Study Of The D-wave Charmonium State ψ₂（3823） In Experiment

Charmonium is the bound state of a charm quark and an anti-charm quark(cc),and considered an ideal environment to test quantum chromodynamics(QCD)in the non-perturbative regime.Just above the open-charm threshold,the J=2 member of the D-wave spin-triplet,the 13D2 charmonium state also known as theψ2(3823),was studied by the E705,Belle,BESⅢ and LHCb experiments.Precise measurements of the ψ2(3823)properties will help to refine the parameters of potential models,and deepen our understanding of the dynamics of the cc system.Further experimental constraints on its quantum numbers would improve our understanding of the ψ2(3823)and charmonium spectroscopy above open-charm threshold.Using a data sample corresponding to an integrated luminosity of 11.3 fb-1 collected at center-of-mass energies from 4.23 to 4.70 GeV with the BESⅢ detector,we study the e+e-→π+π-ψ2(3823)process,and measure the mass of the ψ2(3823)state as(3823.12 ± 0.43±0.13)MeV/c2.Here and below,the first uncertainties are statistical and the second are systematic.An upper limit of 2.9 MeV at 90%confidence level is set on the intrinsic width of ψ2(3823).This is the most precise measurement of the ψ2(3823)mass and the most stringent constraint on its width to date,which will help to reduce the uncertainties of the D-wave charmonium states predicted by the potential model.We also observe its isospin neutral production process e+e-→π0π0ψ2(3823)for the first time with a statistical significance of 6.0 standard deviations.Since the ρ0→π0π0 decay is forbidden,the observation of e+e-→π0π0ψ2(3823)thus further confirms that the ππ system in e+e-→ππψ2(3823)comes from f0(500)decay instead of theρ0.It therefore supports the Jpc=2-assignment for the ψ2(3823).It was long thought that all observed hadrons fall into two classes only:baryons,composed of three quarks,and mesons,bound states of a quark-antiquark pair.The QCD theory also allow for hadron configurations other than conventional baryons and mesons,which are named as "exotic" hadrons.The vector charmoniumlike state ψ(4660),which remains mysterious and cannot easily be accommodat ed in the spectrum of conventional charmoninm states,is one of the candidate of the exotic hadrons.For theoretical models of ψ(4660)’s internal strncture,such as a hadronic molecule,a baryonium or a compact tetraquark state.the coupling of ψ(4660)to the ψ(2S)state with no or weak coupling to other charnonium states is an essential element.Therefore,a search for the decay of ψ(4660)to final state other than ψ(2S)in experiment helps to test various pictures for theψ(4660)structure.Using the same data sample discussed above,we measure the product of the e+e-→π+π-ψ2(3823)cross section and the branching fraction B[ψ2(3823)→γχc1].For the first time,resonance structure is observed in the cross section line shape of e+e-→π+π-ψ2(3823)with significances exceeding 5σ.A fit to data with two coherent Breit-Wigner resonances modeling the(?)-dependent.cross section yields M(R1)=4406.9± 17.2±4.5MeV/c2.Γ(R1)=128.1±37.2±2.3 MeV,and M(R2)=4647.9±8.6±0.8 MeV/c2,Γ(R2)=33.1±18.6±4.1 MeV.These observation.especially for ψ(4660)→π+π-ψ2(3823)(ψ(4660)corresponds to R2),deepen our understanding of the nature of the vector charmoniumlike states.Though weaklv disfavored by the data.a single resonance with M(R)=4417.5±26.2±3.5 MPV/c2.Γ(R)=245±48±13MeV is also possible to interpret data.The ratio of average cross sections for e+e-→π0π0ψ2(3823)and e+e-→π+π-ψ2(3823)is determined to be R=σ[e+e-→π0π0ψ2(3823)]/σ[e+e-→π+π-ψ2(3823)]=0.57±0.14±0.05,which is consistent with expectation from isospin symmetry,and further supports the di-pion transition of the vector charmoniumlike states to the ψ2(3823).In addition,we report a study of B±→K±ψ2(3823)decays;using a 364 fb-1 data sample collected by the Belle Ⅱ detector at the SuperKEKB e+easymmetric-energy collider operating at a center-of-mass energy corresponding to the T(4S)resonance.The product of branching fractions B[B±→K±ψ2(3823)].B[ψ2(3823)→γχc1]is measured.The mass of the ψ2(3823)is measured.With the continuously accumulated data at Belle Ⅱ,the quantum number of ψ2(3823)is also expected to be determined.These results are of great significance for promoting the development of the charmonium spectroscopy.