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Common knowledge has it that when an amount of matter and an amount of antimatter come anywhere near each other, they annihilate, leaving nothing but "pure energy".

In more technical terms, maybe we could say that a particle-antiparticle annihilation has a very high cross-section, and the products have all quantum numbers equal to zero. As pointed out in the comments, for the high cross-section we should probably restrict to annihilation due to strong or electromagnetic interactions.

My question is about the high cross-section. Thinking about the factors influencing the cross-section (especially in QED), we see

  • the number of vertices in the Feynman diagrams involved: the lowest level would just have a single vertex, so that is OK. (Let's ignore that to ensure conservation of momentum this cannot really stand by itself).
  • the mass of the exchange particle: no propagators.
  • the availability of final states.

At least the first two are clearly favorable for a relatively high cross-section, but it is not clear that it would be exceptionally high compared to other elementary interactions.

Is the last one an important contributor? Is there some other contributor that I overlooked? Or is the cross-section not actually that exceptionally high compared to other processes?

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    $\begingroup$ Particle/antiparticle annihilation does not have to have a very large cross section at all, neutrino/antineutrino annihilation cross section is extremely small. Unless you are leaving out neutrinos in your analysis. $\endgroup$ – Triatticus Jun 27 '19 at 8:10
  • $\begingroup$ to continue , it will depend on the number of the low order diagrams that are allowed for the particular annihilation and whether strong, weak or electromagnetic vertices are involved to lowest order in perturbation expansion( strong is dominant as the name says) , see the couplings hyperphysics.phy-astr.gsu.edu/hbase/Forces/funfor.html $\endgroup$ – anna v Jun 27 '19 at 8:20
  • $\begingroup$ What Triatticus said. Also, the common knowledge isn't quite correct. As I said here, while low energy electron + positron annihilation usually results in 2 (or 3) photons, at high KE it can get messy. And for composite particles, like proton + antiproton, it's always messy. $\endgroup$ – PM 2Ring Jun 27 '19 at 8:28
  • $\begingroup$ Thanks all three of you for your comments. @Triatticus is it true that the cross-section is high when neutrinos are left out? Or if we restrict (e.g.) to QED and/or QCD? $\endgroup$ – doetoe Jun 27 '19 at 8:54
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    $\begingroup$ @Michael Walsby it matters because if the theory is wrong, then it should be fixed/adjusted. $\endgroup$ – KF Gauss Jun 27 '19 at 12:04
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It's just not true that particle-antiparticle interactions have particularly large cross-sections, even if it is "common knowledge".

On the timescale of human perception, objects made of protons will immediately react with objects made of antiprotons that touch them. But that's not special to antiprotons. The same would be true for another object made of protons, which is part of why you can't put your hand through a wall. This is simply because humans react amazingly slowly compared to any nuclear timescales. We only treat the particle-antiparticle reaction as more salient because it's more violent.

At the level of cross-sections for high-energy particle collisions, there's no particular reason to favor particle-antiparticle reactions. For example, some past colliders used proton and antiproton beams, while the LHC only uses proton beams. In both cases, most of the time most of the stuff in the beams just passes through each other. You can compute the cross-sections directly, and they are comparable.

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  • $\begingroup$ This is a useful answer, thanks. What made you say I was trying to import pop-science intuition? My intention was the contrary: to understand 1) if it is indeed the case that particle-antiparticle reactions have a very high cross-section 2) if so, what are the contributors to that high cross-sections. $\endgroup$ – doetoe Jun 27 '19 at 16:53
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    $\begingroup$ @doetoe I just meant when you cited "common knowledge". It's not common knowledge among physicists -- it's a common trope in popsci. $\endgroup$ – knzhou Jun 27 '19 at 16:55
  • $\begingroup$ Ah yes, that is exactly what I meant to say. Something that more or less generally accepted, independent of its actual truth, like "don't swim after eating". $\endgroup$ – doetoe Jun 27 '19 at 17:01

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