One of the interesting physical dimensions is the radius of a quantum particle composed of bound sub-particles. The particle’s radius often provides us with hints to understanding the particles’ structure and the interactions between its components.
In order to understand how to use this information, let’s take a look at the structure of known particles, considered as quantum systems of electric charges, and compare it to what we know about hadrons, which are particles composed of quarks.
The radii of the Hydrogen, Helium and Lithium atoms
Let us look at some bound quantum states, which comply with the laws of electromagnetism. The simplest case is that of the Hydrogen atom, composed of a proton and an electron. Another case is the Helium atom, in which there is a nucleus containing a double charge (2 protons + 2 neutrons) and two electrons.
Measurements showed that the radius of the Helium atom is smaller than that of the Hydrogen atom. Why is that? This is because the Helium nucleus is charged with 2 protons, applying a stronger attraction force and bringing its electrons closer together, condensing the Helium atom such that its radius is smaller than that of the Hydrogen atom. The radius of the Lithium atom, containing 3 protons and 3 electrons, is larger than that of the Hydrogen atom. This is because the Lithium’s electrons occupy two shells, whereas the electrons of the Hydrogen and the Helium atoms occupy one single shell. Calculations based on Quantum Theory confirm these results.
By the way, the charge of the positronium’s components, a particle composed of an electron and a positron (anti-electron), is the same as that of the Hydrogen atom, and its radius is also comparable to that of the Hydrogen atom.
Pi-meson’s radius and the Proton’s radius
The proton is characterized by a 3-quark combination. The pi-meson, (or in short, the pion), is composed of a pair of quark-antiquark of the same kind as those composing the proton. Experimental findings show that the pion’s radius is slightly smaller than that of the proton.
Why is that? It is explained in this site why Comay’s model suggests that the proton has a core carrying 3 magnetic monopole charges that attract 3 quarks and that this core contains inner closed shells of quarks. The existence of inner shells explains the proton’s bigger radius, in analogy to the Lithium atom, which has a larger radius because its electrons fill up 2 shells, and not only one.
Comay’s model claims that all baryons have an inner core containing closed shells of quarks, similarly to a multi-electron atom. Due to the extremely short life-span of most hadrons, the radii of only a few hadrons could be measured experimentally, but the results of baryon and meson measurements are totally coherent with Comay’s model. Like in the proton-pion radii, the comparison between the Sigma- baryon and the K-meson (both containing an s-quark) shows that the K-meson’s radius is smaller, which is consistent with the assumption that the baryon contains inner shells.
Additional comment about hadrons’ radius
Comay’s model states that it is possible to determine which meson has a larger radius on the basis of the masses of the quarks composing them. We already know from observing the Electromagnetic Force that a particle composed of a proton and a muon (the muon is heavier than the electron) has a smaller radius than that composed of a proton and an electron. This effect complies with fundamental properties of quantum theory of an electromagnetically bound system. It means that if two oppositely charged particles are bound together, the composite particle’s radius will be smaller if its component’s mass is larger.
The exact same phenomenon should occur in mesons and baryons as well, or else Comay’s model has a problem… And indeed, meson radius measurements confirm Comay’s prediction: the K+ meson, for example, is smaller than the pi+ meson, because the s-quark is heavier than the d-quark, in analogy to the fact that the Sigma- baryon’s radius is smaller than the proton’s radius.
We saw here a few examples of the radius of quark-composed particles. These examples confirm that the particles behave according to the predictions of Quantum Theory and the Electromagnetic Laws. Comay’s model, based on the Regular Charged Monopole Theory, presents an analogy to the Electromagnetic Theory. Therefore, the results discussed here support the Model, providing further validation to the hypothesis of the existence of a massive, non-trivial core inside the baryons, in contradiction to the precepts of the Standard Model.