Study Of The Dilepton Electromagnetic Decay Of D-wave Quarkonia

As a 3-body process,dilepton electromagnetic（EM）decay can provide many information by drawing its form-factor curve and invariant mass spectra of final leptons.Thus,such processes are of significance in revealing the hadronic structure of a meson.dilepton EM decay processions have been well studied in the light quark sector for years while there is still little study of such decays in the charm and bottom sectors.Recently,both BESIII and LHCb have observed the dilepton EM decays of charmonia,including χ_cJ→ J/ψ?+?-and ψ（3686）→ χ_cJ?+?-,where ? refers to electron and muon.This has been bringing more attention on such decays in heavy quark sector.This paper is mainly about the calculation of the dilepton EM decay of D-wave charmonia and bottomonia.So far,no D-wave heavy quarkonium has been recorded by PDG other than ψ（1³D₁）,ψ（1³D₂）and Υ（1³D₂）.Among the recorded mesons,the candidate of ψ（1³D₂）,X（3823）,is recently found by BESIII and Belle.At present,there is still a lack of experimental data to identify this meson.One of the most possible way to give convincing evidence is by measuring its EM decay channel.All the processes calculated in this paper are allowed by the electric dipole transition selection rules.The form-factor curve,invariant mass spectra and decay width are give for processes of different quantum states of initial and final mesons.The properties of electromagnetic decay are analysed for current concerned X（3823）.The numerical results are compared with experimental data and another theoretical method.Our numerical calculation is done by using the instantaneous Bethe-Salpeter method,choosing the Cornell potential to be the integral kernel.A brief derivation of the instantaneous approximation of the Bethe-Salpeter equation and the construction of the Salpeter wave function of the mesons are also given in this paper.The derivation of the exact form of the form-factors are given in detail.