I am trying to calculate the cross-section for electron-positron annihilation into a quark-antiquark pair and a gluon. I find that I need a relative minus sign between the two contributing diagrams in order to have $ q_{\mu} H^{\mu\nu}=0$ with $H^{\mu\nu}$ being the hadronic trace and thus conserve the vector current. Can someone tell me where this minus sign comes from? I cannot see where any fermion positions are interchanged here.
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$\begingroup$ When you talk about two diagrams, are you grouping the ones with $\gamma$ and $Z$ in the s-channel together? I haven't performed the computation, but since for each diagram the gluons can couple to different legs (see 2 first diagrams of this figure), perhaps the gamma matrix algebra gives you the sign you want... Can you provide additional detail? $\endgroup$– J-TCommented Mar 3, 2016 at 16:23
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If you look over the two first diagrams attached by J-T, you will see that they really are interchanging their quark-antiquark lines (instead of changing gluon line), what implies that lovely minus sign.
