# Is it pions or gluons that mediate the strong force between nucleons?

From my recent experience teaching high school students I've found that they are taught that the strong force between nucleons is mediated by virtual-pion exchange, whereas between quarks it's gluons. They are not, however, taught anything about colour or quark-confinement.

At a more sophisticated level of physics, is it just that the maths works equally well for either type of boson, or is one (type of boson) in fact more correct than the other?

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See the answer by Lubos at physics.stackexchange.com/questions/9661/… . The correct type is the gluon. –  anna v May 10 '11 at 12:04
@anna I posed this question after having read @Lubosh's answer. I don't feel that it answers my question and, either way, I was kind of hoping for a slightly more expansive answer. When I get a chance I'll add an edit, containing some LaTex, that should better describe why I posted this query. –  qftme May 10 '11 at 12:08
Lubos gave a complete answer, but one could add that nuclear forces are in analogy with the electromagnetic forces between molecules, the Van der Waals forces. There the mediator is the photon, but the moments of the charge distributions are what control the forces exerted between molecules. In a similar way the strong nuclear forces are such a spillover, except that in contrast to the photon the gluon carries color and couples to itself so it is much more complicated. –  anna v May 10 '11 at 13:42
Yes. Depending on the energy and distance scale in question. –  dmckee May 10 '11 at 14:18

Dear qftme, I agree that your question deserves a more expansive answer. The answer, "pions" or "gluons", depends on the accuracy with which you want to describe the strong force.

Historically, people didn't know about quarks and gluons in the 1930s when they began to study the forces in the nuclei for the first time.

In 1935, Hideki Yukawa made the most important early contribution of Japanese science to physics when he proposed that there may be short-range forces otherwise analogous to long-range electromagnetism whose potential is $$V(r) = K\frac{e^{-\mu r}}{r}$$ The Fourier transform of this potential is simply $1/(p^2+\mu^2)$ which is natural - an inverted propagator of a massless particle. (The exponential was added relatively to the Coulomb potential; and in the Fourier transform, it's equivalent to the addition of $\mu^2$ in the denominator.) The Yukawa particle (a spinless boson) was mediating a force between particles that was only significantly nonzero for short enough distances. The description agreed with the application to protons, neutrons, and the forces among them.

So the mediator of the strong force was thought to be a pion and the model worked pretty well. (In the 1930s, people were also confusing muons and pions in the cosmic rays, using names that sound bizarre to the contemporary physicists' ears - such as a mesotron, a hybrid of pion and muon, but that's another story.)

The pion model was viable even when the nuclear interactions were understood much more quantitatively in the 1960s. The pions are "pseudo-Goldstone bosons". They're spinless (nearly) massless bosons whose existence is guaranteed by the existence of a broken symmetry - in this case, it was the $SU(3)$ symmetry rotating the three flavors we currently know as flavors of the $u,d,s$ light quarks. The symmetry is approximate which is why the pseudo-Goldstone bosons, the pions (and kaons), are not exactly massless. But they're still significantly lighter than the protons and neutrons.

However, the theory with the fundamental pion fields is not renormalizable - it boils down to the Lagrangian's being highly nonlinear and complicated. It inevitably produces absurd predictions at short enough distances or high enough energies - distances that are shorter than the proton radius.

A better theory was needed. Finally, it was found in Quantum Chromodynamics that explains all protons, neutrons, and even pions and kaons (and hundreds of others) as bound states of quarks (and gluons and antiquarks). In that theory, all the hadrons are described as complicated composite particles and all the forces ultimately boil down to the QCD Lagrangian where the force is due to the gluons.

So whenever you study the physics at high enough energy or resolution so that you see "inside" the protons and you see the quarks, you must obviously use gluons as the messengers. Pions as messengers are only good in approximate theories in which the energies are much smaller than the proton mass. This condition also pretty much means that the velocities of the hadrons have to be much smaller than the speed of light.

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@Lubosh, Thanks. I read your answer with great interest (3 times!) Would I be correct to summerize that pion-exchange is merely a crude (non-renormalizable) approximation and it is closer to the truth to teach that it is instead just gluon exchange? (I say closer to the truth because I'm sure that if sea- and valence-quarks, and their associated PDFs, are properly taken into account the situation must be become significantly more complex.) –  qftme May 10 '11 at 13:21
( ), sound of two hands clapping. –  anna v May 10 '11 at 13:28
@qftme: you should use the appropriate level of detail to explain things. Trying to model inter-nucleon interactions with quarks and gluons directly is messy, difficult and clouds the problems. The nucleon/pion model is simple and quantitatively precise up to orders of inverse energy. It is the appropriate model for that scale. –  genneth May 10 '11 at 13:45
@genneth, I completely agree, in general. The student in question however, is particularly inquisitive and specifically asked for an answer that was not 'dummed-down' due to it being too complex. One of my old Professors used to say "Simplify, simplify, but don't through the baby out the bathwater." I think in this instance, whether or not to settle on the pion model is equivalent to the baby sitting on the rim of the bath.. –  qftme May 10 '11 at 13:59
@Lubosh, belay that last request, I just found a 12page study into whether or not the pion model is appropriate to teach at a pre-University level. For anyone interested it's here: teachers.web.cern.ch/teachers/archiv/HST2002/feynman/… –  qftme May 13 '11 at 14:52

gluons mediate the strong force between quarks. Pions mediate the nuclear force or nucleon-nucleon interaction or RESIDUAL strong force. So, the answer to your question is BOTH. In different measure, but both. See Wikipedia:

http://en.wikipedia.org/wiki/Nuclear_force

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