# What is meant by "Since the exchange of (mesons) occurs frequently, the nuclear force is stronger than the electromagnetic force"?

This is from a book written by Y. Nambu.

What role does the mass of mesons (versus mass of photons) have in making the strong force strong? How does this relate to "frequent exchanges" of mesons? What does it mean to exchange frequently (these are virtual particles) and how is this quantified? (as a means of comparison to the electromagnetic force).

From "Quarks: Frontiers in Elementary Particle Physics" Chapter 2, page 13:

The force between two nucleons is thought to arise out of exchange of mesons among the nucleons: one emits a meson and the other aborbs it. Since the exchange occurs frequently, the nuclear force is stronger than the electromagnetic force.

• Could you provide more context? For those who have the book a chapter/page number would probably also help. Having massive force carriers tends to decrease the strength of an interaction (see the weak force, which is weak precisely because of its very massive W/Z bosons). Jun 2, 2019 at 21:57
• It is not the mass but the coupling constant value that determines the strength of the force Jun 2, 2019 at 22:33
• The strength of the coupling of an interaction term quantifies the vigor of the exchange interaction, so the rate for it, in time-dependent perturbation theory. Large coupling leads to high rate. It is a loose metaphor of successive impulses to make up a "force", I suspect, but unless you quote the entire relevant part of the paragraph in question, you might lack for insights. Jun 2, 2019 at 22:35
• Saying that the masons are exchanged more frequently is a hand wavy way of saying this. Jun 2, 2019 at 22:35
• I think you are misreading that page, since there is no discussion of mass and range: Nambu goes on to clarify that on p 52. You are inserting a side issue putting words in his mouth. If anything, mass "weakens" the force in question, by limiting its range, which is what happens in the weak interactions. His is a popular book for the broad public, and his mild metaphors are the best way to sketch simple mathematical facts, covered in all technical particle physics texts. Jun 3, 2019 at 0:28

There are a few things to clarify:

It is very important in your question to differentiate between the strong force and the residual strong force (nuclear). The reason is, because you are asking about the nuclear force, mediated by heavy mesons. Though the strong force itself is mediated by massless gluons inside the nucleons.

1. the rest mass of the mediator (heavy mesons) makes the residual strong force (nuclear) short ranged, just like the weak force. This rest mass does not have anything to do with the relative strength of the residual strong force. Now the short range of this force is a little bit complicated, because the residual strong force is repulsive at very short distances. This keeps the neutrons and protons apart. At 0.8fm, the nuclear force is very strong attractive, and at 1-3fm, it is still strong attractive.

2. it is the coupling constant that determines the relative strength of the strong force. It just happens so, that the strong force is way stronger then any other force at short distances (under the size of the nucleus). Now this is not precisely correct, because the strong force is very strong under 0.8fm (the inside of the nucleon, nothing can come close to it), and is strong at 1-3fm (nucleus), but at very big nucleuses, with over 200 neutrons and protons, the EM force starts to overcome the strong force.

Now you are asking about virtual particles. when we create mathematical models, we try to explain in math the data coming from experiments. These data fit perfectly our currently accepted theories, the SM, together with QM and QFT. When we try to model these interactions between the field (in this case the residual strong field), we use virtual mesons and these are not real particles.

Yes these virtual mesons do have rest mass (off shell), and are not real particles, they are just a mathematical model.

You are asking why the strong force is stronger then the EM force. In reality we do not know why. We just accept that the universe is built so, and built mathematical models for the strong force and the EM force, and the coupling constant happens to be 137.

• ok, makes sense. I was curious as to why Nambu would say: "Since the exchange occurs frequently, the nuclear force is stronger than the electromagnetic force." The quote is old and maybe it was his and the communities understanding at the time. Or maybe, as some other comments have suggested, it's just a hand wavy description for public consumption. Jun 2, 2019 at 23:46