Proposal for an Extended Run of T2K to $20\times10^{21}$ POT

Recent measurements by the T2K neutrino oscillation experiment indicate that CP violation in neutrino mixing may be observed in the future by long-baseline neutrino oscillation experiments. We propose an extension to the currently approved T2K running from $7.8times 10^{21}~mbox{POT}$ to $20times 10^{21}~mbox{POT}$, aiming at initial observation of CP violation with 3$,sigma$ or higher significance for the case of maximum CP violation. The program also contains a measurement of mixing parameters, $theta_{23}$ and $Delta m^2_{32}$, with a precision of 1.7$^circ$ or better and 1%, respectively. With accelerator and beamline upgrades, as well as analysis improvements, this program would occur before the next generation of long-baseline neutrino oscillation experiments that are expected to start operation in 2026.