Reconstructing neutrinoless double beta decay event kinematics in a xenon gas detector with vertex tagging

If neutrinoless double beta decay is discovered, the next natural step would be understanding the lepton number violating physics responsible for it. Several alternatives exist beyond the exchange of light neutrinos. Some of these mechanisms can be distinguished by measuring phase-space observables, namely the opening angle $\cos\theta$ among the two decay electrons, and the electron energy spectra, $T_1$ and $T_2$. In this work, we study the statistical accuracy and precision in measuring these kinematic observables in a future xenon gas detector with the added capability to precisely locate the decay vertex. For realistic detector conditions (a gas pressure of 10 bar and spatial resolution of 4 mm), we find that the average $\overline{\cos\theta}$ and $\overline{T_1}$ values can be reconstructed with a precision of 0.19 and 110 keV, respectively, assuming that only 10 neutrinoless double beta decay events are detected.