Signatures of a light sterile neutrino in T2HK

We investigate the performance of T2HK in the presence of a light eV scale sterile neutrino. We study in detail its influence in resolving fundamental issues like mass hierarchy, CP-violation (CPV) induced by the standard CP-phase ${\delta }_{13}$ and new CP-phase ${\delta }_{14}$, and the octant ambiguity of ${\theta }_{23}$. We show for the first time in detail that due to the impressive energy reconstruction capabilities of T2HK, the available spectral information plays an important role to enhance the mass hierarchy discovery reach of this experiment in 3$\nu$ framework and also to keep it almost intact even in $4\nu$ scheme. This feature is also of the utmost importance in establishing the CPV due to ${\delta }_{14}$. As far as the sensitivity to CPV due to ${\delta }_{13}$ is concerned, it does not change much going from $3\nu$ to 4$\nu$ case. We also examine the reconstruction capability of the two phases ${\delta }_{13}$ and ${\delta }_{14}$, and find that the typical 1$\sigma$ uncertainty on ${\delta }_{13}$ (${\delta }_{14}$) in T2HK is $\sim {15}^0$ (${30}^0$). While determining the octant of ${\theta }_{23}$, we face a complete loss of sensitivity for unfavorable combinations of unknown ${\delta }_{13}$ and ${\delta }_{14}$.