Introduction to QCD slides - P.Hoyer.pdf - High Energy Physics Group

µ +
Paul Hoyer Mugla 2010
µ +
γ* γ*
µ –
Optical Theorem for σtot(e in QED (I)
+ e − )
O (α) O � α 2�
µ –
γ ∗ → µ + µ −
µ +
µ –
γ
µ +
µ –
γ ∗ → µ + µ − γ
µ +
µ –
µ +
µ –
γ ∗ → µ + µ −
At O(α 2 ) there are two contributions to the imaginary part (dashed line).
The IR singularity cancels between them, i.e., between different final states!
Since the γ*→ γ* amplitude does not have external charges, it “has to be” regular.
It means that even in QED we must define cross sections such that they include
(arbitrarily soft) photons. There are no free, “bare electrons”.
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