  We numerically study the dynamics and the phases of self-propelled
disk-shaped particles of different sizes with soft repulsive potential in two
dimensions. Size diversity is introduced by the polydispersity index (PDI)
$\epsilon$, which is the width of the uniform distribution of the particle's
radius. The self-propulsion speed of the particles controls the activity $v$.
We observe enhanced dynamics for large size diversity among the particles. We
calculate the effective diffusion coefficient $D_{eff}$ in the steady-state.
The system exhibits four distinct phases, jammed phase with small $D_{eff}$ for
small activity and liquid phase with enhanced $D_{eff}$ for large activity. The
number fluctuation is larger and smaller than the equilibrium limit in the
liquid and jammed phase, respectively. Further, the jammed phase is of two
types: solid-jammed and liquid jammed for small and large PDI. Whereas the
liquid phase is called motility induced phase separation (MIPS)-liquid for
small PDI and for large PDI, we find enhanced diffusivity and call it the {\em
pure liquid} phase. The system is studied for three packing densities $\phi$,
and the response of the system for polydispersity is the same for all $\phi$'s.
Our study can help understand the behavior of cells of various sizes in a
tissue, artificial self-driven granular particles, or living organisms of
different sizes in a dense environment.
