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This question already has an answer here:

I apologize in advance to experts for the naivety of the question. It should be a duplicate but I didn't find any satifying question or answer about that.

The proton is composed by two up quarks and one down quark.

mass(proton) $\sim 940 \ MeV/c^2 $
mass(up) $\sim 2.3 \ MeV/c^2 $
mass(down) $\sim 4.8 \ MeV/c^2 $

It follows that: $2$mass(up) $+$ mass(down) $\sim 9.4 \sim \frac{1}{100}$ mass(proton).

Question: Where does $99\%$ of the remaining mass of the proton come from?

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marked as duplicate by John Rennie, ACuriousMind, Floris, Kyle Kanos, David Z May 21 '15 at 15:06

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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Your question asks why the "current quark masses" [see http://pdg.lbl.gov/2011/download/rpp-2010-booklet.pdf at page 21] of the quarks that make up a proton don't add up to the mass of the proton. The problem is that, for the light quarks, the "current quark masses" are very different from the "constituent quark masses" [see wikipedia]. "Constituent quark masses" basically means: What you would expect from a naive model where the proton is uud and the neutron is udd. Whereas "current quark masses" means: What you would expect in a mass-independent subtraction scheme such as $\bar {MS}$ at a scale of $\mu\sim 2GeV$, which basically is a fancy way of saying "it's complicated".

The reason these are different is because the strong nuclear force (AKA Quantum Chromodynamics) is "asymptotically free", i.e., it is only easy to understand at very high energies in terms of single particles. At low energies, such as in protons, the "bag of quarks" that make up the proton can not be thought of as single particles because there is a large and difficult to determine interaction among the quarks and gluons inside the proton. This interaction energy can be though of as "making up the mass difference" although it would be just as good to say that a proton is NOT make up of just three quarks. Rather it is made up up many many quark-anti-quark pairs and gluons on top of which sit three "extra" quarks: u, u, and d

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  • $\begingroup$ Is the Higgs field responsible of only 1% of the proton mass (through these three "extra" quarks)? $\endgroup$ – Sebastien Palcoux May 24 '15 at 4:47
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    $\begingroup$ You're on to something there, but it's hard to say exactly. The Higgs can be thought of as responsible for generating all the quark mass terms in the QCD Lagrangian, but it doesn't generate any mass associated with interaction energy by E/c^2. Although I think it's a little more complicated than this. $\endgroup$ – hft May 24 '15 at 19:55
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The equivalence principle tells us that energy and mass are really just two sides of the same coin, and are related by $E = m c^2$. Rearranging, we get that $m = E/c^2$, so instead of asking where all that mass comes from, let's ask where all that energy comes from. In the case of the proton, there are some quarks and gluons that make it up, and those certainly contribute a bit of the energy in the form of their rest energy (the mass of these particles), but most comes from the potential energy of the strong interaction between the various constituent particles of the proton. Since the scale of these interactions is much larger than the rest masses of the up and down quarks, most of the energy of the proton comes from this rather than from the bare masses of any of the constituent quarks.

Similarly, suppose you had two electrons very close to each other, and you measured their total mass together. You would measure the mass to be slightly more than twice the mass of an electron, because there is also a lot of potential energy in having those two charged particles so close together. Also similarly, the mass of a hydrogen atom is slightly less than the mass of a proton plus the mass of an electron, because the proton and the electron together have a negative electromagnetic potential energy (they attract each other) that contributes negatively to the mass of the hydrogen atom.

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The three quarks you talk about are usually called the valence quarks of the proton, and their contribution to the mass of the proton is not it. In particle accelerators, when we hit protons with high energy beams, we discover that protons are made of a cluster of smaller constituents (like quarks and gluons, which constantly are created and destroyed in particle-antiparticle pairs.) At lower energies, the proton appears to be made of three quarks, but for higher energy collisions, we find that the proton is actually made up of loads of such particles. These particles make up the 'missing' mass of the proton.

Edit: Looking at the proton like it is a particle would be wrong, because it is actually made up of quantum fields. (like everything else.) These fields 'act out' differently depending on how much energy you 'supply' to observe them. For lower energies, the proton behaves like three particles, but you can observe that it is made up of a much denser mix at higher energies.

(Sorry if I used weird words like act out and supply, QM and words doesn't go too well for me.)

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  • $\begingroup$ Where are these particles making the 'missing' mass of the proton, at lower energies? $\endgroup$ – Sebastien Palcoux May 21 '15 at 6:32
  • $\begingroup$ Edited out to clear that. $\endgroup$ – Hritik Narayan May 21 '15 at 6:41

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