A proton is made of quarks and gluons bound by the strong force in a confined system. Further, all protons are basically interchangeable parts for the purposes of this question. Each one is identical in all material respects.(adsbygoogle = window.adsbygoogle || []).push({});

Scientists know a lot about gluon energy density in protons. We have, in principle, the exact equations that govern strong force interactions, although, in practice we use good approximations of them. In particular, we know to moderate accuracy (always, always less than we'd like) the value of the strong force coupling constant that among other things, tells us the likelihood that a color charged particle with emit or absorb a gluon in a particular time frame.

Admittedly, what we know is probabilistic. But, it seems to me that it ought to be possible to determine how many individual gluons are present, on average, in any given proton (and indeed, the answer should be almost identical for a neutron), at any given point in time.

I have looked for articles (technical or layman oriented) doing this calculation, and haven't found one. But, surely somebody must have done it, because we seem to know everything we need to know to do that calculation, and it seems like an obvious, foundational thing to want to calculate. Even if it doesn't change the math used to calculate physical observables, this kind of number is helpful in conceptualizing what is going on in your head, like an illustration for a story problem in algebra.

Is this perhaps something that everyone does as a homework exercise in their first graduate school QCD course (I recall doing derivations of Kepler's laws, e.g., when I was in first year physics), and so it isn't considered worth publishing?

Indeed, if we knew that, we could also easily extrapolate to the total number of gluons in existence at any one time in the universe (determining the total mass-energy attributable to gluons in the universe is trivial, even without the number of gluons in existence), which doesn't have a lot of practical value, but would nonetheless be interesting to know as just sort of a basic fact about the universe.

To the extent it is relevant, I would be looking for the "ground state" of minimum energy and temperature. Basically, a hydrogen-1 atom's nucleus in a vacuum, although factors that would impact this would be nice to know.

Extreme precision isn't a priority. An order of magnitude estimate or +/- 30% or something like that , would be fine. I'm not asking for a three year long NNNLO calculation unless one is already readily available in the literature.

So, what is the answer, or if this hasn't been determined, is there a reason that this is harder than it seems to determine?

(I struggled with the difficulty level for this question. Ultimately, I classified this as "basic" level because the ideal answer should be a simple number plus or minus a margin of error, and would still make sense with only the barest sense of the quark-gluon model of the proton. But, I recognize that coming up with the answer is no double an advanced matter requiring graduate school level knowledge, and that even having a sense of what goes into the calculation and why it should or shouldn't be possible to do the calculation is probably an intermediate level matter at minimum.)

FWIW, my intuition is that the number ought to be in the double digits or high single digits, but that doesn't really have a well thought out basis and I recognize that my intuition may be and indeed probably is, totally wrong.

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# B How many gluons on average are there in a proton at once?

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