Evidence for leptonic CP phase from NO$\nu$A, T2K and ICAL: A chronological progression

We study the synergy between the long-baseline (LBL) experiments NO$\nu$A and T2K and the atmospheric neutrino experiment ICAL@INO for obtaining the first hint of CP violation in the lepton sector. We also discuss how precisely the leptonic CP phase ($\delta_{CP}$) can be measured by these experiments. The CP sensitivity is first described at the level of oscillation probabilities, discussing its dependence on the parameters -- $\theta_{13}$, mass hierarchy and $\theta_{23}$. In particular, we discuss how the precise knowledge or lack thereof of these parameters can affect the CP sensitivity of LBL experiments. We follow a staged approach and analyze the $\delta_{CP}$ sensitivity that can be achieved at different points of time over the next 15 years from these LBL experiments alone and/or in conjunction with ICAL@INO. We find that the CP sensitivity of NO$\nu$A/T2K is enhanced due to the synergies between the different channels and between the two experiments. On the other hand the lack of knowledge of hierarchy and octant makes the CP sensitivity poorer for some parameter ranges. Addition of ICAL data to T2K and NO$\nu$A can exclude these spurious wrong-hierarchy and/or wrong-octant solutions and cause a significant increase in the range of $\delta_{CP}$ values for which a hint of CP violation can be achieved. In fact in parameter regions unfavourable for NO$\nu$A/T2K, we may get the first evidence of CP violation by adding the ICAL data to these. Similarly the precision with which $\delta_{CP}$ can be measured also improves with inclusion of ICAL data.