Expanding neutrino oscillation parameter measurements in NOvA using a Bayesian approach

NOvA is a long-baseline neutrino oscillation experiment that measures oscillations in charged-current ${\nu }_{\mu }\to {\nu }_{\mu }$ (disappearance) and ${\nu }_{\mu }\to {\nu }_e$ (appearance) channels, and their antineutrino counterparts, using neutrinos of energies around 2 GeV over a distance of 810 km. In this work we reanalyze the dataset first examined in our previous paper [Phys. Rev. D 106, 032004 (2022)] using an alternative statistical approach based on Bayesian Markov chain Monte Carlo. We measure oscillation parameters consistent with the previous results. We also extend our inferences to include the first NOvA measurements of the reactor mixing angle ${\theta }_{13}$, where we find $0.071\le {\sin }^{2}2{\theta }_{13}\le 0.107$, and the Jarlskog invariant, where we observe no significant preference for the $CP$-conserving value $J=0$ over values favoring $CP$ violation. We use these results to examine the effects of constraints from short-baseline measurements of ${\theta }_{13}$ using antineutrinos from nuclear reactors when making NOvA measurements of ${\theta }_{23}$. Our long-baseline measurement of ${\theta }_{13}$ is shown to be consistent with the reactor measurements, supporting the general applicability and robustness of the Pontecorvo-Maki-Nakagawa-Sakata framework for neutrino oscillations.