Study of open-charm decays and radiative transitions of the X(3872)
The processes $X(3872)\to D^{*0}\bar{D^{0}}+c.c.,~γJ/ψ,~γψ(2S),$ and $γD^{+}D^{-}$ are searched for in a $9.0~\rm fb^{-1}$ data sample collected at center-of-mass energies between $4.178$ and $4.278$ GeV with the BESIII detector. We observe $X(3872)\to D^{*0}\bar{D^{0}}+c.c.$ and find evidence for $X(3872)\toγJ/ψ$ with statistical significances of $7.4σ$ and $3.5σ$, respectively. No evident signals for $X(3872)\toγψ(2S)$ and $γD^{+}D^{-}$ are found, and upper limit on the relative branching ratio $R_{γψ} \equiv\frac{\mathcal{B}(X(3872)\toγψ(2S))}{\mathcal{B}(X(3872)\toγJ/ψ)}<0.59$ is set at 90$\%$ confidence level. Measurements of branching ratios relative to decay $X(3872)\toπ^+π^- J/ψ$ are also reported for decays $X(3872)\to D^{*0}\bar{D^{0}}+c.c., ~γψ(2S),~γJ/ψ$, $γD^{+}D^{-}$, as well as the non-$D^{*0}\bar{D}^{0}$ three-body decays $π^0 D^{0}\bar{D}^{0}$ and $γD^{0}\bar{D}^{0}$.