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The proton anti-proton annihilation at Wikipedia describes the process as not as simple as the electron-positron annihilation. Especially it states:

Reactions in which proton-antiproton annihilation produces as many as nine mesons have been observed, while production of thirteen mesons is theoretically possible. The generated mesons leave the site of the annihilation at moderate fractions of the speed of light, and decay with whatever lifetime is appropriate for their type of meson.

Now the proton/anti-proton contain a sum of 6 quarks/anti-quarks while 13 mesons contain 26 quarks/anti-quarks.

How does the theory explain the massive increase in quarks/anti-quarks?

Johannes Maria Frank
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2 Answers2

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In annihilation it is the quantum numbers that add up to zero, baryon number is zero, as strangeness etc. After annihilation, the quarks have to be produced in quark antiquark pairs, which then will combine appropriateley to make hadrons. These can be produced as long as the quantum numbers will be adding up to zero.( for example, if a strange quark is produced an antistrange must accompany it).

It is the energy limitations that will give a limit to the number of hadrons that can be possibly produced.The limits given in the quote in number of possible mesons must come from considering annihilation at rest , or low energies. All the links in the wiki quote state "low energy".

Edit after comment:

The composite particles, protons and antiprotons, proceed in annihilation by the strong interactions that are allowed , and the situation is not simple. Here is a diagram of quark interactions :

quarks

This diagram can also be read time going from left to right, where it depicts the annihilation of a quark antiquark pair to a gluon and the gluon generates a different quark antiquark pair, because only color has to be conserved in the peculiar way of the laws of strong interactions. The other quantum numbers, strangeness, bottomness, topnes, charmness, upness and downness disappear in the interaction. This is in contrast to reading the feynman diagram time from bottom to top.

You might think that the number of pairs is conserved, BUT you are counting without taking into account the nature of strong interactions. Gluons, in contrast to photons, self interact. The intermediary gluon is carrying a lot of energy in proton antiproton annihilations,( about two thousand Mev, to the order of up,down quark masses which are of order of mev) and there is a very large probability that it will radiate away to many gluons which gluons will finally manifest into new quark antiquark pairs. The pair numbers are limited by the available energy and the probabilities of the quantum mechanical calculations.

anna v
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Have a look at my answer to Conversion of energy to matter? for an explanation of how particles are created in nuclear reactions. You say in a comment to Anna's answer:

The quark is an elementary particle. How can it be produced out of nothing?

But particles are created routinely in particle scattering events. This is exactly how new particles are discovered at particle colliders.

The particles are not created from nothing of course. They are created from energy in accordance with Einstein's famous equation $E=mc^2$. In a collider the energy is supplied from the kinetic energy of the colliding particles. In a proton annihilation the energy comes from the binding energy of the proton.

In a proton the masses of the three valence quarks are around 2MeV for the up quark and 4.8MeV for the down quark, which is only around 1% of the 1GeV mass of the proton. The other 99% of the proton mass comes from the binding energy. Mesons have a much lower binding energy, so the binding energy of the proton can be converted into the creation of the valence quarks of the mesons. If you add up the total energy of the proton and antiproton. i.e. rest mass energy and kinetic energy, and compare it to the total energy of the mesons, photons etc produced in the annihilation then you will discover that the two energies are the same. Hardly surprising since we know energy is conserved.

John Rennie
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