# QCD Correction to DIS

1. Feb 19, 2016

### CAF123

I am considering the following virtual correction to the DIS process between a quark and photon. The process on the left in the attachment is one such QCD correction I can make but the diagram on the right is another (I just changed where the gluon vertices lie). It seems to me that both diagrams should give equal weighting as a correction, but I don't see this come through in the math.

In both cases, I need to evaluate a trace, where in case a) this is equal to $$\text{Tr}((\not p + \not q) \gamma^{\nu} \not p \gamma^{\sigma} (\not p - \not l) \gamma_{\nu} (\not p + \not q + \not l) \gamma_{\sigma})$$ and in case b) it is $$\text{Tr}(\not p \gamma^{\nu} (\not p + \not q) \gamma^{\sigma} (\not q + \not p - \not l) \gamma_{\nu} (\not p - \not l) \gamma_{\sigma})$$ and a lorentz invariant phase space for one final state species premultiplying it which is equal to $\int d^{(d)} p \delta^{(d)}(p+q-p)$ up to some factors. I am just trying to see if first my intuition about these giving same contributions is indeed correct and, if so, how I can see this explicitly - I thought about using the integral over all p to shift the momenta but shifting by such and such an amount did not give agreement.

Thanks for any tips!

#### Attached Files:

• ###### QCDcorrection.png
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2. Feb 24, 2016