Measurement of higher-order multipole amplitudes in $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c1,2}$ with $\ddot{I}{‡}_{c1,2}\to {\hat{I}}^{3}J/\ddot{I}ˆ$ and search for the transition $\hat{I}{\cdot }_c(2S)\to {\hat{I}}^{3}J/\ddot{I}ˆ$

Abstract

Using 106~million $\ddot{I}ˆ(3686)$ events collected with the BESIII detector, we measure multipole amplitudes for the decay $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c1,2}\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ beyond the dominant electric-dipole amplitudes. The normalized magnetic-quadrupole amplitude for $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c1,2}\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ and the normalized electric-octupole amplitudes for $\ddot{I}ˆ(3686)rightarrow{\hat{I}}^3\ddot{I}{‡}_{c2}$,~$\ddot{I}{‡}_{c2}\to {\hat{I}}^{3}J/\ddot{I}ˆ$ are determined. The M2 amplitudes for $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c1}$ and $\ddot{I}{‡}_{c1,2}\to {\hat{I}}^{3}J/\ddot{I}ˆ$ are found to differ significantly from zero and are consistent with theoretical predictions. We also obtain the ratios of M2 contributions of $\ddot{I}ˆ(3686)$ and $J/\ddot{I}ˆ$ decays to $\ddot{I}{‡}_{c1,2}$, $b_2^1/b_2^2=1.35\pm 0.72$ and $a_2^1/a_2^2=0.617\pm 0.083$, which agree well with theoretical expectations. By considering the multipole contributions of $\ddot{I}{‡}_{c1,2}$, we measure the product branching fractions for the cascade decays $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c0,1,2}\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ and search for the process $\hat{I}{\cdot }_c(2S)\to {\hat{I}}^{3}J/\ddot{I}ˆ$ through $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)$. The product branching fraction for $\ddot{I}ˆ(3686)\to {\hat{I}}^3\ddot{I}{‡}_{c0}\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ is 3$\ddot{I}ƒ$ larger than published measurements, while those of $\ddot{I}ˆ(3686)rightarrow{\hat{I}}^3\ddot{I}{‡}_{c1,2}\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ are consistent. No significant signal for the decay $\ddot{I}ˆ(3686)\to {\hat{I}}^3\hat{I}{\cdot }_c(2S)\to {\hat{I}}^3{\hat{I}}^{3}J/\ddot{I}ˆ$ is observed, and the upper limit of the product branching fraction at the 90\% confidence level is determined.

12 pages, 5 figures