Study of the dilepton electromagnetic decays of $$\chi _{cJ}(1P)$$

Abstract

AbstractIn this paper, the dilepton electromagnetic decays $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$χcJ(1P)→J/ψe+e- and $$\chi _{cJ}(1P) \rightarrow J\psi \mu ^+\mu ^-$$χcJ(1P)→Jψμ+μ-, where $$\chi _{cJ}$$χcJ denotes $$\chi _{c0}$$χc0, $$\chi _{c1}$$χc1 and $$\chi _{c2}$$χc2, are calculated systematically in the improved Bethe–Salpeter method. The numerical results of decay widths and the invariant mass distributions of the final lepton pairs are given. The comparison is made with the recently measured experimental data of BESIII. It is shown that for the cases including $$e^+e^-$$e+e-, the gauge invariance is decisive and should be considered carefully. For the processes of $$\chi _{cJ}(1P) \rightarrow J/\psi e^+e^-$$χcJ(1P)→J/ψe+e-, the branching fraction are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi e^+e^-]=1.06^{+0.16}_{-0.18} \times 10^{-4}$$B[χc0(1P)→J/ψe+e-]=1.06-0.18+0.16×10-4, $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi e^+e^-]=2.88^{+0.50}_{-0.53} \times 10^{-3}$$B[χc1(1P)→J/ψe+e-]=2.88-0.53+0.50×10-3, and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi e^+e^-]=1.74^{+0.22}_{-0.21} \times 10^{-3}$$B[χc2(1P)→J/ψe+e-]=1.74-0.21+0.22×10-3. The calculated branching fractions of $$\chi _{cJ}(1P)\rightarrow J/\psi \mu ^+\mu ^-$$χcJ(1P)→J/ψμ+μ- channels are: $$\mathcal {B}[\chi _{c0}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=3.80^{+0.59}_{-0.64} \times 10^{-6}$$B[χc0(1P)→J/ψμ+μ-]=3.80-0.64+0.59×10-6, $$\mathcal {B}[\chi _{c1}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=2.04^{+0.36}_{-0.38} \times 10^{-4}$$B[χc1(1P)→J/ψμ+μ-]=2.04-0.38+0.36×10-4, and $$\mathcal {B}[\chi _{c2}(1P) \rightarrow J/\psi \mu ^+\mu ^-]=1.66^{+0.19}_{-0.19} \times 10^{-4}$$B[χc2(1P)→J/ψμ+μ-]=1.66-0.19+0.19×10-4.