# Where is the mass of a proton coming from? From empty space or gluonfields?

Protons are made quarks and bosons. I think most physicists would agree that the mass of a proton is not coming from the quarks itself. About 90% is coming from something else, but what is that.

-The mass is coming from empty space (virtual particles?). See 2.40 https://www.youtube.com/watch?v=y4D6qY2c0Z8

-The mass is coming form the gluonfields. See https://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-structure-of-matter/protons-and-neutrons/

Now are these really two different possiblities or could they both at the same time be true (they are a bit the same)

• Possible Duplicate of physics.stackexchange.com/q/185149 The majority of mass comes from "temporary" quarks, as far as I know, but there are alway 3 valance quarks in nucleons and 2 in mesons. – user108787 Nov 23 '16 at 21:30
• No, these are distinctly not two different possibilities: they address the same mechanism, spontaneous chiral symmetry breaking, which is a feature of the QCD vacuum, driven by gluon interactions. Reading up further could explain to you why your artificial dichotomy is a bogus artifact of miscommunicated popular language. – Cosmas Zachos Nov 23 '16 at 21:48
• Wilczek says that most of the mass of protons and neutron is kinetic energy of quarks and gluons (the two articles "Mass without mass" in Physics Today 1999/2000). A back-of-the-envelope estimate of the kinetic energy of a massless particle confined in a femtometer-sized box already gives the right order of magnitude. – user137289 Nov 27 '16 at 1:34

Here is a pictorial representation of a proton

This represents the sea of particles that have to be taken into account if one wanted to think in terms of Feynman diagrams.The theory is quantum chromodynamics. QCD leads to:

Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do separate a quark from other quarks, the energy in the gluon field is enough to create another quark pair; they are thus forever bound into hadrons such as the proton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD.

Thus the three valence quarks are confined within the proton and other hadrons, by numerous exchanges of quark antiquark colored pairs and gluons. These have a mathematical description with four vectors, and it is the invariant mass of the whole conglomerate in the figure that is the mass of the proton, i.e. the instantaneous addition of all four vectors has the four dimensional "length" of the mass of the proton.

Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma.

The existence of jets in e+e- scattering validated the QCD theory for strong interactions, and the quark gluon plasma is part of the studies in experiment in the LHC.

So the mass is from all the four vectors contributing in the bag that is a proton, in the case of the proton mass.

Lattice QCD calculations follow the logic of virtual exchanges , but on the lattice, in order to avoid infinities, and have managed to calculate the mass of the proton:

Lattice QCD has already made successful contact with many experiments. For example, the mass of the proton has been determined theoretically with an error of less than 2 percent.

• I'm right that the exchanges of quark antiquark pairs is actually what L.Krauss meant with that the mass is from the vacuum? But what causes the valence quarks to create these vacuumpairs as it looks that the only appear when the quarks are driven apart. – Marijn Nov 26 '16 at 18:47
• The bag of proton is not a vacuum , it has the initial three valence quarks that have strong interaction exchanges, depicted by Feynmn diagrams . These diagrams grow exponentialy because of the color force and the gluon-gluon coupling. All these virtual particles have four vectors (E,p_vector) which added up have the "length" of the proton mass, E^2-p^2=m^2 ( c=1 here). the exchanges are equally with gluons – anna v Nov 26 '16 at 18:57
• @annav you misunderstood the nature of Feynman diagram. It's in principle a perturbation method thus cannot describe strongly interaction quarks and gluons inside a proton (or any hadron). – Turgon Jul 25 '18 at 13:28
• @Turgon one can always expand in a perturbative expansion, whether it will converge is a different story, but people are familiar with virtual exchanges and four vectors and is an "easy" way to get an intuition. – anna v Jul 25 '18 at 14:21
• Well, I admit that's one way to put it...But no one will actually use Feynman diagram, otherwise they'll have to resum all orders of them...Maybe that's a bit like Dyson Schwinger equation? – Turgon Jul 26 '18 at 15:11

The mass of the proton comes from the mass of the quarks which make the proton and the strong interaction between the quarks.

• From en.wikipedia.org/wiki/Quark#Mass A proton has a mass of approximately $938 MeV/c^2$, of which the rest mass of its three valence quarks only contributes about $9 MeV/c^2$; much of the remainder can be attributed to the field energy of the gluons. – PM 2Ring Nov 5 '20 at 13:37