The planet HD 106906 b was found at 650 AU from its home star, which is not a star much different from the Sun. Fomalhaut b is also a young planet that is orbiting very far away from its sun.
These two planets were discovered mainly because they are still hot enough to be seen in infrared images, and this happens because they are young. I think that old planets in far away orbits would be entirely black with a temperature below 10K, and thus invisible.
Back to our Solar System, some people support the hypothesis that beyond Neptune, some Sun-orbiting non-dwarf planets might exist. The existence of HD 106906 b and Fomalhaut b suggests that this is possible. What are the odds that we find at least one of these planets in the Solar System? If they do exists, how could we find it?