QCD example 9.1 from Elementary Particles by Griffiths



Could somebody take a look at example 9.1 from David Griffith's
Elementary Particles book? It might be enough just to read the problem
I quote below. I think there's a mistake in the setup but I'm totally
confused because he gets the correct answer and when I "fix" the
mistake, I get the wrong answer. But I'm fairly certain he's made at
least one mistake so he might be making another that disguises that.
The basic problem is to calculate the color factor from first-order
exchange for quark-antiquark interaction.

-------------
EXAMPLE 9.1 (p. 285)
A typical octet state (Eq. 9.4) is (red-antiblue) ( any of the other
[octet states] would do just as well; see Problem 9.4). Here the
incoming quark is red, and the incoming antiquark is antiblue. Because
color is conserved, the outgoing quark must also be red and the
antiquark antiblue. Thusly [the rest of the problem with equations]...
-----------

Doesn't the exiting quark have to be blue and the exiting anti-quark
have to be anti-red for a (red-antiblue) exchange? After all, they are
not exchanging a singlet so color changes at a vertex. Plus, this
would match the vertex diagram on p. 280. The problem is when I fix
the problem I get a different number for the color factor than -1/6.
The -1/6 I'm fairly sure is correct.

This is not a homework problem. It's just for self-study. I've tried
several permutations on the words in the problem to "fix" the problem
but nothing has worked. I'm confused. Hopefully I'm not just doing
something stupid. Any comments would be appreciated.

Jason

.



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