Is my Feynman diagram for production of ##W^-## boson correct?

[Nirmal Padwal]

Homework Statement

The $W^−$ was discovered in 1983 at CERN using proton-antiproton scattering
$$p + \bar{p} \to W^- + X$$,
where $X$ represents one or more particles. What is the most likely $X$ for this process?
Draw a Feynman diagram for your reaction, and explain why your $X$ is more probable than the various alternatives?

Relevant Equations

(Not applicable)

I think $X$ appears to be $\pi^{+}$ because it is light and energetically more favourable. Pion should be positive to ensure charge conservation. I am stuck at drawing a Feynman diagram for $$p+\bar{p} \to W^- + \pi^+$$.

Is this correct? Is this the leading order diagram or is there a diagram with fewer vertices possible? I tried seeing if a digram with fewer vertices is possible but this is the best I am able to do.

 

[topsquark]

Homework Statement:: The $W^−$ was discovered in 1983 at CERN using proton-antiproton scattering
$$p + \bar{p} \to W^- + X$$,
where $X$ represents one or more particles. What is the most likely $X$ for this process?
Draw a Feynman diagram for your reaction, and explain why your $X$ is more probable than the various alternatives?
Relevant Equations:: (Not applicable)

I think $X$ appears to be $\pi^{+}$ because it is light and energetically more favourable. Pion should be positive to ensure charge conservation. I am stuck at drawing a Feynman diagram for $$p+\bar{p} \to W^- + \pi^+$$.

View attachment 315811

Is this correct? Is this the leading order diagram or is there a diagram with fewer vertices possible? I tried seeing if a digram with fewer vertices is possible but this is the best I am able to do.

The extra u and d quarks are going to get you into trouble. They aren't just going to annihilate into gluons, the gluons themselves would decay into something else.

Think about this a bit more directly. What mesons are made up of $u \overline{u}$ and $d \overline{d}$?

-Dan

 

[Nirmal Padwal]

$\pi^0$ are made up of $u\bar{u}$ and $d\bar{d}$.

So after reading your post, I came up with this,

Is this correct?

 

[topsquark]

$\pi^0$ are made up of $u\bar{u}$ and $d\bar{d}$.

So after reading your post, I came up with this,

View attachment 315882

Is this correct?

You are almost there. The up and anti-up collision is going to be energetic and you have two of them happening. So perhaps you will get two more particles coming out of this reaction...

-Dan

 

[Nirmal Padwal]

So perhaps you will get two more particles coming out of this reaction

Photons?

Does this make sense?

 

[topsquark]

Photons?

View attachment 315921
Does this make sense?

Sort of. Remember that, in general, the more vertices we have the less likely it is to happen. And I'm not quite sure what you have going on with the four up quarks and the $\pi ^0$.

Try it this way. Each up-antiup pair can create two photons, right? So do that directly. Then you are predicting $\overline{p} + p \to W^- +2 \gamma +2 \gamma + \pi ^+$.

Now, this is correct. But I think, given the likely energies involved, it is more likely to have the following diagram:

The up-antiup pairs can both form $\pi ^0$s. So here we would have $\overline{p} + p \to W^- + \pi ^0 + \pi ^0 + \pi ^+$.

Can you think of any other possibilities based on this idea?

-Dan