Please tell me where I go wrong in my understanding:

If the valence quarks-gluons male up 1,5 % of total mass how can the remaining so-called sea contain "innumerable" virtual particles? At most there should be 80 times the valence quarks, which falls short of a sea definition

  • $\begingroup$ Assuming this is about hadron masses, what reference claims that "the valence quarks-gluons make up 1,5% of total mass"? See physics.stackexchange.com/q/474084/50583 for discussion on contributions to the hadron mass - as a bound state in the strongly interacting regime of QCD, the picture of a hadron as "three quarks somehow stuck to each other" is essentially useless in understanding any of its properties other than what it can decay/scatter into. $\endgroup$
    – ACuriousMind
    Apr 13, 2022 at 9:27
  • $\begingroup$ @ACuriousMind, *"The mass of a proton is about 80–100 times greater than the sum of the rest masses of its three valence quarks, while the gluons have zero rest mass. The extra energy of the quarks and gluons in a proton, as compared to the rest energy of the quarks alone in the QCD vacuum, accounts for almost 99% of the proton's mass."*wiki:quark $\endgroup$
    – user157860
    Apr 13, 2022 at 9:32

1 Answer 1


The attribution of hadron masses to particular contributions is a subtle and not at all intuitive matter. See this question and its answers for extended discussion on where hadron mass "comes from". Saying "the valence quarks make up 1,5%" and attributing the rest to "sea particles" is simply wrong - the "rest" is a complex combination of different energies, which are related to "virtual particles" only insofar as that - like most QFT computations - virtual particles appear when you try to compute these perturbations perturbatively. In particular about 1/4th of the mass comes from the "trace anomaly", whose nature you cannot even explain in any naive picture of just a bunch of particles bound together.

The "sea" of particles inside a hadron refers to the parton model that gives us parton distribution functions for which particles we are likely to observe when we probe a hadron at a certain energy scale. Crucially, these are a function of the energy of the probe, i.e. what we expect to find "inside" a hadron depends on how we're looking at it. Since quantum chromodynamics is strongly interacting at every day energies, perturbation theory (and hence by extension the concept of virtual particles) is useless in understanding how hadrons that are just sitting around work.


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