Gluons bond quarks into baryons (i.e., protons and neutrons). For example, two up quarks and one down quark form a proton while one up quark and two down quarks form a neutron. Is there one gluon per one baryon or two gluons per one baryon or what is the ratio of gluons to baryons?
I asked a question very much like this several years ago (in person, not online, but someone else asked it here): "what's the baryon asymmetry of the proton?" Thinking, of course, about the three valence quarks and the so-called "sea" of quark-antiquark pairs.
After talking with several people in my department and at conferences and at other places I visited, I finally came to an unsatisfactory conclusion: the answer to my question depends on the momentum scale at which you examine the proton. For a proton at rest, you don't really have evidence of sea quarks. For a proton at modest energy, evidence of excitations in the strong field begin to appear — but "nucleons and mesons" are a more succinct set of degrees of freedom at low energy than "quarks, antiquarks, and gluons." It's only if you look at relatively high energy — or equivalently, at very short distances — that quarks and gluons become the most parsimonious way to describe the strong interaction.
I think you're going to find the same sort of frustrating non-answer to your question about gluons. Gluons are the force-carrying particle in QCD, like the photon is the force-carrying particle in electromagnetism. If you have a hydrogen atom in its ground state, which is pretty well-described by the one-photon-exchange Coulomb potential, the equivalent question would be something like "how many virtual photons are exchanged as the electron orbits the proton once?" But of course as you study quantum mechanics you learn that "orbit" isn't really a good description of the electron-proton interaction for low-energy hydrogen states, and likewise the virtual photons are not really things you can count.
Is there one gluon per one baryon or two gluons per one baryon or what is the ratio of gluons to baryons?
Gluons are elementary particles in the current standard model of particle physics.
The first three columns from the left are fermions. Fermions obey Fermi-Dirac statistics, and carry charge. the lower two rows of these columns are leptons, and in addition carry lepton number; the upper two rows carry baryon number.
Conservation of charge and lepton and baryon number conservation for each set make sure that the currently total baryon and lepton number under observation is conserved.
The last two columns are bosons, obey Bose-Enstein statistics and do not carry conservable quantum numbers as they are neutral and (, before electroweak symmetry breaking, zero mass.). The only conservation laws that have to be obeyed are energy and momentum conservation laws. Following the interaction possibilities allows them to multiply themselves with no constraints.
A single charge accelerating or decelerating can create any number of photons.
Gluons are in our everyday world bound within a baryon and because they are bosons, their numbers can only be limited by energy and momentum conservation in the overall modelling of a proton..
So one cannot have a ratio of quarks ( they carry either +/-1/3 or +/- 2/3 , charge, and1/3 baryon number)to gluons . Over all the baryon number of a proton sums up to 1, and there is no definitive sum of gluons, as they also depend on the energy of the observing interaction, as the other answer explains.
The question is analogous to asking "is the black body radiation leaving a body countable so that a ratio between photons and baryons in that body can be calculated?"