Proton structure: are there photons, electrons and neutrinos in there too? I've read that the proton is not simply made up of three (valence) quarks; rather, there is a continuous exchange of gluons between the three quarks, and these gluons can produce quark-antiquark pairs that usually annihilate soon after, so that at any given instant, the proton is actually a mess of gluons and quarks and antiquarks. This is my understanding, please do correct me if I am mistaken.
However, the quarks also couple to the electromagnetic force, and Feynman diagrams of quarks "emitting" photons certainly exist. So are there photons within the proton as well?
And if so, surely these photons can pair produce electrons and positrons -- so, are these particles present within a proton (or any other hadron for that matter)?
Quarks couple to the weak force too. Does this mean there are neutrinos in the proton as well?
I'm aware that, if these EM and weak force couplings were present, the strong force one would still be vastly dominant; however, it still intrigues me to know whether there are all these particles within something so seemingly simple as the proton.
 A: [EDIT: On rereading the question, it seems I have taken an overly pedagogic approach, underestimating the level of the asker. Sorry about that. Consider it a service to any hobby readers of the future.]
Protons can be quite precisely described as three quarks held together by the strong force as mediated by gluons. As you say a gluon can emit a quark-antiquark pair, which can annihilate into a gluon - but this hardly means that the protons "contains" these pairs. The key concept to understand is when something is "energetically favorable". A ball on a hill can win energy by rolling down to the bottom - this is an energetically favorable process.
As far as we know, protons are in an energetically favorable position - they have found a minimum in energy, and will not decay into something else unless we put energy into it. That means that you will not measure a proton suddenly emitting a meson (a quark - antiquart particle) without you investing considerable energy into it. If you make that investment, however, you can get all sorts of fun particles. This is what they are doing at LHC - knocking together protons to force the quarks out of their comfy energy minimum and into creating a bunch of exotic particles.
So no, protons do not contain anything else than three quarks in the way that a stable state of those quarks are our best model of the proton, and no are suddenly emitted from the proton. What I suspect you might be thinking of is "virtual particles". These are a little complicated. Consider a gluon travelling between two quarks, mediating their strong attraction (or confinement if you will). On the way, that gluon might decide to split into a quark - antiquark pair, which then almost immediately annihilate into a gluon which continues as if nothing happened. This is a lot less energetically favorable than the gluon just staying a gluon, but it still appears to happen every now and then. We need to include them in the model to get the correct results, and they are allowed due to quantum uncertainty. But! These particles are virtual, not real. There is no measurement which can ever observe them. In some sense, they exist more as math than as physics.
An analogy in easier to understand terms could be a light travelling through empty space as a photon. The photon has the virtual process of emitting an electron and a positron which then annihilate back into a photon which goes on as if nothing happened. This does mean that empty space is a bit more complicated than first thought, but it can hardly be interpreted as empty space being full of electrons and positrons. After all, empty space is empty.
I can recommend looking into Feynman diagrams to get a better feel for the situation. The relevant concepts are that virtual processes correspond to lines which start and stop inside the diagram and thus never escape the diagram to be measured, and the fact that the more complicated a diagram looks, the more energy it costs and thus the more rare it is.
Sorry for the long answer. I hope it helps!
A: Yes.  The interior of a proton includes not only virtual quark-antiquark pairs, but virtual photons, virtual electron-positron pairs, and virtual neutrino-antineutrino pairs, for exactly the reasons you describe.  However, each of these species is less important than the one before it.
As you say in your question, not only do quarks couple to the QCD color force (and therefore interact by exchanging gluons), but quarks also have nonzero electric charge, and interact by exchanging virtual photons.  The electromagnetic interaction between quarks includes the full machinery of QED, including virtual particle-antiparticle loops coupling to the virtual photons.  All of the charged particles participate in such loops, but the electrons are the most important because they have the smallest mass.
The valence quarks in a proton, and the virtual fermions in the quark-antiquark “ocean,” also couple to the charged and neutral weak currents, and therefore interact by exchanging virtual $W$ and $Z$ bosons.  Just as with photons and QED, the virtual $W$ includes some correction from $e\nu$ loops, and the virtual $Z$ includes some correction from $e^+ e^-$ and $\nu\bar\nu$ loops.
In principle, at least.  The weak interaction is weak, and precision measurements are hard.  For example in this measurement of proton-electron scattering by $Z$-boson exchange, an analysis-delaying correction came from the “gamma-$Z$ box diagram.” The amplitude of the neutrino loops will be related to the existence (or non-existence) of neutrinoless double beta decay, which depends in turn on whether the neutrino is its own antiparticle.
A: Photons:
It is very important to understand what a static EM field is. Yes , quarks do have EM charge, and they do have a static EM field around them. The EM charge of the quarks does contribute to the stability of the proton.
https://en.wikipedia.org/wiki/Electromagnetic_field
Now when these static EM fields of the quarks interact with other quarks inside the proton, we use virtual photons to model the effects that we see in experiments. These virtual photons are not real. So the answer to your question about photons is there are no real photons in this context inside the proton flying inbetween quarks.
Virtual photons, what makes them virtual?
Electrons:
Yes, real photons could pair-produce electron positron pairs, but since there are not real photons inside the proton, there should be no pair produced electrons inside the proton. Now you can read about electrons being inside the proton, but that is the case when you talk about one of the electrons from the electron shells around the nucleus, and since we are talking about QM, it is all probabilities, and the electrons do have a nonzero probability to be inside the proton. But that is not what you are asking about.
Can an electron be inside a proton?
Neutrinos:
When the neutron converts to a proton or vica versa, that is, the up quarks convert into a down quark or vica versa, a neutrino is absorbed or emitted. But that is not what you are asking about. If you are asking about the stable proton, then there are no neutrinos inside. Except, if you are asking about the fact that even a cubic feet of empty space contains a lot of neutrinos that remained from the big bang, just like the CMB has photons. Now neutrinos fly through protons without mostly interacting with the proton through the empty space inbetween the quarks, that is why you could say there are neutrinos inside the proton. But that is not what you are asking about.

There are also believed to be lots of leftover neutrinos everywhere, a kind of lightweight matter.

If everything is made up of atoms, what is vacuum made up of?
