Is it possible, according to the standard model, to create proton-antiproton pairs from the vacuum? I know it is possible to do it with photons and electrons, but is it theoretically possible in the standard model with protons, given high enough energy levels? I understand there is no experimentally feasible way to produce them, but what does theory say?
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2$\begingroup$ Are you asking about pair production by an electric field, i.e. the Schwinger process, or are you asking about the virtual particles that briefly pop into existence in a vacuum? $\endgroup$– John RennieCommented Dec 5 at 6:24
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$\begingroup$ I am talking about the stable production of a particle-anti particle pair via processes such as the dynamical casimir effect or the schwinger process. I'm looking to understand how this type of polarization works and what its limits are. $\endgroup$– sakurashinkenCommented Dec 5 at 18:05
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1 Answer
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Except for the greater mass energy required, there is no major difference between how different charged particle-antiparticle pairs are produced by a strong electric field $\vec{E}$. The lowest-order contribution to this effect (the Schwinger process) has a production rate per unit volume $$\Gamma = \frac{q^{2} E^{2}}{4 \pi^3 \hbar^{2}c}\sum_{n=1}^\infty \frac{1}{n^2} \exp\left(-\frac{\pi m^2 c^3 n}{\hbar qE}\right)$$ for any species with charge $q$ and mass $m$. Since the exponential terms always have a factor of the mass squared, the rate falls off very quickly with increasing mass, but the effect can still, in principle, occur.
The above expression is nonperturbative in the field strength $E$ but it is only the leading term in the number of virtual particle loops required. The next sub-leading terms will differ for electrons and protons in more ways than just the involvement of different masses. Because the proton has a large anomalous magnetic moment, that will affect the higher-order terms. (Production of neutral particle-antiparticle pairs can also occur, if their species—like the neutron, for example—has a magnetic moment; however, in that case the production must come entirely from the smaller higher-order terms.)
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1$\begingroup$ Wouldn't there be a difference due to protons being composite? I'd think they would need to have the constituent quarks created (along with their anti-quarks), which would need to then combine to make the proton. That seems a lot less likely than creating a single fundamental particle with the same mass would be. $\endgroup$– BaddDaddCommented Dec 4 at 21:29
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$\begingroup$ @BaddDadd Yes, there are differences, but they don't show up at the lowest order. The anomalous magnetic moment I mentioned, for example, is a product of the proton's composite character. $\endgroup$– Buzz ♦Commented Dec 4 at 22:10
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$\begingroup$ This is an amazing answer. Where can I learn more about this type of polarization? Any books you would reccommend? $\endgroup$ Commented Dec 5 at 18:04