Feynman diagram of K0 transmutation

[Gulli]

Homework Statement

I need to find the Feynman diagram of the transmutation of a K0 particle (one anti-strange quark and one down quark) into its anti-particle (one strange quark and one anti-down quark).

Homework Equations

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The Attempt at a Solution

s- has a charge of +1/3, d has a charge of -1/3, so together they are neutral and they both have spin 1/2, so maybe they could annihilate into a gluon (0 charge, spin 1) which could then decay into an s and d- , so maybe it's just:

Although maybe an interaction involving the quarks changing flavour via Z0 particles (s- into d- and d into s) is also possible...

 

[sgd37]

strangeness is conserved in the strong interaction but broken by the weak

 

[Gulli]

strangeness is conserved in the strong interaction but broken by the weak

So the interaction involving Z0 particles is impossible, while an interaction involving gluons is possible. Can you tell me if the diagram I drew is correct?

 

[sgd37]

the other way round since the s quark has strangeness -1 and the sbar has strangeness 1 so in the interaction you have strangeness is not conserved so the gluon interaction is not possible

 

[Gulli]

the other way round since the s quark has strangeness -1 and the sbar has strangeness 1 so in the interaction you have strangeness is not conserved so the gluon interaction is not possible

Oh yeah, strangeness is inverted for the anti-particle, so then I have to use a Z0 instead of a gluon in my diagram?

 

[vela]

The Z doesn't change the flavor of quarks. The only vertex that does involves the W.

Hint: The diagram won't be a simple one where the two incoming quarks simply exchange a W. It's a bit more complicated.

 

[Gulli]

Do they have to change flavour to change into their own anti-particles?

 

[vela]

Of course. The K_0 and \bar{K}_0 aren't made up of the same flavors of quarks, so the flavors have to change when the neutral kaon turns into its antiparticle.

 

[Gulli]

Of course. The K_0 and \bar{K}_0 aren't made up of the same flavors of quarks, so the flavors have to change when the neutral kaon turns into its antiparticle.

Well, all I know is that the strangeness and bottomness of the meson become reversed, while total charge, mass and spin remain the same. The thing is this exercise comes from an undergraduate course that didn't delve into feynman diagrams too deep, so I probably don't need a lot of vertices.

 

[sgd37]

http://en.wikipedia.org/wiki/File:Kaon-box-diagram-with-bar.svg

think again

 

[Gulli]

http://en.wikipedia.org/wiki/File:Kaon-box-diagram-with-bar.svg

think again

Is that the simplest diagram possible? If so then I give up. Feynman diagrams are definitely not covered that thoroughly in the course.