Enhancing the hierarchy and octant sensitivity of ESS$ u$SB in conjunction with T2K, NO$ u$A and ICAL@INO

The main aim of the ESS$ u$SB proposal is the discovery of the leptonic CP phase $delta_{CP}$ with a high significance ($5sigma$ for 50% values of $delta_{CP}$) by utilizing the physics at the second oscillation maxima of the $P_{mu e}$ channel. It can achieve $3sigma$ sensitivity to hierarchy for all values of $delta_{CP}$. In this work, we concentrate on the hierarchy and octant sensitivity of the ESS$ u$SB experiment. We show that combining the ESS$ u$SB experiment with the atmospheric neutrino data from the proposed India-based Neutrino Observatory(INO) experiment can result in an increased sensitivity to mass hierarchy. In addition, we also combine the results from the ongoing experiments T2K and NO$ u$A assuming their full runtime and present the combined sensitivity of ESS$ u$SB + ICAL@INO + T2K + NO$ u$A. We show that while by itself ESS$ u$SB can have up to $3sigma$ hierarchy sensitivity, the combination of all the experiments can give up to $5sigma$ sensitivity depending on the true hierarchy-octant combination. The octant sensitivity of ESS$ u$SB is low by itself. However the combined sensitivity of all the above experiments can give up to $3sigma$ sensitivity depending on the choice of true hierarchy and octant. We discuss the various degeneracies and the synergies that lead to the enhanced sensitivity when combining different experimental data.