Enhanced search sensitivity to the double beta decay of $^{136}$Xe to excited states with topological signatures

Double beta decay of $^{136}$Xe to excited states of $^{136}$Ba (DBD-ES) has not yet been discovered experimentally yet. The experimental signature of such decays, one or two gamma rays following the beta signals, can be identified more effectively in a gaseous detector with the help of topological signatures. We have investigated key parameters of particle trajectories of DBD-ES with Monte Carlo simulation data of the proposed PandaX-III detector as an example. The background rates can be reduced by about one order of magnitude while keeping more than half of signals with topological analysis. The estimated half-life sensitivity of DBD-ES can be improved by 1.8 times to 4.1$\times$10$^{23}$ yr (90\% CL). Similarly, the half-life sensitivity of neutrinoless double beta decay of $^{136}$Xe to excited states of $^{136}$Ba can be improved by a factor of 4.8 with topological signatures.