Gluon radiation Feynman diagram

[kashiark]

can someone please explain the attached picture to me? if the electron and positron are just annihilating each other shouldn't the positron be going the other way? and shouldn't the antiquark be going the other way too? and what's up w/ the ->t thing at the bottom?

 

[humanino]

The bottom arrow indicates time flow. The positive-energy positron coming in can be described as a negative-energy electron flowing backward in time, this both just a trick to keep track of quantum numbers and a fundamental symmetry of quantum field theory. In this sense, electron-positron annihilation can be understood as the continuous flow of the quantum numbers carried by the lepton in space-time, forward in time as the electron and backward in time as a positron. Same thing hold for the final state quark-antiquark pair creation.

 

[kashiark]

i don't understand is the electron really there or just a math trick to keep the quantum numbers straight? I am really confused

 

[Vanadium 50]

Arrows in Feynman diagrams do not indicate direction of motion. They label fermions and anti-fermions.

 

[humanino]

Then think of what happens here. You have just an electron and a positron heading towards each other at very high energy. We pumped out the electron from somewhere ourselves, and we accelerated it, and we also independently created the positron, no matted how, but at another place probably. So we know they are not related at first. You bring them together in collision, and you see emerging from the interaction vertices (think of it as a black box for now) three jets of hadrons (say for instance). It fits well with the theory which tells you this must happen sometimes, when the electron and positron annihilation created a quark antiquark pair, and one of the quark radiated a gluon. This is what your diagram describes. Even more specifically, your diagram is this part of the process for which a virtual photon emerged from the electron positron annihilation, and decayed into the quark antiquark pair. There are kinematical regimes in which this part of the process dominates over anything else.

Now indeed it is a mathematical trick in your calculations to think of the incoming positron as a negative energy electron going back in time. However this is really not worth confusing you. Once you get to actually perform those calculations, you may go back to this detail and search for the historical context in which this trick was introduced.

 

[blechman]

It is VERY important to remember that Feynman diagrams are NOT spacetime diagrams: they are a powerful mnemonic for keeping track of integrals. Do not confuse arrows and lines and vertices on a Feynman diagram with an actual, physical spacetime picture of the interaction! Technically, a single F.D. contains an infinite number of spacetime diagrams.

 

[humanino]

It is VERY important to remember that Feynman diagrams are NOT spacetime diagrams: they are a powerful mnemonic for keeping track of integrals. Do not confuse arrows and lines and vertices on a Feynman diagram with an actual, physical spacetime picture of the interaction! Technically, a single F.D. contains an infinite number of spacetime diagrams.

Are not they, strictly speaking, topological equivalent classes of integrals under re-parametrizations ?

You are perfectly right, but as I said, there are kinematical regimes in which the quoted single diagrams dominates the total amplitude. In this case, to a certain level of accuracy, I do not see a physically motivated distinction between the total amplitude and the single dominant contribution.

 

[blechman]

all I'm saying is that the op's original confusion seems to stem from the idea that this is a "physical picture" of the interaction in question, and this is the wrong way to interpret feynman diagrams. rather, you should think of these diagrams as complicated integrals. trying to take them too literally leads to mistakes.

that's all.

 

[kashiark]

oooh ok i get it tyvm guys!

 

[humanino]

the op's original confusion seems to stem from the idea that this is a "physical picture" of the interaction in question, and this is the wrong way to interpret feynman diagrams. rather, you should think of these diagrams as complicated integrals. trying to take them too literally leads to mistakes.

Oh yes ! I was thinking specifically about Feynman's "Reason for antiparticles" as in "Elementary particles and the laws of physics" (not an original, technical, reference, but quite pleasant to read). But indeed, picturing Feynman diagrams as real processes leads to many inconsistencies in general.