Search for Light Higgs at Belle and Prospects at Belle II

The NMSSM theory suggests an additional light CP-odd Higgs boson which can be produced in $\Upsilon $ transitions and decay to invisible particles. We attempt to find evidence for on-shell and off-shell production of the light Higgs in $\Upsilon $(1S) decays via tagged dipion transitions from $\Upsilon $(2S) to $\Upsilon $(1S) at Belle. We investigate final states with a single high energy photon and missing energy. In this talk, we will report on the current status of this search and on future prospect at Belle II which will collect 50 times greater luminosity than Belle.