Drawing the quark flow diagram for proton-pion interaction

[vbrasic]

Homework Statement

I am given the following interaction, $$\pi^-+p\rightarrow \pi^++\pi^-+n,$$ and asked to draw the Feynman (quark flow diagram).

Homework Equations

None; just baryon number conservation, quark flavor conservation, etc.

The Attempt at a Solution

First, as baryon number and quark flavors are all conserved, I deduced that this must be a strong interaction, with pair-production of $d\bar{d}$. That is, $$d\bar{u}+uud\rightarrow u\bar{d}+d\bar{u}+udd,$$ is the quark composition of the interaction.

From what I can deduce then, the $\pi^-$ remains as is (i.e. $d\bar{u}\rightarrow d\bar{u}$), while the proton follows the interaction, $$uud\rightarrow u\bar{d}+udd,$$ with the $d\bar{d}$ pair-production, which would be diagrammatically represented by the following Feynman diagram.

Thing is, I'm not entirely sure if my reasoning is correct. Specifically, is the pion in the initial state just a spectator?

 

[mfb]

That diagram is a free proton decay to neutron plus pion, it violates conservation of energy. You'll need the interaction with the pion. You can let one quark (or both) from the incoming pion become one of the quarks of neutron or the other pion, or you can use the incoming pion to produce the d/d-bar pair.

 

[vbrasic]

Okay. So would this be a more appropriate diagram then?

 

[mfb]

It could be cleaned up a bit, and adding a gluon for the pair production wouldn't harm, but that should be a possible process. Processes with a less chaotic quark flow should contribute more to the overall amplitude.