Study of the dilepton electromagnetic decays of χ_cJ(1 P)

In this paper, the dilepton electromagnetic decays χ_cJ(1 P) → J/ ψe⁺e^- and χ_cJ(1 P) → Jψμ⁺μ^-, where χ_cJ denotes χ_c, χ_{c 1} and χ_{c 2}, 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^-, the gauge invariance is decisive and should be considered carefully. For the processes of χ_cJ(1 P) → J/ ψe⁺e^-, the branching fraction are: B[χc0(1P)→J/ψe+e-]=1.06-0.18+0.16×10-4, B[χc1(1P)→J/ψe+e-]=2.88-0.53+0.50×10-3, and B[χc2(1P)→J/ψe+e-]=1.74-0.21+0.22×10-3. The calculated branching fractions of χ_cJ(1 P) → J/ ψμ⁺μ^- channels are: B[χc0(1P)→J/ψμ+μ-]=3.80-0.64+0.59×10-6, B[χc1(1P)→J/ψμ+μ-]=2.04-0.38+0.36×10-4, and B[χc2(1P)→J/ψμ+μ-]=1.66-0.19+0.19×10-4.