“I’m a fan of supersymmetry, largely because it seems to be the only route by which gravity can be brought into the scheme. It’s probably not even enough, but it’s a way forward to get gravity involved. If you have supersymmetry, then there are more of these particles. That would be my favourite outcome.” -Peter Higgs
The “diphoton bump” at 750 GeV is perhaps the best active signal we have for the possibility of fundamental new particles beyond the Standard Model. While the upgraded LHC should collect enough data that we’ll know by the end of the year whether it looks real or goes away, there are six different possibilities for what it could be if it pans out.

Image credit: The ATLAS collaboration, 2015, of the various decay channels of the Higgs. The parameter mu = 1 corresponds to a Standard Model Higgs only. Via https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/CONFNOTES/ATLAS-CONF-2015-007/.
They include: a second Higgs, dark matter, extra dimensions, neutrino physics, a composite particle or even a surprise! But don’t get too excited; a similar bump at three times that energy has already gone away, and this one might be next.