Brian Bi

## If particles and antiparticles destroy each other upon interaction, how do a quark and an antiquark create a meson?

A meson is said to be a hadron that is composed of a single quark and an antiquark held together by the strong force. If a particle and an antiparticle meet, it's said that they would destroy each other and release energy.
The annihilation of particles with their antiparticles is not instant. In fact, no process occurs "instantly" in physics. I think some people are under the impression that some processes are instant, for example, the excitation of an electron by a photon—because electrons can't exist "between" orbitals. However, this reflects a misunderstanding of quantum mechanics. The transition takes a nonzero amount of time to occur [1]. In fact, as the electron interacts with the photon, its wave function changes continuously from the initial orbital to the final orbital. During the transition, if you attempt to observe the electron's quantum numbers, you'll have a certain probability of finding it in the initial orbital and a certain probability of finding it in the final orbital. However, that implies that the state of the electron before the measurement was a superposition.

It is the same when particles and antiparticles annihilate. At time zero, say you have a neutral pi meson. If you measure the number of quarks or the number of antiquarks, you will get a nonzero result with probability nearly 100%. [2] A few attoseconds or so later, if you were to measure the number of quarks or the number of antiquarks, there would be a small probability of observing zero, and if you were to measure the number of photons, there would be a small probability of observing two (the result of the most common decay). As time passes, the probability of observing zero quarks and two photons increases. After about a femtosecond, the probability of observing zero quarks will have grown to approximately 100%, and the probability of observing two photons will have grown to approximately 99%. (There is also some probability that the decay produces a different final state.)

So that's why the neutral pi meson is able to exist at all: annihilation is not instant.

This is not the whole story, however. If the neutral pi meson were unstable enough, you would never see it. That is to say, in a high-energy collsion that produces a quark and antiquark, it takes some time before they evolve into the bound quark-antiquark state we call the meson. This time is (I believe) on the yoctosecond scale ($$10^{-24}$$ s). If it took a femtosecond to form the meson, you'd never see it, because the quark and antiquark would annihiliate each other first.

The strong interaction binds quarks together into hadrons. Because the strong interaction is quite strong, it acts on very short time scales. The electromagnetic interaction is weaker, and therefore slower. It is the electromagnetic interaction that's responsible for causing annihilation of the quark-antiquark pair. The weak interaction is usually weaker still, so particles that decay due to the weak interaction typically have even longer lifetimes. However, there are exceptions. For example, the weak interaction is quite strong for very massive particles. For this reason, the top quark decays in about $$10^{-25}$$ seconds, before it can form hadrons. In this case the weak interaction is even faster than the strong interaction.

So the complete answer to your question is: annihilation is not instant and is in fact slower than hadronization because the electromagnetic interaction is weaker than the strong interaction.

(Actually, one thing I forgot to mention is that a particle can only annihilate with its own antiparticle; an up quark cannot annihilate with a down antiquark for example. So the charged pi mesons, in contrast to the neutral pi mesons, do not decay by annihilation, but rather by a weak process. That's why they have longer lifetimes than the neutral pi meson.)

[1] Many physicists would say "a finite amount of time" but I think this is among the worst notational abuses by physicists.

[2] I said "a nonzero number" instead of exactly one because there is some subtletly associated with the question of how many quarks are inside a hadron. See, e.g., Protons and Neutrons: The Massive Pandemonium in Matter