QCD perturbation theory at large orders with large renormalization scales in the large $β_0$ limit

Details QCD perturbation theory at large orders with large renormalization scales in the large $β_0$ limit QCD perturbation theory at large orders with large renormalization scales in the large $β_0$ limit

2003-07-04

arxiv.org/abs/hep-ph/0307070v2

Phys.Rev. D69 (2004) 125006

Physics

High Energy Physics

High Energy Physics - Phenomenology

14 pages, 5 figures, elaborated conclusions

Scientific paper

10.1103/PhysRevD.69.125006

We examine the QCD perturbation series at large orders, for different values of the 'large $\beta_0$ renormalization scale'. It is found that if we let this scale grow exponentially with the order, the divergent series can be turned into an expansion that converges to the Borel integral, with a certain cut off. In the case of the first IR renormalon at $2/\beta_0$, corresponding to a dimension four operator in the operator product expansion, this qualitatively improves the perturbative predictions. Furthermore, our results allow us to establish formulations of the principle of minimal sensitivity and the fastest apparent convergence criterion that result in a convergent expansion.

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