•Renormalization

This is the sum of all unrenormalized amplitudes:

ampfinal = amploopfull + ampl2mult + ampl4 ;

This is then the full renormalized amplitude:

ampfinalren = ((WriteString["stdout", "."] ; ILimit[#, ParticleMass[Vector[1], RenormalizationState[1]] -> 0]) & /@ (Renormalize[ampfinal // ChargeEliminate] // manred[MandelstamU])) // Expand ;

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The infinities cancel:

Coefficient[ampfinalren, LeutwylerLambda[]] // Simplify

0

The result is independent of the renormalization scale:

Coefficient[ampfinalren /. scaleRule /. logRule1 /. logRule, Log[1/ScaleMu^2]] // Simplify

0

Converted by Mathematica  (July 10, 2003)