Measurement of higher-order multipole amplitudes in ψ ( 3686 ) → γ χ c 1 , 2 with χ c 1 , 2 → γ J / ψ and search for the transition η c ( 2 S ) → γ J / ψ
Using 106 ×10 6 ψ (3686) events collected with the BESIII detector, we measure multipole amplitudes for the decay ψ (3686) → γχ c1,2 → γγ J/ψ beyond the dominant electric-dipole amplitudes. The normalized magnetic-quadrupole (M2) amplitude for ψ (3686) → γχ c1,2 → γγ J/ψ and the normalized electric-octupole amplitudes for ψ ( 3686 ) → γχ c2 , χ c2 → γJ/ψ are determined. The M2 amplitudes for ψ (3686) → γ χ c1 and χ c1,2 → γ J / ψ are found to differ significantly from zero and are consistent with theoretical predictions. We also obtain the ratios of M2 contributions of ψ ( 3686 ) and J /ψ decays to χ c1,2 , b$1\atop{2}$/ b$2\atop{2}$ = 1.35 ± 0.72 and a$1\atop{2}$/a$2\atop{2}$ = 0.617 ± 0.083 , which agree well with theoretical expectations. By considering the multipole contributions of χ c 1 , 2 , we measure the product branching fractions for the cascade decays ψ ( 3686 ) → γχ c0,1,2 → γγJ/ψ and search for the process η c (2S) → γJ/ψ through ψ ( 3686 ) → γη c (2S). The product branching fraction for ψ (3686) → γχ c0 → γγJ/ψ is 3σ larger than published measurements, while those of ψ (3686) → γχ c1,2 → γγJ/ψ are consistent. In conclusion, no significant signal for the decay ψ ( 3686 ) → γη c (2S) → γγJ/ψ is observed, and the upper limit of the product branching fraction at the 90% confidence level is determined.