Charge-state dynamics of barium ions in high-pressure xenon and its implications for Barium-Tagging in $0\nu\beta\beta$ searches

Barium tagging (BaTa) is one of the most promising techniques for achieving a nearly background-free search for neutrinoless double-beta decay ($0\nu\beta\beta$) in high-pressure xenon time detection chambers. However, the experimental implementation of BaTa depends critically on the chage-state dynamics of the daughter Ba$^{2+}$ ion produced in the nuclear decay event. In this work, I review the possible recombination channels and evaluate their physical viability. The obtained results indicate that although binary recombination channels are strongly suppressed, three-body recombination assisted by neutral xenon atoms constitutes a physically plausible mechanism for the conversion of Ba$^{2+}$ into Ba$^+$ on timescales -milliseconds- comparable to the characteristic detection times in the NEXT experiment. These results suggest that the barium charge state should be regarded as a dynamical quantity with direct implications for the design and experimental implementation of BaTa techniques.