Study Of The P-wave Charmonium Family On Mass Spectrum And Decay Behavior

In recent 20 years,the study on charmonium family is popular in the hadron physics.As early as 1974,the first charmonium particle J/? was observed by experimentalists.In the subsequent years,1S,2S,and 1P states in charmonium family were also established.Focusing on these new particles,their production mechanism,mass spectrum,and decay behavior have been studied by theorists extensively.Meanwhile,the Belle,BABAR,BES?,and LHCb Collaborations also made many careful measurements in the charmonium energy range.In 2003,Belle accidentally observed a particle around DD*threshold,which was named as X(3872).The mass and decay width of X(3872)are totally different from the predictions of charmonium family from the potential model.Then,many other XYZ particles have been quickly observed by people one after another.The discoveries of XYZ particles have attracted the wide interests from scientists,and make us have a deeper understanding on the structures and interactions of hadrons.In the charmonium energy range,the XYZ particles are mixed with charmonium family,which makes it difficult to decide whether a new particle is a conventional charmonium or not.To find the charmonium states and complete the spectroscopy of charmonium family,we need to analyse the properties of the uncovered charmonium states explicitly,by which the difference with XYZ particles can be indicated.In this paper,we will discuss the mass spectrum and decay behavior of the P wave charmonium family.At first,the question whether the X(3915)can be categorized as an ?c0(2P)state is studied seriously.In 2010,the Belle Collaboration measured the signals on ????J/? process and discovered a new resonance in the energy range of 2P charmonium states.After the discovery,it has been argued for a long time whether the X(3915)can be categorized as a ?c0(2P)state.In our study,we find the coupled-channel effects are outstanding in the ?c0(2P),?c1(2P)?and Xc2(2P)charmonium states.The results indicate that with the coupled-channel effects,the mass and decay width of ?c0(2P)are in accordance with X(3915)particle.Meanwhile,the results of ?c1(2P)and ?c2(2P)also correspond to X(3872)and Z(3930),respectively.In order to understand our coupled-channel results deeply,we have also studied the node effects in the radial wave functions of ?c0(2P)state.With the node effects,we have clearly shown why the decay width of ?c0(2P)is so narrow,which support our results powerfully.As a conclusion,we believe X(3915)can be categorized as a ?c0(2P)state.In 2020,the LHCb Collaboration had released the data in B?KDD process.In their study,the invariant mass spectrum of DD channel and the corresponding angular distribution around 3.9 GeV were shown in detail.Their measurement confirmed our prediction of X(3915)completely.As a good opportunity,we further studied the production of ?c0(2P)in the B decay process.Comparing with the experimental data of ?(3770),we can extract branching ratio B[B?KX(3915)].At the same time,we also calculate the branching ratio B[B?K?c0(2P)]with the rescattering mechanism,by which the theoretical results are consistent with our extracted branching ratio from experimental data perfectly.The study has further confirmed that X(3915)is an ?c0(2P)state.Based on the result,we have also discussed the product branching ratio B[B?K?c0(2P)]�B[?c0(2P)??J/?]and whether the Y(3940)signal is also from a ?c0(2P)state.In the theoretical and experimental aspects,we have succeeded to uncover the nature of the states around 3.9 GeV.Now,we wonder where 3P and higher P wave charmonium states are.With the constraint of 2P charmonium in experiments,we can try to study the 3P,4P,and 5P charmonium states.With the coupled-channel model,we have calculated the masses and decay widths of 3P,4P,and 5P states.Through the calculation,the masses of 3P charmonium states are around 4.2 GeV,and their decay widths are about 50 MeV.For the 4P and 5P charmonium states,their masses are predicted to be 4.35 GeV and 4.5 GeV,respectively.Besides,we also calculated the mass of P wave charmonium with modified potential model,by which refitted GI model can give a similar result with the coupled-channel model.The result indicates that the coupled-channel model and the refitted GI model are valid for the higher excited states in the charmonium family.