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

No exclusive amplitudes for charged particles (II)
In the perturbation expansion the Born
term is well-defined and ≠ 0:
This problem shows up at order α 2 as an
infrared singularity in the loop integral for k → 0:
This may be seen without calculation:
The two fermion propagators ∝ k, e.g.:
(p1 − k) 2 − m 2 µ = −2p1 · k + k 2 ∝ k
The photon propagator ∝ k 2 , giving a log singularity at k = 0
Paul Hoyer Mugla 2010
e +
e –
e +
e –
γ*
γ*
q
�
0
p1
p2
d 4 k
k 4
⇒ The exclusive process e + e – → µ + µ – is ill defined.
µ +
µ –
µ +
k
µ –
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