摘要
Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).
Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).
基金
supported in part by the National Natural Science Foundation of China (Grant Nos.10847001,10875155,10675038 and 10875032)
supported in part by the Project of Knowledge Innovation Program of Chinese Academy of Sciences (Grant No.KJCX2.YW.W10)
