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 Lissajoux May2-10 06:46 AM

Feynman Diagrams

1. The problem statement, all variables and given/known data

I need to draw a series of Feynman diagrams to show some processes, but I'm unsure if I'm doing these correctly. I've put them together in this one post and detailed each below in turn, hopefully this is going to make sense. I know there's a few, but I want to make sure I'm getting them all right.

Also I'll apologise now for the drawings, best I could do in MS Paint :wink:

Part 1:

"Top quark pairs
$\bar{t}t$ are produced through $\bar{q}q$ annihilation. Protons and anti-protons are collided at high energies, and top quarks are produced via the strong interaction process $p+\bar{p} \rightarrow t+ \bar{t} +jets$. Draw the simplest tree-level Feynman diagram for one of the possible underlying fundamental processes, clearly showing initial and final states on the diagram and label all particles."

Part 2:

"Draw the Feynam diagram for $\pi^{0}$ decay to two photons. Label all particles and initial and final states."

Q: "Via which force does this decay occur? Explain."

Part 3:

"The decay $p \rightarrow n + e^{+} + \nu_{e}$ does not occur in free space in the Standard Model, but does occur inside a nucleus. Draw the corresponding Feynman diagram for the underlying fundamental process. Clearly show initial and final states and label all particles."

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The next 3 are rather similar to each other.

Part 4A:

"Write a balanced equation for $\tau^{-}\rightarrow \mu^{-}$decay and draw the Feynman diagram, clearly showing the initial and final states and labelling all particles."

Part 4B:

"Write a balanced equation for $\tau^{-}\rightarrow \pi^{-}$decay and draw the Feynman diagram."

Part 4C:

"Write a balanced equation for $\tau^{-}\rightarrow K^{-}$decay and draw the Feynman diagram."

Q: "Which of the latter two decays (4B or 4C here) would have the higher probability of proceeding?"

2. Relevant equations

Relevant equations and images within the solution attempt

3. The attempt at a solution

I've put links to the images of the Feynman diagrams (F.d.'s) rather than posting the images and making this post rather much longer.

Part 1:

This is the F.d. I've drawn:

http://yfrog.com/evfydiagp1j

Part 2:

This is the F.d. I've drawn:

http://yfrog.com/f1fydiagp2j

Q: In regards the the question.. decay occurs via weak force?

Part 3:

This is the F.d. I've drawn:

http://yfrog.com/fvfydiagp3j

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Part 4A:

F.d:

http://yfrog.com/0bfydiagp4j

Equation:

$$\tau^{-}\rightarrow \mu^{-}+\nu_{\tau}+\bar{\nu}_{\tau}$$

Part 4B:

F.d:

http://yfrog.com/f1fydiagp5j

Equation:

$$\tau^{-}\rightarrow \bar{\nu}_{\tau}+\bar{u}+d$$

Part 4C:

F.d:

http://yfrog.com/2qfydiagp6j

Equation:

$$\tau^{-}\rightarrow \bar{\nu}_{\tau}+ \bar{u}+s$$

Q: I think that (4B) decay has a higher probability of proceeding than (4C) decay as nature prefers to pair $u$ with $d$ rather thatn $s$. I'm sure there's a more scientific explaination.

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I think I've got the jist of these, hopefully, just a bit unsure on some of the arrow directions and other bits of notiations. Some advice on these would be great, make sure I'm not making any stupid mistakes. :smile:

 diazona May2-10 12:45 PM

Re: Feynman Diagrams

For #1, remember that a proton is made up of three quarks, and an antiproton is made of three antiquarks. So you can't have the whole proton and antiproton annihilating together into one gluon. I think you need to draw an incoming line for each quark. (Remember that it's not always the case that all the quarks will be involved in the interaction.)

For #2, you have the wrong interaction. Think about this: charge needs to be conserved as you move from left to right in the diagram (or equivalently, charge needs to be conserved at each vertex). You can't turn a W+ into two photons, which have zero charge. (However, you were correct in identifying the force based on your diagram - if what you'd drawn had been correct, it would indeed have been a weak interaction.)

Your #3 looks almost correct, just check the direction of your arrows. One of them (well, the arrows on one of your lines) is pointing the wrong way.

Same with #4a, #4b, and #4c, in each of them you have one arrow pointing the wrong way but otherwise correct. (Also in 4a it looks like you mistyped the equation)

For the more scientific explanation of which of 4b or 4c is more probable, look up the CKM matrix. It contains the relative probabilities of various kinds of quarks being involved in weak interactions. (The values in the matrix are experimentally measured, and we have no plausible theoretical explanation for why they are what they are.)

 Lissajoux May2-10 02:33 PM

Re: Feynman Diagrams

#1:

Erm, not sure how to draw it that way, or if need to. I'm sure I looked it up somewhere and it was like that, perhaps that was wrong though. Similarly to #2 not sure how to redraw it without getting in a muddle.

#2:

Not sure how to draw it differently, without it getting rather messy. Can I just not put the $W^{+}$ notation there? Would it be the strong force instead then? It would balance as charge on $\pi^{0}$ is $0$ and charge on $\gamma$ is $0$ and would be simple.

#3:

I'm guessing it's the arrow on either the $e^{+}$ or $\nu_{e}$ lines? I was unsure on these when I drew it. I'm not sure but should the $\nu_{e}$ one be the other way around? I.e. pointing outwards like the $e^{+}$ one?

#4A:

The $\bar{\nu}_{\mu}$ arrow should be the other way around?

$$\tau^{-}\rightarrow \mu^{-}+\nu_{\tau}+\bar{\nu}_{\mu}$$

#4B:

The $\bar{u}$ arrow should be the other way around?

#4C:

The $\bar{u}$ arrow should be the other way around?

#

Still not sure on the question.

. . . .

How's that now? :smile:

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