Measurement of higher-order multipole amplitudes in ψ(3686)→γχc1,2 with χc1,2→γJ/ψ and search for the transition ηc(2S)→γJ/ψ

Using 106 ×106 ψ(3686) events collected with the BESIII detector, we measure multipole amplitudes for the decay ψ(3686) → γχc1;2 → γγJ/ψ beyond the dominant electric-dipole amplitudes. The normalized magnetic-quadrupole (M2) amplitude for ψ(3686) → γχc1;2 → γγJ/ψ and the normalized electric- octupole amplitudes for ψ(3686) → γχc2, χc2 → γJ/ψ are determined. The M2 amplitudes for ψ(3686) → γχc1 and χc1;2 → γJ/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 χc1;2, b12=b2 = 1.35 +- 0.72 and a12=a21 = 0.617 +- 0.083, which agree well with theoretical expectations. By considering the multipole contributions of χc1;2, we measure the product branching fractions for the cascade decays ψ(3686) → γχc0;1;2 → γγJ/ψ and search for the process ηc(2S) → γJ/ψ through ψ(3686) → γηc(2S). The product branching fraction for ψ(3686) → γχc0 → γγJ/ψ is 3σ larger than published measurements, while those of ψ(3686) → γχc1;2 → γγJ/ψ are consistent. No significant signal for the decay ψ(3686) → γηc(2S) → γγJ/ψ is observed, and the upper limit of the product branching fraction at the 90% confidence level is determined