Why Don't Neutral Mesons Annihilate Immediately?

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Ant92
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I have been learning about quarks which is really interesting, but i have become confused when it comes to mesons. I have learned the basics of annhilation, particle and anti-particle, etc, but I have learned that neutral mesons, such as the pi neutral meson are made of a quark, (e.g. up), and its corresponding anti-particle, (e.g. anti-up), so why do the particles join together to form the meson, shouldn't the particles annhilate?

Pi+ meson= up quark, anti-down quark
Pi neutral meson= up quark, anti-up quark/ down quark, anti-down quark
Pi- meson= down quark, anti-up quark
 
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Ant92 said:
I have been learning about quarks which is really interesting, but i have become confused when it comes to mesons. I have learned the basics of annhilation, particle and anti-particle, etc, but I have learned that neutral mesons, such as the pi neutral meson are made of a quark, (e.g. up), and its corresponding anti-particle, (e.g. anti-up), so why do the particles join together to form the meson, shouldn't the particles annhilate?

...apparently this is why we don't see a lot of Pi mesons around on a day to day basis... the lifetime of the Pi is pretty short (or long depending on what you compare it to)...

The situation is *similar* (I stress similar because the analogy is quite imperfect, yet perhaps helpful) with "positronium" in which a positron and an electron can briefly form a bound state. But, they eventually annihilate.