Explaining role of Pions in Strong force interactions.

[JacobS.]

Let me start off by saying that I am no professor of any kind, i am simply a high school student in way over his head concerning particle interactions. Without a class to teach me, i have used the magic of the internet to attempt to get a rudimentary understanding of these interactions. I understand (somewhat) color charge and how it works, how the gluons facilitate the color change. I understand that in simplified terms, the strong interaction between hadrons is like excess color force from inside the particle. What i don't understand is how pions facilitate this force, for all i know i have this all wrong. the information I am trying to understand came from this picture. Any help by explaining this picture would be great, preferably in layman's terms with as little math as possible.

 

[mitchell porter]

Are you familiar with the idea that an electron and a positron can combine to become a photon, or the reverse process, that a photon can turn into an electron and a positron? Something similar applies to gluons: a gluon can split into a quark and an antiquark, or a quark and an antiquark can combine into a gluon.

If we just focus on the neutron in the left diagram, starting from the bottom (time goes upwards), what happens is that one of the down quarks emits a gluon, and the gluon splits into an up quark and an up antiquark. The down quark and the up antiquark combine to make a pion, which leaves, and the new up quark takes the place of the original down quark. But now that makes the overall particle a proton, rather than a neutron.

Meanwhile, the pion travels across to the proton, the up antiquark in the pion annihilates with one of the up quarks in the proton, creating a gluon which is then absorbed, and the down quark that came across in the pion takes the place of the annihilated up quark; so now the proton (up up down) has become a neutron (down up down).

Along the way (while traveling between neutron and proton), the pion was held together by gluon exchange between down quark and up antiquark.

 

[JacobS.]

Aah, okay, the role of the pion makes a lot more sense now, thanks so much for clearing up the meaning of the diagram. Of course, as understanding does, now i just have so many questions...

where does the actual force holding them together come from? Is it simply the fact that there is a constant equilibrium and exchange of particles?

And also, I was a bit confused when you talked about Gluons splitting, I was pretty sure that they were elementary and therefore had no component parts. Then i read about Gluons interacting with one another, forming "virtual quark-antiquark pairs". I somewhat grasp the concept after reading through things concerning Hawking Radiation and how the "imaginary" universe is the one that makes sense mathmatically, But is there a process to generating these pairs...? is it the same as in Hawking Radiation, pulling the pairs out of the vacuum...?

 

[mitchell porter]

where does the actual force holding them together come from? Is it simply the fact that there is a constant equilibrium and exchange of particles?

Cause and effect in quantum physics can be a little problematic to find. The way these theories were first defined by Feynman was to make a list of all the elementary things that can happen - like "a particle moves from A to B" and "at a point in space, particle X turns into particles Y and Z" - and then each basic possibility has a "probability amplitude" (which is a complex number that you square to get a probability). And then, if you want the probability for something to happen, like "proton and neutron exchange a pion", you have to consider all the ways that you can build that complex process out of the elementary processes, and apply the probability rules to get your answer.

So let's consider the simpler case of a hydrogen atom - a proton and an electron held together by electromagnetism. In classical physics you say: the proton and the electron each have a charge, and they each produce a little electric field. And the charge of a particle both determines how strong its field is, and also determines how the particle moves in response to the field of another particle. In quantum physics you say that electromagnetism consists of photons, and the force field is just a shorthand for photon probabilities, and the charge of a particle tells you the probability that it emits or absorbs a photon. So when you want to understand why the proton and the electron stick together, not in terms of force fields, but in terms of photons, it ends up being a statement about how the quantum probabilities for particle motion and particle interaction add up to produce a most-probable behavior (i.e. the atom stays in one piece).

It's like this for why the quarks inside a proton, or inside a pion, stick together. You can think in terms of a "chromoelectric field" or color force field that each quark emits, but once again, that's just a shorthand for gluon probabilities. And the way the probabilities come together for quarks and gluons is a lot more complicated than for photons, because gluons themselves can emit gluons, because color charge is more complicated than electric charge (red, blue, green, not just positive and negative), and also because the probability to emit gluons is very high. The classical-physics prototype for why the atom holds together is just circular motion, like a planet orbiting a star, but then with some extra complications because of how quantum probabilities work (e.g. the possible "orbits" of an electron come in discrete levels). With quarks, the intuitive pictures are more complicated and also somewhat disputed. In some sense, a pion is probably a "flux tube" of gluons going back and forth between the quark and the antiquark, and a proton or neutron may be a "bag" in which the three quarks are surrounded by a whole cloud of gluons and transiently existing quarks and antiquarks. (These "pictures" are simple mathematical approximations that people use in order to calculate, they're not just words.)

Since you mention that gluons have no component parts, I should clarify something else about these basic interactions. I mentioned that, the way Feynman did it, the definition of the theory, its starting point, is to say, there are two sorts of things that can happen, a particle moves, and a particle is replaced at the same point by some other particles, and then we have rules of calculation for probabilities. If you took that description absolutely seriously, then what happens when you have quark-antiquark creation from a gluon, is that the gluon simply ceases to exist and is immediately replaced with a quark and an antiquark at the same point in space where the gluon was.

If you went to a deeper framework, like string theory, the theory might tell you more. In string theory, such an event would correspond to a gluon string splitting into a quark string and an antiquark string. Also, mathematics usually offers many different ways of looking at something, and it's fairly certain that there are other, quite different ways of organizing and interpreting the calculations that give you the probabilities. The "twistor" approach to field theory is causing a slow mathematical revolution at the moment, which I am sure will ultimately result in new physical concepts, but I don't know what they are at this point.

But if we just stick with the picture that physicists still learn in university, the picture of particles interacting according to the rules of quantum probability, then it's as I have described it.

 

[edguy99]

Great posts, very clear and informative - thank you.

It has been posted here both that the timing of the decay (1/2 life of baryons) can be predicted and that it cannot be predicted from 1st principles. I assume the answer is somewhere inbetween, either because our model is not deep enough or maybe it requires too much calculation. Do you have an opinion on this?

 

[naima]

Can we draw a parallel with the color change of a quark?
When a blue quark emits a blue antired gluon it becomes red.
this corresponds to a 3*3 ladder matrix with one 1 at one place the 8 other being nul.
Can this generalized?

 

[tom.stoer]

Pions are low-energy effective degrees of freedom of QCD; this is due to the fact that massless QCD has an exact chiral flavour-symmetry which is spontaneously broken resulting in Goldstone bosons, the massles pions (introducing quarks masses results in an explicit breaking of chiral symmetry and non-zero pion masses). Afaik there are some indications that low-energy effective theories with pions, vector mesons etc. can be derived from full QCD.

The reason one prefers this kind of derivation is b/c it omitts perturbation theory (Feynman diagrams) which is strictly speaking WRONG in the infrared regime. So it's nice to draw diagrams with quark-antiquark pairs and to visualize them as 'pions' but in practice this is the wrong way to go.