The physics of antineutrinos in DUNE and determination of octant and $\delta_{CP}$

The octant of $\theta_{23}$ and $\delta_{CP}$ are the two major unknowns in neutrino oscillation physics. The precise determination of octant and $\delta_{CP}$ is interlinked through the octant-$\delta_{CP}$ degeneracy. In this paper we study the proficiency of the DUNE experiment to determine these parameters, in particular, the role played by the antineutrinos, the broadband nature of the beam and the matter effect. For $P_{\mu e}$ and $P_{\bar{\mu} \bar{e}}$ the octant-$\delta_{CP}$ degeneracy occurs at different values of $\delta_{CP}$, combination of neutrino and antineutrino runs help to resolve this. However, in regions where neutrinos do not have octant degeneracy adding antineutrino data is expected to decrease the sensitivity because of the degeneracy and reduced statistics. However we find that in case of DUNE baseline, the antineutrino runs help even in parameter space where the antineutrino probabilities suffer from degeneracies. We explore this point in detail and point out that this happens because of the (i) broad-band nature of the beam so that even if there is degeneracy at a particular energy bin, over the whole spectrum the degeneracy may not be there; (ii) the enhanced matter effect due to the comparatively longer baseline which creates an increased tension between the neutrino and the antineutrino probabilities which raises the overall $\chi^2$ in case of combined runs. This feature is more prominent for IH since the antineutrino probabilities in this case are much higher than the neutrino probabilities due to matter effects. The main role of antineutrinos in enhancing CP sensitivity is their ability to remove the octant-$\delta_{CP}$ degeneracy. However even if one assumes octant to be known the addition of antineutrinos can give enhanced CP sensitivity in some parameter regions due to the tension between the neutrino and antineutrino $\chi^2$s.