To understand how this is possible, you need to learn about quarks. By now, we know that some particles consist out of quarks. Some - because there are indeed elementary particles (electrons, neutrinos, photons, quarks and gauge bosons). But particles like neutrons, protons and mesons are compound particles. There are 6 quarks - up (u), down (d), strange (s), charm (c), beauty (b) and top(t), and corresponding to them antiquarks.
Quark composition of proton: p=uud; neutron: n=udd. Mesons are particles that consists of only 2 quarks. The lightest mesons are pions.
As an example, we can analyse reaction
"\\pi^- + p \\rightarrow \\pi^0 + n"
"(\\bar u d) + (uud) \\rightarrow (u\\bar u -d \\bar d) + (udd)"
As every particle-antiparticle pair, quarks can annihilate, and as opposite quark-antiquark pairs can be born when there is enough energy for creation of its bounded state. Neutral pion is a mixture of two states. As you can see, quark composition remain the same except pair "d \\bar d" that appears because the total energy of "\\pi^- + p" is enough to create it and, therefore, enough to born heavier particles "\\pi^0 + n".
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