QCD perturbation theory at large orders with large renormalization scales in the large ${\beta }_0$ limit

Abstract

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.

arXiv comment14 pages, 5 figures, elaborated conclusions

References in corpus (1)

• Renormalons

Cited by in corpus (8)

• Optimization of QCD Perturbation Theory: Results for R(e+e-) at fourth order
• Static QCD Potential at r < 1/Lambda_QCD: Perturbative expansion and operator-product expansion
• Superasymptotic and hyperasymptotic approximation to the operator product expansion
• Hyperasymptotic approximation to the top, bottom and charm pole mass
• Non-perturbative match of ultraviolet renormalon
• Fixed and Unfixed Points: Infrared limits in optimized QCD perturbation theory
• Exploring arbitrarily high orders of optimized perturbation theory in QCD with nf -> 16.5
• The Banks-Zaks expansion in perturbative QCD: an update