Your initial premise is: Matter and antimatter [should] annihilate each other completely releasing energy in the form of photon. This is incorrect.
Rather, an electron-positron collision will annihilate both particles and produce a boson. A boson is a class of particle, one of which is a photon. But you can also produce other bosons, such as the Higgs or a $Z^{0}$.
It is the boson that subsequently decays to form the shower of particles we detect. It is from the rate, shape and distribution of these showers that we determine what boson was originally present.
These processes are usually visualised by drawing Feynman Diagrams.