Both gravity and the electromagnetic force obey the inverse-square distance law.
Evidently, the strong force exhibits some other relation.
Quark-antiquark pair formation seems to be the result of adding potential energy to the bond between two quarks by separating them. At some point, the potential energy in the bond is able to be converted into a quark-antiquark pair which then "screens" the original force between the first two quarks, creating two "flux-tubes" in series where previously there was just one. ( I am just parroting back the terminology mentioned above, I don't know what a flux-tube is. I am assuming that it is similar to magnetic "flux" in that it describes the field between the two particles and the word "tube" implies that the field is confined to a region surrounding the line between the two particles.)
Each of the resulting flux-tubes will now behave just like the original flux tube behaved when it was at the smaller spacing of the new flux-tubes.
The quark-antiquark pair formation is a quantum physical event which is outside the scope of my question. My question being "what is the force versus distance law that applies to the original "flux-tube" prior to such quark-antiquark pair formation"?
I will look up the linked article on QCD and see what I can make of it.
Let me lay out the possibilities.
Empirical evidence may exist to suggest that the strong force is not inverse-square. There may be such evidence that the strong force law takes some other mathematical form. There may be evidence that the form of the force law is not a simple algebraic function. It may be that the empirical evidence does not suggest any underlying physical mechanism.
Theoretical "evidence" might exist that the strong force law is not inverse-square. There may be theory which specifies the value at one or two points within the presumed continuous range of the function but without reason to assign any specific function to the relation. There may be competing theories, each of which is consistent with empirical evidence but each of which suggests a different relation for the strong force versus distance. It may be that all of the theories rule out inverse-square law.
My interest in this question is to gain a qualitative sense of the degree to which detailed physical theory has advanced beyond the present state of my knowledge, not necessarily a need to know the specifics. When I went to school the strong force was just described as being "very short range" but I don't think there was much to suggest the mechanism of the force or a mathematical law for it.
One of the interesting facts which I have learned from this thread is that the inverse-square law relation is "special" in that it allows for an "escape velocity" at each point in space such that a particle with a velocity exceeding that will not return to the source of the force. Other force relations may not exhibit this property. Specifically, if the strong force law is such that there is no "escape velocity" then this alone becomes an explanation for why a quark may never be seen in isolation. One might be able to imagine a force law such that the force tends toward infinity as the distance approaches some finite upper limit. Without something like "quark-antiquark pair formation" to complicate things, then one could calculate that it might take all the energy of the universe to move two quarks apart to this upper limit.
Theories concerning whether the universe will continue expanding address the issue of whether there is sufficient mass in the universe to cause the expansion to come to a halt bringing on the "big crunch". Is it the case that the assumption is made that the fastest moving masses in the universe are at the periphery and are moving at near the speed of light away from the center of gravity of the universe. Or, in other words, is the question whether a particle at the periphery of the universe traveling at near the speed of light is above the "escape velocity" which would be calculated knowing the entire mass of the universe and assuming that it is located at the center of gravity of the universe?
Thanks for your help.