Borel summation and momentum-plane analyticity in perturbative QCD

Details Borel summation and momentum-plane analyticity in perturbative QCD Borel summation and momentum-plane analyticity in perturbative QCD

1999-02-05

arxiv.org/abs/hep-ph/9902244v1

JHEP 9903 (1999) 007

Physics

High Energy Physics

High Energy Physics - Phenomenology

22 pages, uses JHEP.cls (included), submitted to JHEP

Scientific paper

10.1088/1126-6708/1999/03/007

We derive a compact expression for the Borel sum of a QCD amplitude in terms of the inverse Mellin transform of the corresponding Borel function. The result allows us to investigate the momentum-plane analyticity properties of the Borel-summed Green functions in perturbative QCD. An interesting connection between the asymptotic behaviour of the Borel transform and the Landau singularities in the momentum plane is established. We consider for illustration the polarization function of massless quarks and the resummation of one-loop renormalon chains in the large-$\beta_0$ limit, but our conclusions have a more general validity.

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