+e~-→π~+π~-Ψ(3686) And The Study Of Intermediate States In The Process

The electroweak interaction and strong interaction of the standard model at high energy range have been fully tested in experiments.However,since the weak-coupling perturbation theory fails at low energy,the strong interaction still needs be studied in both theory and experiment.Over the past several decades,a series of charmonium-like states have been discovered and confirmed by numerous experiments,and they are called as XYZ states and considered as the candidates of exotic states.However,the internal structure of these states remains controversial.Possible interpretations include hybrid mesons,hadron molecules,hadrocharmonium,and compact tetraquarks,but none of them has so far been proved conclusively.Therefore,comprehensive studies of production and decay patterns,as well as the measurement of resonance parameters from different experiments,are desirable to provide information that will help probe the nature of the XY Z states.Using data samples with total integral luminosity of 20.1 fb-1 collected by the BESⅢ detector operating at the BEPCⅡ collider,the cross section of the process e+e-→π+π-Ψ/(3686)is measured at the center-of-mass energies between 4.0 GeV and 4.7 GeV.The measured cross sections are consistent with previous BESⅢ results,and are consistent with results of Belle and BaBar in the analysis of same process.With more data,the results in this work are with much improved precision.Aχ2 fit to the measured energy-dependent cross section is performed with PDF including three Breit-Wigner functions and a non-resonant contribution.After testing with different functions of non-resonant term,a function with power of energy is used as the default function,and the difference comparing to the case with exponential function is considered as systematic uncertainty.The fit result confirms the existence of the charmonium-like states Y(4220),Y(4390),Y(4660).This is the first observation of the Y(4660)at the BESⅢ experiments.To examine the existence of extra resonances,fits including an additional resonance with fixed mass and width taken from the PDG,e.g.Ψ(4160)/Y(4320)/Ψ(4415),or floating mass and width are performed.However,none of the extra resonances is observed with a significance larger than 3 σ.The Y(4220)and Y(4390)observed in this work describe the same resonant structure as Y(4360)observed by Belle and BaBar,but the results of this work provide a finer depiction.Partial wave analysis(PWA)is performed to study the intermediate states observed in the invariant mass distribution of π±Ψ(3686).Structures at around 3.9 GeV and 4.02 GeV are clear for energy points between 4246 MeV and 4290 MeV,and the structure turns out to be Zc(3900)by simultaneous fit.The mass and width are determined to be M=(3895.8±2.4)MeV/c2,Γ=(34.7±4.0)MeV/c2 by scanning fit and the significance of Zc(3900)is 7.3 σ.By performing simultaneous fit for energy points between 4400 MeV and 4440 MeV,the existence of Zc(4020)is confirmed with significance of 8.8 σ and Zc(3900)is also observed with significance of 4.4 σ.The mass and width of Zc(4020)are determined to be M =(4021.6±1.3)MeV/c2,Γ=(19.4±3.3)MeV/c2 by scanning fit.The fraction of e+e-→π?Zc±→π+π-Ψ(3686)is extracted from PWA results and the cross section is also calculated.A structure is observed at around 4.22 GeV,which is consistent with Y(4220),in the e+e-→π±Zc(3900)related cross section line shape.And an additional structure is found at about 4.28 GeV,which should be studied by further experiments and theories.An increasing tendency exists in the e+e-→π±Zc(4020)related cross section line shape as energy goes higher,however with limited data,it is impossible to make a conclusion whether resonance exists or not.The results in this theory indicate the relationship between Y(4220)and Zc(3900).And the complicate structures in the πZc cross section line shape mean that further studies of experiments and theories are necessary for understanding the nature of XYZ states.