Numerical analysis of renormalon technique in quantum mechanics

Abstract

We discuss the ways of extracting a low energy scale of an underlying theory using high energy scattering data. Within an exactly solvable model of quantum mechanics we analyze a technique based on introduction of nonperturbative power corrections accounting for asymptotically small terms and an alternative approach exploiting a modified running coupling constant of the model and nonperturbative continuation of evolution equations into an infrared region. Numerical estimates show that the latter is more efficient in approximating low-energy data of the model.

14 pages, Latex, the text is corrected according to the Phys.Lett.B referee comments

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• On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order
• Perturbative relations between $e^{+}{e}^{-}$ annihilation and $\tau$ decay observables including resummation effects
• Understanding perturbative results for decays of τleptons into hadrons
• Renormalons in quantum mechanics
• Generalized Borel Transform Technique in Quantum Mechanics
• Spectrality, coupling constant analyticity and the renormalization group
• Analytical continuation and resummed perturbation theory