Thecurrent "standard model" of physics holds that each particle -protons, electrons, neutrons and a zoo of more exotic particles - has itsmirror image antiparticle.
Until recently, the LHC only accelerated protons and collided them inside the particle accelerator mainly to search for the infamous Higgs boson and other exotic particles.
While particle-physics colliders and space-based observatories could rule out some of the more exotic versions of each, no one has been able to suggest a way to decide between them in general.