Measurement of higher-order multipole amplitudes in $ψ(3686)\rightarrowγχ_{c1,2}$ with $χ_{c1,2}\toγJ/ψ$ and search for the transition $η_{c}(2S)\toγJ/ψ$

Abstract

Using 106~million $ψ(3686)$ events collected with the BESIII detector, we measure multipole amplitudes for the decay $ψ(3686)\rightarrowγχ_{c1,2}\toγγJ/ψ$ beyond the dominant electric-dipole amplitudes. The normalized magnetic-quadrupole amplitude for $ψ(3686)\rightarrowγχ_{c1,2}\rightarrowγγJ/ψ$ and the normalized electric-octupole amplitudes for $ψ(3686)rightarrowγχ_{c2}$,~$χ_{c2}\rightarrowγJ/ψ$ are determined. The M2 amplitudes for $ψ(3686)\rightarrowγχ_{c1}$ and $χ_{c1,2}\rightarrowγJ/ψ$ 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 $χ_{c1,2}$, $b_{2}^{1}/b_{2}^{2} = 1.35\pm0.72$ and $a_{2}^{1}/a_{2}^{2} = 0.617\pm0.083$, which agree well with theoretical expectations. By considering the multipole contributions of $χ_{c1,2}$, we measure the product branching fractions for the cascade decays $ψ(3686)\rightarrowγχ_{c0,1,2}\toγγJ/ψ$ and search for the process $η_{c}(2S)\toγJ/ψ$ through $ψ(3686)\rightarrowγη_{c}(2S)$. The product branching fraction for $ψ(3686)\rightarrowγχ_{c0}\toγγJ/ψ$ is 3$σ$ larger than published measurements, while those of $ψ(3686)rightarrowγχ_{c1,2}\toγγJ/ψ$ are consistent. No significant signal for the decay $ψ(3686)\toγη_c(2S)\toγγJ/ψ$ is observed, and the upper limit of the product branching fraction at the 90\% confidence level is determined.

12 pages, 5 figures