No official Mega Man Zero release exists on PSP. The series (Zero 1–4) launched exclusively on Game Boy Advance (2002–2005).
.gba ROMs in /PSP/GAME/gpSP/ROMs/.Downloading GBA ROMs without owning the cartridge = piracy. Dump your own via GBxCart RW, EZ-Flash Omega, or 3DS + GodMode9.