= Real-virtual infrared cancellation in inclusive QCD
For an <infrared-safe observable>, loop corrections and integrated unresolved real emissions have compensating <infrared divergences> and <collinear divergences>. Keep a common regulator until they are added. At the first QCD correction to photon-mediated quark production, virtual gluon exchange corrects the two-parton state and real emission supplies the three-parton state. Their inclusive sum is finite after ultraviolet renormalization; resolved three-jet rates additionally depend on an infrared-safe resolution prescription.
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