To be fair, there are plenty of particles that can go faster than the speed of light in a particular medium, but there are no experimentally observed particles that exceed the speed of light in a vacuum.
The refractive index of a transparent medium is simply the ratio that is speed of light in a vacuum divided by the speed of light through that medium. So light is slower going through glass than a vacuum - the speed used for light going down an optical fibre (like submarine cables) is approximately 2/3 c, so the refractive index is roughly 1.5 (For water, it is roughly 1.333)
So, what you need is a particle that goes through glass faster than light goes through glass. Or one that goes through water faster than light goes through water. it turns out that the speed at which particles are ejected from atoms during radioactive decay can easily exceed the speed of light in glass or water.
So locally, while in the glass or water, particles ejected from a radioactive atoms can exceed the local speed of light (usually electons ie beta-decay). Simplifying a bit, electrically charged particles going a medium faster than light emit light - called Cherenkov radiation, which appears as a blue glow. This is why you get the blue glow around reactor rods operating in water-cooled research nuclear reactors.