Here we sit, though, on a planet made of protons and electrons, in a galaxy made of protons and electrons. There is no antimatter to be found! This means one of two things: either, a) the Big Bang somehow "violated baryon number" and actually didn't make (or destroyed) the expected antimatter, or b) the Big Bang made antimatter somewhere else, and Earth happens to be in a matter zone. While physicists at accelerators are trying to understand possibility (a), if AMS sees antimatter nuclei, it would prove possibility (b).
Seeing a mere antiproton or antielectron does not mean much - after all, these particles are byproducts of high-energy particle collisions. However, complex nuclei like anti-helium or anti-carbon are almost never created in collisions. But they would be made abundantly by nuclear fusion in an anti-star!
So, AMS will search for anti-helium nuclei. First we try to very cleanly identify particles with the right charge (+-2); then we examine these particles' tracks and see how they bend in the magnetic field. Ordinary helium will bend to the left, antimatter helium will bend to the right. A single really clean detection would be really exciting!
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