# How many quarks in a proton?

I am confused by different papers I have seen on the internet. Some say there are three valence quarks and an infinite of sea quarks in a proton. Others say there are 3 valence quarks but a large amount but finite number of sea quarks(quark, antiquark virtual pairs) in the proton

What is the answer? are there an infinite amount of quarks in a proton at any one time? how can this make any sense?

• can you give a link on who is saying there is a finite number of quark antiquark pairs? There are three valence quarks which make up to baryon number 1, then there are gluons morphing into quark antiquark pairs. The infinity is a mathematical infinity: how many real numbers are there on the x axis between 0 and 1? Mar 11 '13 at 12:18
• anna the link to your question is down below. it was strasslers post. I was confused because literally I thought there was an inifite amount of quarks/anti quarks in the proton at any one time not a mathmatical infinte. I knew it couldnt be right that there was a literal infinite amount Mar 11 '13 at 12:41
• The constituents of a proton are described by parton distribution functions, which tell you how much of a proton's momentum is being carried, on average, by a particular type of constituent quark/gluon. You can see by glancing at a few of the plots that the majority of the momentum of a proton is carried by a large number of low energy particles. Take the limit and you get an infinite number of zero energy particles - but I don't know how real this is since QCD is strongly coupled and I'm out of my depth. :) Mar 11 '13 at 13:43
• Ps. You may want to merge your accounts. Mar 11 '13 at 15:11

There are an infinite number of sea quarks in any hadron, it is important to remember that these sea quarks are "off shell" particles as such, they are temporary particles, that do not exist before or after the interaction in the final or initial state, they are particle-antiparticle pairs created as part of the energy in the interaction, they do not effect the interaction in the same way that the valence quarks do, in that they have no impact on anything outside the hadron. Think of them as energy in the system manifesting as unstable particles for limited amounts of time before returning to energy again, for a majority of the time they do not exist, but their potential for existence must be accounted for (this isn't the best way to approach thinking about QFT, which should be dealt with exclusively mathematically, otherwise we will be wrong in some way, or our heads will explode).

In QFT, we use Feynman diagrams to represent an interaction, but there are many ways to represent the same interaction (same initial and final states), it can be shown that in order to get the correct measurements for any aspect of an interaction, we must add together contributions from all possible Feynman diagrams for that interaction (I won't explain this here, my answer is long enough as it is). If you're familiar with Feynman diagrams, these are the particle represented as being "inside" the diagram, the intermediate steps between the initial and final states. An important feature of Feynman diagrams is that this intermediate step of off shell particles can be infinite in complexity and still preserve the interaction, i.e. there can be an infinite number of these off shell particles. We then organize these Feynman diagrams into a hierarchy. The simple "tree level" diagrams, which represent the interaction with only one off-shell intermediate state are first, then comes the "one-loop" diagrams where a "loop" pair of creating and annihilating particles is formed as part of the intermediate state. Here's a few diagrams I found illustrating this:

Tree level QED processes:

One loop diagram of the same interaction:

This hierarchy continues with two loops, three, etc to infinity. It is these loops of created an annihilated pairs that are our sea quarks (in QCD only obviously). Since the hierarchy continues to a infinite number of loops for every interaction, we conclude that there are an infinite number of sea quarks (can also be gluons by the way).

In response to your question about this being a problem, well, to an extent it is. In QED (electrons and photons remember, not quarks) we interpret these "interactions with infinite parts" in this way: To get the overall interaction mathematically, we must add together all of the infinite diagrams together, but in QED, the more loops the diagram possesses, the less it contributes to the overall interaction, this addition becomes a convergent series and can be solved through perturbation techniques.

However, in QCD this series doesn't lessen due to the strength of the appropriately named strong force. As such each of the infinite diagrams makes an non-negligible contribution to the interaction. This is an unsolved problem in theoretical physics. There are suggested solutions, the one with the most success so far is Lattice QCD. This involves performing calculations for QCD phenomenon (energy levels, coupling strengths) in a discrete space-time, and extrapolating to the continuum limit.

If you are confused by my description of Lattice QCD, firstly I don't blame you, it's not a simple idea. My favourite guide can be found here: http://arxiv.org/abs/hep-ph/0205181

I feel the need to summarize this answer, the problem is that summarizing QCD almost always involves making something wrong, but here goes: All Quantum Field theory interactions involve us having to account for an infinite number of created an annihilated pairs that could occur in our calculations. These don't technically exist in the way valence particles do but they effect the interaction all the same and give us infinities in our calculations, but theoretical methods like Lattice QCD offer us ways around this. The sea quarks may spontaneously pop in and out of existence in finite numbers, but these have no measurable effects outside the hadron.

• This answer seems reasonable, but perhaps clarify that the infinite quarks are merely probabilistic and temporary. The three stable quarks are the only ones with any importance outside the hadron. Mar 11 '13 at 14:33
• Hi Matt, I think you may wanna look at the answer (probably a comment for you) posted by another user ;-) Mar 11 '13 at 14:40
• Are there an infinite amount of sea quarks at any instant? Or over the whole lifetime of the hadron? Also, how can two hardrons be identical when they have a sea of infinite (or finite) quarks that are randomly popping in and out of existence? Jun 3 '18 at 10:38